Innovative Systems Approach for Facilitating Smarter World 9811977755, 9789811977756

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Design Science and Innovation

Toshiya Kaihara Hajime Kita Shingo Takahashi Motohisa Funabashi   Editors

Innovative Systems Approach for Facilitating Smarter World

Design Science and Innovation Series Editor Amaresh Chakrabarti, Centre for Product Design and Manufacturing Indian Institute of Science Bangalore, India

The book series is intended to provide a platform for disseminating knowledge in all areas of design science and innovation, and is intended for all stakeholders in design and innovation, e.g. educators, researchers, practitioners, policy makers and students of design and innovation. With leading international experts as members of its editorial board, the series aims to disseminate knowledge that combines academic rigour and practical relevance in this area of crucial importance to the society.

Toshiya Kaihara  •  Hajime Kita Shingo Takahashi • Motohisa Funabashi Editors

Innovative Systems Approach for Facilitating Smarter World

Editors Toshiya Kaihara Graduate School of System Informatics Kobe University Kobe, Japan Shingo Takahashi School of Science and Engineering Waseda University Tokyo, Tokyo, Japan

Hajime Kita Institute for Liberal Arts and Sciences Kyoto University Kyoto, Japan Motohisa Funabashi TRAFST, Tokyo, Japan

ISSN 2509-5986     ISSN 2509-5994 (electronic) Design Science and Innovation ISBN 978-981-19-7775-6    ISBN 978-981-19-7776-3 (eBook) https://doi.org/10.1007/978-981-19-7776-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

The concept of Society 5.0 (super-smart society) proposed in Japan’s Fifth Science and Technology Basic Plan continues to be emphasized in its Sixth Plan, and various research and development efforts are currently underway, mainly in industry and academia, to realize this concept. In order to realize Society 5.0, a grand design of social systems that seamlessly integrates the various heterogeneous systems to make up social systems and creates new value for society as a whole is essential. The Systems and Information Division of the Society of Instrument and Control Engineers (SICE) has been conducting a cross-divisional survey and research on a new systems approach that will enable this grand design in the “Study Group for the Realization of a New Systems Approach for the Smarter World” since 2022. The group shares a view of a Smarter World combining the various heterogeneous social systems and proposes a new development of SoS (System of Systems) with an evolutionary concept of a spiral systems approach based on a cycle of analysis, abduction, and synthesis. These efforts were published in our previous book, Innovative Systems Approach for Designing Smarter World, in 2021. In the book, we define smarter world as an innovative society in which autonomous value networks are formed quickly and sustainably for the various actors that make up society, while maintaining sustainability as a more advanced social infrastructure becomes larger, more advanced, more complex, and more information intensive. We have also summarized a new systems approach for designing such a society. This book outlines the latest research trends and prospects of the new systems approach that we have proposed and introduces specific examples that lead to the solution of social issues. In this book, we will explain the new systems approach that we have been working on to solve social problems, broadly classifying it into (1) System Structure and Modeling, (2) System Optimization, (3) System Adaptation and Evolution, and (4) System Case Studies, while introducing perspectives, explanations, and case studies. The following sections introduce the contents of each category. First, (1) System Structure and Modeling presents a new systems approach to system structure and modeling methods for solving social problems. Chapter 1 by Toshiya Kaihara outlines a framework of Multiscale Social Modeling and Simulation (MSMS) methods for transparently integrating different types of systems. Chapter 2 by Eitaro Aiyoshi, Keiichiro Yasuda, and Kenichi Tamura presents the design, planning, and operation of smart social infrastructure platforms based on v

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mathematical interpretation from the viewpoint of system optimization in the framework of the circulating and spiral-up systems approach. Chapter 3 by Hajime Kita describes the economic efficiency and value creation of social systems, presents six types of linkages among systems based on their structures, and discusses recent trends and issues to be considered in the future. Chapter 4 by Yasuaki Kuroe explains the importance of understanding systems from the perspective of boundaries and relationships, and then looks forward to the construction of a new systems approach that takes these perspectives. Finally, Chap. 5 by Katsunori Shimohara discusses the equity-based approach based on the premise of clinical wisdom and the inevitability in taking a clinical approach in relationality design toward creating an SoS in a local community. Next, (2) From the viewpoint of system optimization, Chap. 6 by Wataru Kumagai and Keiichiro Yasuda describes a new black-box optimization method using only decision variable value and evaluation value information for SoS and so on. Next, in Chap. 7 by Ryohei Funaki and Junichi Murata the estimation method of the objective function as a hypothesis generator for modeling and decision-making processes in the cyclic and spiral systems approach that we have been proposing is presented. In Chap. 8 by Tatsushi Nishi, a dynamic model configuration platform for multi-agent supply chains is introduced. Using the platform as an integration of machine learning and optimization, a co-evolutionary decision-making method that estimates the decision-maker’s objective function and constraints from big data is presented for automatically generating an optimization model. The book then continues with (3) Adaptation and evolution techniques for systems, introducing a variety of new approaches. Chapter 9 by Takamasa Kikuchi, Masaaki Kunigami, and Takao Terano discusses the usage of both agent modeling and gaming simulation for political decision-making tasks, and it proposes a formal descriptive model named the Managerial Decision-Making Description Model (MDDM) to tackle the difficulty of specification of models in practical situations. Next, Chap. 10 by Setsuya Kurahashi describes a systems approach that integrates causal inference based on data (propensity score matching method) and deductive inference based on models (agent-based simulation) in socioeconomic systems and its application to policy formation. Chapter 11 by Shingo Takahashi describes co-­ creative modeling as an adaptive decision-making process for designing spiral social systems. In Chap. 12 by Hiroshi Kawakami, the relationship between systems and humans that grow together through the expression of antifragile phenomena is presented, and it is argued that the design of systems that grow together is human-­ centered design in the true sense of the word. Finally, Chap. 13 by Motohisa Funabashi provides a bird’s-eye view of systems and information technology against the backdrop of transition management aimed at achieving the SDGs and explains the challenges to embodying SoS evolution and its social significance. Finally, (4) System Case Studies presents four application examples as suggestions for the validity and effectiveness of the new systems approach introduced in this book. First, Chap. 14 by Ken-ichi Tokoro and Kazuyuki Mori introduces actual examples of the application of the various new systems approaches described above to electric power infrastructure, followed by an overview of representative electric

Preface

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power markets, including new markets that are expected to open in Japan. Chapter 15 by Toru Amau describes the system technology in the actual power network and introduces two concrete examples of SoS practices in electric power companies. Chapter 16 by Tetsuo Uzuka explains that a railway is a huge SoS in which subsystems such as rolling stock, stations, signaling, power supply, and communications interoperate with each other over multiple railway companies. Finally, in Chap. 17, Takashi Nishiyama explains the organization of smart home technology based on environmental intelligence and its consideration from the SoS viewpoint, targeting home systems. This book summarizes the efforts to pursue a new systems approach to realize Society 5.0 from both theoretical and applied perspectives. We hope that the contents of this book will help to realize a well-being society under the concept of Society 5.0 in the future. Kobe, Japan Kyoto, Japan  Tokyo, Japan  Tokyo, Japan  May 2022

Toshiya Kaihara Hajime Kita Shingo Takahashi Motohisa Funabashi

Contents

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Toward Realization of Innovative Systems Approach for Societal Design: Multiscale Social Modeling and Simulation (MSMS) Methodology����������������������������������������������������   1 Toshiya Kaihara and Nikhanbayev Nursultan

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 Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their Solution Strategies: A Risk-­Management Perspective in the Circulating and Spiral-up Systems Approach����������  29 Eitaro Aiyoshi, Keiichiro Yasuda, and Kenichi Tamura

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Issues of System Cooperation from a Viewpoint of System Structure������������������������������������������������������������������������������������  47 Hajime Kita

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Boundary and Relationality Perspective Systems Approach: Towards Its Development ������������������������������������������������������������������������  57 Yasuaki Kuroe

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Relationality Design Emphasizing Clinical Aspects of System of Systems in Local Community ��������������������������������������������������������������  67 Katsunori Shimohara

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 Black-Box Optimization and Its Applications ����������������������������������������  81 Wataru Kumagai and Keiichiro Yasuda

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Estimation of Objective Functions: Modeling of Problems and Understanding of Decision-Making Processes Towards the Spiral-up Systems Approach�������������������������������������������������������������� 101 Ryohei Funaki and Junichi Murata

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Co-evolutionary Decision-Making Modeling Via Integration of Machine Learning and Optimization ������������������������������������������������ 111 Tatsushi Nishi

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Agent Modeling, Gaming Simulation, and Their Formal Description������������������������������������������������������������������������������������ 125 Takamasa Kikuchi, Masaaki Kunigami, and Takao Terano

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Contents

10 Causal  and Deductive Reasoning in Socio-Economic Systems�������������� 139 Setsuya Kurahashi 11 Co-Creative  Modeling as Adaptive Decision-Making Process�������������� 149 Shingo Takahashi 12 Mutual  Growth of Human and System in Smarter World�������������������� 159 Hiroshi Kawakami 13 Towards  SoS Evolution Management for Developing Smarter Cities: Social Significance and Approaches������������������������������ 165 Motohisa Funabashi 14 Power  System Progressing with Systems Approach ������������������������������ 179 Ken-ichi Tokoro and Kazuyuki Mori 15 Power  Network System Technology: A Focus on SoS���������������������������� 189 Toru Amau 16 System  of Systems in Railway������������������������������������������������������������������ 199 Tetsuo Uzuka 17 Current  and Future Trends on Smart Home Technology: Including SoS Perspective ������������������������������������������������������������������������ 211 Takashi Nishiyama

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Toward Realization of Innovative Systems Approach for Societal Design: Multiscale Social Modeling and Simulation (MSMS) Methodology Toshiya Kaihara

and Nikhanbayev Nursultan

1 Introduction The Fifth Science and Technology Basic Plan advocates a Society 5.0 (i.e., super-­ smart society). Various research and development efforts are currently underway, mainly in industry and academia (Cabinet Office n.d.; Society 5.0 n.d.; Hitachi n.d.). Social infrastructure roughly comprises components of the bases of public infrastructure such as traffic, energy, communication, water, and sewage, the bases of business operations such as manufacturing, distribution, information processing, sightseeing, and services, and the bases of daily life activities such as education, medical treatment, care, and disaster prevention. Furthermore, as social infrastructure increases to ever-larger scale, with sophisticated information, conjugation, and networking, it becomes increasingly necessary to realize a new society that is able to create new values and services continuously for all the stakeholders composing Society 5.0. To realize Society 5.0, a grand design of social systems that seamlessly integrates the various heterogeneous systems that make up social systems and creates new value for society as a whole is necessary. Therefore, the “Research and Study Group on New Systems Approach for Realization of Smarter World (2017.1–2019.12)” and its successor “Research and Study Group for the Actual Development of New Systems Approach for the Smarter World (2020.1~)” have been conducting cross-divisional research and a study of a new systems approach that will enable this grand design. Smarter world, which has been defined as an T. Kaihara (*) Graduate School of System Informatics, Kobe University, Kobe, Japan e-mail: [email protected] N. Nursultan ProField Co., Ltd., Osaka, Japan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 T. Kaihara et al. (eds.), Innovative Systems Approach for Facilitating Smarter World, Design Science and Innovation, https://doi.org/10.1007/978-981-19-7776-3_1

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innovative society in which autonomous and sustainable formation of value networks for various subjects composing the society, is proceeding quickly and continuously. Innovative systems approaches for designing such a world have been described both from academic and industrial viewpoints as the outreach of our above-described research and study group in our earlier book (Innovative systems approach for designing smarter world 2021). With sharing of the view of the various heterogeneous social systems that constitute Society 5.0 as systems at an abstract level, new developments in System of Systems (SoS) (Maier 1998) and the idea of a spiral systems approach through a cycle of analysis, abduction, and synthesis are gradually being clarified. New systems approaches to solve social problems that have been discussed in our group activities are roughly classifiable into (1) system structure and modeling, (2) system optimization, (3) system adaptation and evolution, and (4) system case studies. This chapter contributes mainly to the systems structure and modeling domain. Societal simulation modeling and simulation methodology are newly proposed as one innovative system approach. This chapter is organized in the following ways. In the next section, past studies about Multiscale Social Modeling and Simulation (MSMS) for societal systems and other modeling techniques are presented. In Sect. 3, terminology of MSMS is introduced. A detailed explanation of MSMS with a target model is described in Sect. 4. In Sect. 5, validation of MSMS is performed using computational experiments. Finally, we summarize the chapter in Sect. 6.

2 Multiscale Modeling and Simulation Methods for Social Systems Design Realize Society 5.0 requires a new systems approach able to accommodate various decisions flexibly in different time and space, which is a characteristic of social systems consisting of widely diverse stakeholders by organically combining the cyber world and the real world in a sophisticated manner. A super-smart society characteristically comprises heterogeneous systems that have a general hierarchical structure in which various heterogeneous systems with fine spatiotemporal granularity are developed at the meso-level and micro-level, mediated by a common macro-model of society. The multiscale social simulation enables us to point out the ideal state of a new super-smart society in which heterogeneous systems are integrated seamlessly. The goal of the IoT service platform in a super-smart society is to create new social value through the coordination and integration of systems. We propose a new systems approach based on social simulation to realize seamless integration among multiple systems that constitute a social system. Moreover, we propose a new methodology to realize this goal. We also specifically examine the hierarchy inherent in social systems, and connect micro-models such as individual behavior models, meso-models such as industrial structures, and macro-models such as policy and economic evaluation. We aim at establishing a Multiscale Social Modeling and

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Simulation (MSMS) method that can use such micro-, meso-, and macro-models in a balanced manner according to the characteristics and goals of the targeted social problem.

2.1 Social Systems Modeling and Simulation In recent years, the advanced development of Information and Communication Technologies (ICT) linking heterogeneous systems has emerged. Technologies such as the Internet of Things (IoT), Artificial Intelligence (AI), and robotics are reshaping society and industries. Digitalization is spreading around the world as a trend: it is known broadly as Industry 4.0  in Germany, Industrial Internet in the United States, and Smart Nation in Singapore. Anticipating digital transformation, the Japanese government proposed a new concept of direction for additional development of society, called Super smart society or Society 5.0 (Cabinet Office n.d.). In general, Society 5.0 is about building a human-centered society using advanced technology. It also includes smaller objectives such as the connection of heterogeneous systems. In Fig.  1.1, one can view the concept of the connected society (Brookings n.d.), which represents the platform for transforming current society to the society 5.0. Connected society represents the idea of connecting core systems that are ensuring proper functionality of the society, such as electricity, gas, water supply, transportation, manufacturing and such to realize this concept several obstacles such as the ministries, agencies, legal system, and social acceptance, must be passed (Innovative systems approach for designing smarter world 2021). At the same time, social risks and possible unpleasant scenarios must also be observed (CIA n.d.). Computer simulation models are useful to foresee unpleasant scenarios with consideration of possible social effects and to overcome the previously described barriers. Simulation of the case in the cyberspace before its implementation in the real world can help to avoid unnecessary loses. Furthermore, simulation models are

Fig. 1.1 Connected society

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useful as a demonstration tool, to show stakeholders possible value gain, and help to secure investment. Existing agent-based models for Social Simulation (SS), in most cases, cover only a single perspective of the case. However, while trying to model and simulate complex concepts such as Society 5.0 or connected society, the multiscale nature of society should be examined (Multiscale ABSS Method for Social Policy Making n.d.). An example will provide a better vision what multiscale nature of society means. For instance, one can consider the case in which one must model the connection of electricity and manufacturing systems. Figure 1.2 shows that connection of those systems would affect society and the government as well. Consumers normally make daily operational decisions on a tight time frame, whereas government presumably emphasizes long-term strategic decisions. These decision differences in spatiotemporal granularity frequency illustrate the multiscale nature of social systems. The authors suggest that one technique which is useful to model connected society, while considering multiscale characteristics of the case (Fig. 1.1), is Multiscale Social Modeling and Simulation (MSMS). By definition, MSMS uses multiple models at different scales simultaneously to describe a system. The salient feature Fig. 1.2  Example of multiscale connection of electricity and manufacturing systems

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of MSMS is its ability to breakdown cases by a particular characteristic, such as temporal or spatial, and to clarify connections between scales. One limitation of MSMS for modeling social systems is that it is mostly used in exact sciences (Eldabi et al. 2016) and entails only a little attention in the field of simulation modeling. In this chapter, we address MSMS limitations, particularly a lack of theoretical background and deficits of application studies of MSMS on social systems. We develop a multiscale model of interactions among electricity and economic sectors by adapting basic multiscale modeling steps for social systems. Computational experiments can elucidate the possibilities for usage of MSMS in modeling of connected society. Results of simulations demonstrate how changes and decisions can mitigate the scales and how multiscale modeling allows views from different perspectives.

2.2 Related Studies Several modeling techniques are useful for creating simulation models of multiple connected systems. Aside from MSMS, modeling techniques explained in the literature include hybrid simulation (Eldabi et  al. 2016) and multimethod modeling (Borshchev 2013). Hybrid simulation has been described more frequently in the recent literature because it is not linked to a particular modeling framework. It follows a general idea modeling complex cases. However, in general, those techniques have a common idea of mixing different simulation modeling techniques such as System Dynamics (SD) (Forrester 1961), Discrete-Event Simulation (DES) (Gordon 1978), and Agent-Based Modeling (ABM) (Bonabeau 2002). In a review paper describing hybrid simulation of Brailsford et al. (2019), the authors mention a lack of theoretical background for the connection of several techniques and subsystems, alongside synchronization problems among them. MSMS has similarities with hybrid simulation, in terms of usage of different techniques and connection of several submodels. However, MSMS offers a different perspective on the case: a system is divided into several subsystems. Later on, subsystems are organized into several scales. The connection of subsystems, as well as scales, is performed afterwards in the scale connection phase. In this sense, MSMS can be a promising technique for overcoming difficulties of connection and synchronization for additional development of simulation modeling (Brailsford et al. 2019). Although research on MSMS has quite a long history (first appearance points back to the late 1800s), it still lacks a solid theoretical background. The majority of the available literature is less concentrated on a theoretical part of the approach and specifically examines details of the specific case (Horstemeyer 2009). A similar pattern can be found in the literature review on hybrid simulation (Brailsford et  al. 2019), where the same as MSMS only a few research articles are trying to design a theoretical approach rather than resolve a certain case. Among the few studies which put effort into building background for multiscale modeling, two can be emphasized here. The first is Multiscale Modeling Language (MML) (Falcone et al. 2010), a framework for multiscale modeling (Chopard et  al. 2014) and a description language based on graphical representation, with the main idea of helping people from

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various disciplines to collaborate on a single model. The main limitation of MML is the point that it is more of representational support (same as XML), rather than a solid theoretical approach. Chopard’s research group described two steps for creation of multiscale models: the creation of a scale separation map and scale connection (Chopard et al. 2014). A framework for multiscale modeling is the basic step of MSMS. However, the scale connection step is not considered in depth. Scale separation in most cases is performed based intuitively on temporal or spatial characteristics. It is noteworthy that the scale separation phase has attracted very little attention by looking at the review paper of Horstemeyer (2009), where scale separation is not considered. Scale connection, however, has much theoretical work done underpinning it. Several scale connection techniques are concurrent connection, sampling, projection, upscaling, homogenization, and via transition function (Weinan et  al. 2007; Fish 2009; Ayton et  al. 2007). Nevertheless, without modifications, these techniques are inapplicable to social systems. Few studies have specifically examined creation of theoretical background for application of multiscale modeling on social systems. The main reason is that social systems include people. Consequently, they are subject to be affected by decision-making, alongside other aspects such as human factors. Therefore, scale connection techniques should be modified. Alternatively, new ones must be created for social simulation. In the next chapter, we explain the process of creating the multiscale model together with necessary modifications to existing methods.

3 Multiscale Social Modeling and Simulation (MSMS) Terminology To create multiscale model of social systems, we are using two generic steps (Chopard et  al. 2014): specifically scale separation and scale connection. Before giving a deeper explanation of each step, we would like to clarify the related terminology.

3.1 Terminology Scale—several definitions exist by which word “scale” can be characterized. In our context of multiscale modeling, term scale is used to represent the level. From a social systems perspective, the definition will sound as though scale is the level which separates subsystems of social system according to certain characteristics such as time, space, or decision frequency. Submodel—part of the model with own objectives. It can run in isolation from the overall model assuming other parts of the model as a “blackbox.” Subsystem—a self-contained system within the larger system (Oxford dictionary).

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Level of abstraction of a scale—the measure of how detailed particular scale is implemented. Common levels of abstraction are the following. –– Low abstraction level—individuals and entities are considered in detail. An important shortcoming of models on a low abstraction level is their computational cost. –– Medium abstraction level—characterizes models for which the abstraction level is between high and low. Usually for such models, we consider certain processes and events that encapsulate multiple low-level entities, while avoiding details of each or entity. –– High abstraction level—minimum details, data of individuals considered in an aggregated manner. One shortcoming of models of a high abstraction level is that averaging and aggregation might engender loss of some important information. Scale separation—initial phase of multiscale modeling. The main idea of the current phase is dividing a model into several scales based on certain characteristic. Scale connection—later phase of multiscale modeling where connection scales are performed.

3.2 Scale Separation Initially, we perform the scale separation step in the most common way, intuitively. Referring to Fig. 1.1, one can consider the electricity system as an example to gain greater insight into how scale separation can be performed. Generally, electricity systems affect all levels of society: they affect households and the general population, affect industries, and have irreplaceable importance for governments. Following the idea of levels of abstraction, one can perform scale separation on (1) an abstract governmental scale (macro), (2) a detailed electricity user scale (micro), and intermediate of them, (3) an electricity-generation (power companies) scale (meso). Scale separation can also be performed by relying on certain characteristics. Figure 1.3 demonstrates possible scale separation based on characteristics such as the area, decision frequency, and decision level. It is noteworthy that the scale separation of both approaches provides the same division. After analyzing the presented scale separation methods, we can derive that, in most cases, performing scale division intuitively is sufficiently good to design a multiscale model. However, in the case of more complex cases, performing scale separation based on certain characteristics should be prioritized. An additional point that can be argued here is that power companies can make annual and daily decisions as well. This characteristic of the meso-scale can ensure a connection between the macro-scales and micro-scales.

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Fig. 1.3  Scale separation based on different characteristics

Fig. 1.4  Example of scale connection via propagation variables

3.3 Scale Connection After identification of all scales, one can manage their connections or scale bridging. For the target model, we implemented the scale connection using sequential and concurrent scale connection techniques. Connections are directed by and dependent on which direction information is transmitted. A core idea for scale connection is the usage of propagation variables. A propagation variable is one characteristic of a certain scale that is sent to the connected scales. Figure 1.4 shows bottom-up and top-down connections between two submodels allocated in different scales. When data are transmitted from bottom scale to upper, the data are analyzed or aggregated. When data move in the other

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direction, from top to bottom, they include some restriction (constraint) or general information such as price. Bottom-up connection is sequential. In other words, data can be sent to the upper scale only after all processes of the current scale are completed. Top-down connection is concurrent: information can be sent to the lower scale independently from operations happening on the scale itself.

4 MSMS Application into Social Systems for the Electric Power Industry To assess the benefits and shortcomings of multiscale modeling and simulation compared to other approaches, the electricity market of a hypothetical country is chosen as a target system (Nikhanbayev et al. 2019). The electricity market has importance at various levels of society. Processes, decisions, and solutions that are made at different layers have different timescales, different scopes, and different areas of effects. For instance, a normal person regards electricity as a convenience. However, for large industries or power companies, electricity has greater importance. A shortage of electricity for even several hours might be a reason for colossal losses. Government considers larger aspects, such as environmental protection, and international trade. We can infer that the ecosystem of the electricity market consists of several layers, and that multiscale modeling can address the characteristics of each particular layer. In the target system, we consider interactions among the government, power company, and residents (electricity users).

4.1 High-Level Decision-Maker: The Government In reality, the government includes many sectors that are responsible for the well-­ being of a country. However, to avoid unnecessary complexity, in this particular case, only economic and energy sectors are considered. Energy and economy are in very tight relations. In the current model, both macro-economical and micro-economical aspects of the electricity market are captured. The micro-economy, or supply demand interaction, is expressed lightly by other submodels (model of electricity supply and model of electricity users). In the government model, macro-economy is specifically emphasized. The economic sector of the government is responsible for economic variables such as gross domestic product (GDP), balance of trade (BoT), and the exchange rate (er). Only these variables are considered, for two reasons. Firstly, they directly affect the electricity market. Secondly, considering them alone can avoid unnecessarily detailed analyses. To calculate the economic variables, the following equations are used: BoT = EX − IM where EX represents exports and IM represents imports.

GDP = C + I + G + BoT

(1.1) (1.2)

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where C stands for consumption, I denotes investments, and G expresses government spending. Generally, calculation of real exchange rate appears as er =

pd ∗θ pf

(1.3)

where pd denotes the domestic price level, and pf stands for the foreign price level. Measuring the price level for the country and abroad is very complicated task. Therefore, for simplicity, the following equation is used.

er = (1 − α ) ∗ θ

(1.4)

Therein, α represents effects of the trade balance. Also, signifies the actual exchange rate. The effect of the trade balance is examined because it affects the exchange rate through the supply and demand for the currency. When BoT is negative, then α is positive and vice versa. That occurs because, when BoT is positive, a high demand exists for its products, and consequently, for its currency. Finally, α is implemented as

α=

BoTt −1 − BoTt BoTt

(1.5)

The absolute value of α is normalized to be in the range of [0, 0.05]. To design the government model, the experience of earlier studies was considered. Historically, system dynamics (SD) (Forrester 1961) has proved itself as a good tool for macro-economic modeling. The main reason is its ability to handle cases and formulations as aggregates. Part of the system dynamics model is presented in Fig. 1.5. The three main variables are GDP, BoT, and er. As might be apparent from (Eq. 1.2), GDP is affected by investments, government spending, consumption, and BoT. Consumption includes the cost of generated electricity, which is connected to the submodel of the electricity market. BoT also has a connection to the energy part of the model via imports of energy fuels. Exports are implemented to have static behavior and set up a particular value. Variables on the right side (orange circles) in Fig. 1.5 are interfaces that ensure connection of a submodel of government to a submodel of the power company. The submodel of the government is provided with control parameters such as setting basic electricity price (pb), CO2 taxation (CO2 tax), and limitations for the usage of particular fuels.

4.2 Mid-Level Decision-Maker: Power Company The next submodel in a queue is that of power companies. They interact with electricity users on an hourly basis. Power companies must satisfy total demand, which derives from electricity consumers. Their decision-making about which kind of fuel mix to use to meet electricity demand of a particular hour is implemented using a cost minimization objective function with load prioritization:

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Fig. 1.5  SD implementation of the economic sector

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PCi ∗ clf i ≤ xit ≤ PCi (1.8)



0 ≤ clf i < 1 (1.9)

where N : number of energy sources i : index of particular energy source FCi : fuel cost of ith energy source OCi : operation cost of ith energy source MCi : maintenance cost of ith energy source PCi : power capacity of ith energy source dt : demand for hour t clfi : Capacity Load Factor (CLF) of ith energy source xit : amount of electricity generated by ith energy source at hour t αi : constant which converts kWh to according measure unit of ith energy source wi: load prioritization coefficient of ith energy source (Table 5)

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The first constraint (Eq. 1.7) controls the overall generated supply will satisfy the demand of the particular hour. The second one (Eq. 1.8) is included to maintain the generated power by each energy source within a feasible range. Six types of energy sources are considered in this study: oil, natural gas, coal, nuclear, hydroelectric generation, and other renewable energy sources such as solar and wind. The upper end of this range is power capacity, whereas the bottom side represents the average capacity load for a particular fuel type. Capacity load factor is used to control the minimum amount of fuel that is used. Usually, it is set to zero to avoid becoming negative. Only in specific cases, it is used to avoid a level of generation below a particular value. The power company also makes decisions about setting electricity prices. Simulation of electricity price (pt) fluctuations is implemented in the following way: pt = pb + ( β load t + γ ct )

where

(1.10)

pb : basic electricity price ct : cost of electricity generation β : impact of load on electricity price at hour t loadt : load of power company at hour t γ : impact of electricity cost generation While ct have next form:

ct = ∑ ( xit ∗ fuel pricei ) + i

∑

σ j CO 2 tax ∗ x jt

j∈fossil fuels



(1.11)

Therein, α is the coefficient used to convert the amount of fuel to the corresponding amount of CO2 emissions. Fossil fuels is the set which consists of three energy sources: coal, liquefied natural gas, and oil. Electricity pricing equations are created by investigation of the main factors which affect it. The basic electricity price pb is the minimal price. To monitor the profit of power companies, simple equations are used.

TotalProfitt = TotalEarningst − TotalCostt (1.12) TotalEarningst = xt ∗ pt (1.13)

Therein, xt denotes the sum of the amount of the electricity generated by each energy source at time t. We can obtain TotalProfit, TotalEarning, and TotalCost for each hour. The daily or monthly values of those variables are calculated simply by summing them up. For instance, calculation of daily TotalProfit resembles. One more variable controlled by the power company is $CO_2$ emissions. It is formulated as shown below: CO2− emissionst = xit ∗ converteri ∗ emmissionRatePerUnit , {i ∈ fossil fuels} (1.14)

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In that equation, converteri is a constant used to convert kilowatt hours into the amount of fuel needed to generate this electricity. For example, burning 1 kg of coal produces about 450 kWh of electrical energy. The next one is emissionRatePerUnit, which is the amount of CO2 emissions by measured unit. For instance, in the case of coal, it would be per kilogram of coal, for oil per gallon, and so on. Operations of the power company are implemented as an analytical model.

4.3 Low-Level Decision-Maker: Electricity Consumers—Residents Residents are modeled in a detailed way. This intention is derived from the point that one of the main pillars of Society 5.0: the creation of a human-centered society. Therefore, to evaluate effects of policies and innovations of Society 5.0 on the general public, residents, who are its main building blocks, must be modeled in a detailed manner. Residents perform hour-to-hour actions, based on which they use electric appliances. Appliances used in the model are presented in bold typeface in Fig. 1.6. The blocks in normal font are types of particular electric appliances. In the initialization stage, each household agent gets set of electric appliances, which are used later on during simulation. The reason for using several types of the same electric appliance is the diversity. The set of appliances depends on how many people live in a certain house. For a person living alone, the set might be the following: an LCD TV, a weak air conditioner, a small refrigerator, a microwave oven, a rice cooker, and lights.

Fig. 1.6  Electric appliances

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Residents are assumed to be divided into several classes based on the two characteristics. The first characteristic is the number of residents in a particular household (Fig.  1.7). Presumably, there are three types: one person, two persons, and three or more persons. The second classification characteristic represents whether a particular household has someone staying home, or not. After setting up all classifications, in the initialization stage, assignment of appliances is conducted. Appliances and their types are assigned according to the first classification, i.e., based on the number of residents. The second classification is used to establish time patterns. The time pattern is some sort of schedule generated for each household at the beginning of the day. It includes information about what kind of activity a particular agent does at a particular hour. Presumably, there are activities of six types: waking up, pre-work, work, come back from work, after work, and finally sleeping. Those activities are based on those for which the household uses particular electric appliances and requests electricity from the electric power company. Also, Fig. 1.8 presents an example of a time pattern and an example of relations between activities and appliances.

Fig. 1.7  Types of residents Fig. 1.8  Example of usage of appliances at particular activity

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4.4 Scale Connection and Implementation of the Target Model The government is highly abstracted. It is not interested in hour-to-hour or daily activities of households. Households are not necessarily interested directly in the import of energy fuels or CO2 emission regulations, or other such considerations. To glue the abstracted government side and detailed electricity user’s side, power company is made to be in-between (Fig. 1.9). As shown in Fig. 1.9, the power company makes hour-to-hour interactions with households. Propagation variables that connect those scales are the following: –– Bottom-up direction (from micro to meso): electricity demand –– Top-down direction (from meso to micro): electricity price Later, information is aggregated and analyzed by the power company. Then results are presented to the government. Government–power company interaction occurs on a monthly basis. Propagation variables that are sent by a power company (meso-scale) represent the total amount of energy and the energy mix, which ensures bottom-up connection between the macro-scale and meso-scale. The top-down propagation variable is CO2_emission taxes. To model the scales described previously, we used modeling techniques that suit most of the certain aspects of each scale. The detailed micro-scale of electricity users includes many interactions in addition to the specificity of each user. Therefore, electricity users are implemented using ABM, which allows capturing individuals in a detailed way. However, the government is located at the top and works with aggregated data. The best practices to address abstract and aggregated cases are SD. The

Fig. 1.9  Interactions and processes of the target model

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main reason is that SD allocates structures such as stocks, flows, and feedback loops, all of which can be useful in dealing with abstractions. Finally, the model of the power company is produced by mixing analytical and simulation modeling paradigms. Identifying optimal energy fuels to use is a problem that is modeled as an optimization, whereas connection with models on remaining scales is implemented using simulation modeling. Particularly, interaction among households and power companies is done through demand for electricity. The power company summarizes all demands that are made by consumers at a particular hour; it then identifies what fuels to use to meet that demand. Communication between the power company and the government is done using specific variables. Those variables store aggregated values of the supplied electricity for energy sources of the respective types. Furthermore, once per month, they provide aggregated information to the government. The model is executed based on stylized data, which are created using a modeling tool named Anylogic (Abar et al. 2017).

5 MSMS Validation with Computational Experiments To identify important advantages of MSMS, we conducted a computational experiment, while keeping in mind two important factors: it should be the case related to the electricity aspects of Society 5.0; it should affect various levels of society. Therefore, we have chosen to conduct an experiment that is related to mass smartmeter installation.

5.1 Experiment Setup 5.1.1 Residents As described in Sect. 4, residents are assumed to have main setup parameters of three types used for the experiment. They are the number of residents, timeline setups, and setups of electric appliances. Table  1.1 shows the shares of households with electricity consumers who are staying at home. Electric appliances are assigned to households according to two characteristics: the number of persons residing there and whether someone is staying at home. Models that can be comparable to the real world are very limited. Consideration of all existing electric appliances is too complicated for basic analysis. For that reason, only a few types of electric appliances are considered herein. Table 1.2 presents the power consumption of a particular electric appliance per hour. Table 1.1  Share of number of persons per household and home-staying probability

1 person 2 persons 3 persons or more

Share 35–45% 30–40% 15–25%

Home-staying prob 20% 30% 40%

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Table 1.2  Electric appliances (kWh) Appliance TV Air cond. Refrig. Light Rice cooker Microoven Toaster Kettle Coffee Fan

Types and power consumption Plasma LCD 0.339 0.213 Large 0.55 Large 0.0055 Halogen 0.0004 Type 1 0.065 0.46 0.98 0.45 0.25 0.1

Table 1.3  Timeline setups (o’clock)

Activity Wake up time Work start(ws) Comeback time Activity Wake up time Work start(ws) Comeback time Activity Wake up time Work start(ws) Comeback time

25 in. 0.150 Medium 0.45 Medium 0.0038 60 W 0.0006 Type 2 0.17

1 person Home-staying 6.5–9 – – 2 person Home-staying 6.5–10 – – 3 person or more Home-staying 6.5–10 – –

19 in. 0.07 Small 0.35 Small 0.002 100 W 0.001

Not ws–(1–2) 8.5–10 17–21 Not ws–(1–2) 8.5–10 16–20 Not ws–(1-2) 7.5–11 16–19

5.1.2 Timeline Setup Timeline setup is also highly dependent on the number of persons living in the household. The time at which all residents are sleeping is assumed to be during 21–24 PM. In Table 1.3 are timeline setups of citizens that depend on the number of persons and whether someone is staying at home, or not. Also, “-” represents that this particular household has no work start or comeback time. To analyze the possible implications of mass smartmeter installation (as one idea behind smart grid concept), certain households are assumed to have a smartmeter that they can use to reduce their electricity usage. The decision flow of a household agent using a smartmeter is depicted in Fig. 1.10.

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Fig. 1.10 Decision flowchart of household agents with a smartmeter

Describing Fig.  1.10, at each hour t, a household that owns a smartmeter has probability of noticing that their electricity usage is high. Then they reduce their electricity usage by 10–20%.

5.1.3 Power Companies Table 1.4 shows that power capacities are set up in percentage equivalence with the real-world power companies. Setups of these kinds are used by drawing parallels from setups of the number of agents. Setups of prioritization coefficients used in the model are depicted in Table 1.5 (Kansai Electric Power Inc. 2019). The basic price is the price of electricity, which derives from fixed costs from modes of generation used by the company. To make the value somewhat different from those of other power companies, it is set as uniformly distributed between 20–21. The parameter setups of Eq. (1.10) are the following:



γ = 0.0001 β, on the other hand, depends on the utilization rate (ur)of the power company.  0.1, if ur < 0.5  0.3, if 0.5 ≤ ur < 0.7  β 0.7, if 0.7 ≤ ur < 0.9  0.9, otherwise

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1  Toward Realization of Innovative Systems Approach for Societal Design… Table 1.4  Total power capacities of power companies of each area (MWh) Oil 200

Coal 300

LNG 125

Nuclear 150

Hydro 210

New 65

Nuclear 0.6

New 0.8

Table 1.5  Prioritization coefficients Coal 0.7

Oil 1.0

LNG 1.0

Hydro 0.8

Fig. 1.11  Crude oil price projections

Energy fuel prices are referred from web services. They represent its value for the current moment. Energy fuel pricing can be regarded as outside the model. The fuel prices are decided by neither decision-maker of each scale. Crude oil price projections are depicted in Fig. 1.11 (U.S. Energy Information Administration 2019). The operational costs of particular power plants were referred from the official website of the Department of Energy of the United States of America (Electric Power Annual n.d.), as shown in Table 1.6. Setups of power companies are done as stylized facts (Heine et al. 2005) to increase the applicability of the obtained results with the reality. Optimization was achieved for the data using IBM ILOG CPLEX.

5.1.4 Government Government includes parameter setup of (Eq.  1.3), which takes values between [−0.1;0.1]. In addition, investments and government spending, as used in Eq. (1.2), are implemented by referencing numbers from the real world. For example, in the case of developed countries, the C–I–G–BoT ratio resembles 60%–15%–25%–0% (CIA n.d.). Identification of investments and government spending use this ratio for reference and implement it by correlation to those values.

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Table 1.6  Operational costs (currency/kWh) Coal 0.1

Oil 0.1

LNG 0.085

Nuclear 0.095

Hydro 0.15

New 0.167

5.2 Multiscale Simulation of Smartmeter Installation 5.2.1 Objective of Experiment This experiment has two main objectives: (1) identification of an effect of customer participation rate and (2) evaluation of smartmeter installation on peak demand of power supply. Most importantly, the analysis can show how scale separation and scale bridging affect the obtained results. 5.2.2 Experimental Outline A smartmeter is a device that provides an information bridge between the customer and the electricity provider. Based on the data, the power company can provide personalized information to customers, for example, by providing real-time electricity pricing information so that customers can control their spending. However, one concern about smartmeters is the awareness of customers. Smartmeters are expensive devices. Installing them for everyone with a low customer participation rate is not a good allocation of capital in many cases. Therefore, from this computational experiment, we would like to address this issue and identify possible effects of the smartmeter case on the meso-level and macro-levels. To perform computational experiments, we introduced two more variables to the model: share of households with a smartmeter installed and the probability of a certain household member noticing that the household electricity usage is high. The share of the households owning smartmeter illustrates that only some part of the household agents has a smartmeter. That share is identified as Share =

Ns N

(1.15) where Share represents the smartmeter share, Ns denotes the number of residents who have a smartmeter, and N stands for the total number of residents. Notice probability introduces a stochastic aspect to the experiment. Figure 1.10 shows how the notice probability is handled in the model. Consequently, our goal is identification of the cumulative effects of overall agents on other scales.

5.2.3 Results of the Computational Experiment Table 1.7 presents results of the computational experiment with smartmeter installation. It shows a connection between the micro-scale as households and the meso-­ scale, as represented by the power company. A clear tendency is apparent in their interaction: as the share and notice probability increases, the peak demand of residential electricity usage decreases.

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Table 1.7  Decrease in peak demand of daily residential electricity usage (%) N.p. 30% 50% 70%

Share 0.2 3.49 5.15 7.53

0.4 8.56 13.10 19.57

0.6 9.92 18.30 23.81

0.8 10.70 17.70 23.72

Fig. 1.12  Decrease in peak demand

Based on data of Table 1.7 and Fig. 1.12, we can derive several interesting points: –– As the share of residents who own smartmeters increases, the demand of the peak hour decreases. –– Sensitivity analysis shows that notice probability (N.p.) has stronger effects on the result than the share of residents who own a smartmeter. –– The decrease in peak demand does not change a lot after the notice probability becomes greater than 0.4. Reasons for this behavior derive from the point that there exists an upper limit for the decrease of peak demand. As both our variables increase (share of customers with a smartmeter and notice probability), the results slowly converge to this limit. From the last remark, we infer that the customer participation rate is sufficient to be effective: slightly more than 40% mass smartmeter installation. Sensitivity analysis provides interesting insights into the problem by showing that smartmeters for well-informed people are more effective than simply installing as many smartmeters as it is possible. In other words, this result demonstrates that a qualitative approach in this particular case is better in comparison to a quantitative one.

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Table 1.8  Comparison of cases in long-term experiment (kWh) Oil LNG Coal Nuclear Hydro Renewable Total CO2 (kg)

No changes 53585.16 1780492.39 535851.60 1292522.80 142137.85 29125.60 3833715.39 1.5713 × 109

0.4/50 53585.16 1779887.03 535851.60 1292522.80 140918.65 29125.60 3831890.83 1.57 × 109

Diff (%) 0.00 0.03 0.00 0.00 0.86 0.00 0.05 0.083

Additionally, it would be proper to evaluate the scale separation and bridging technique effectiveness. Comparison of intuitive and characteristic-based scale separations caused the same separation pattern for this certain model. However, that might not be always the case. Therefore, the authors suggest the use of characteristic-­ based scale separation for identification of a valid separation pattern. To evaluate the effects of scale connection techniques, a long-term experiment is conducted. Only a comparison of cases without changes and case with Np = 0.4 and Share = 50% is shown because it is sufficient to demonstrate the smartmeter effects in the long run. The results are presented in Table 1.8. Results demonstrate that the total electricity usage reduction is 0.05%, which is quite small. However, we can achieve 1.3 × 107 kg less CO2 emissions per month, which can contribute to achievement of Sustainable Development Goals. An effect of the scale connection is apparent in terms of interactions achieved among several submodels. By applying the proposed MSMS method for social systems, we were able to create a multiscale model of electricity–economic interactions and evaluate the effect of a small device such as a smartmeter, on vast phenomena such as global warming. The authors believe that more complex and sophisticated cases of social systems can be designed and analyzed using multiscale modeling for social systems.

5.3 Comparative Experiment: Model Restricted at Macro-Scale Against Multiscale Model 5.3.1 Objective of Experiment As described in this subsection, a comparison of multiscale and macro-scale models was performed. Here, SD was used for the implementation of macro-scale because it is a common approach in the creation of macro-scale models. A long-term experiment was conducted to elucidate rising of fossil fuel prices according to Fig. 1.11 because of the fact that they are scarce, and they affect GDP and BoT. 5.3.2 Experimental Outline Two main variables exist in the macro-scale of the target model: GDP and BoT. Currently, GDP and BoT are affected by the energy mixes, exchange rate, electricity prices, energy fuel prices, and CO2_emissions. At the same time, CO2_emissions depend on the energy generation mix, which depends on the

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electricity usage of the agents. If one considers that only an SD model exists and that all inputs that are outside of the SD derive from some sort of black box, then our obtainable results and our effect on the model are expected to be very limited. The main parameters to monitor are GDP and BoT. Currently, GDP depends on four variables consumption, investments, government spending, and BoT (Eq. 1.2). In the multiscale model, consumption and BoT are affected by meso-scale outputs and micro-scale outputs. Changes in these scales can be expected to influence the behavior of GDP. However, in the macro-scale model, for which we only have the SD part, those changes are not traceable. To identify and record differences described above, computational experiments are conducted as explained below. –– Macro-scale model: having a model of energy-economic interactions we are trying to identify effects of energy consumption on economic variables, particularly on GDP and BoT. –– Multiscale model: identify effects of energy consumption on GDP and BoT, with consideration of different inputs and behavior of models on other scales.

5.3.3 Results of Computational Experiment Currently, the economic sector looks as depicted in Fig. 1.13. Variables TotalNuclear, TotalLNG, TotalCoal, and TotalOil and the average electricity price are outputs of the meso-scale model. The first assumption is that there are no other scales and that all inputs that should have been taken from other scales are now regarded as average (Fig. 1.14). They fluctuate around the average value. In Fig. 1.15, one can see GDP projections for 10 years for both cases. As might be expected, with no other actions,

Fig. 1.13  SD model used in multiscale model

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Fig. 1.14  SD model used in macro-scale only

Fig. 1.15  GDP changes in both cases

GDP is declining. Some fluctuations are apparent in the case of the multiscale model, which derive from micro-scale and meso-scale fluctuation. A slight difference between the two cases results from more complex calculations that are executed on the multiscale model: GDP calculation requires the execution of models on other scales. However, in a macro-scale-only model, everything is regarded as average. This difference appears because of lost data.

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1  Toward Realization of Innovative Systems Approach for Societal Design… Table 1.9  Energy mixes of power companies after 1 year Oil 349400.00

Coal 3112858.37

LNG 700794.93

Nuclear 1921700.00

Hydro 330988.42

Renewable 69880.00

Hydro 643441.52

Renewable 70080.00

Table 1.10  Energy mixes of power companies after 10 years Oil 350400.00

Coal 3124716.62

LNG 394200.00

Nuclear 1927200.00

An important shortcoming of macro-scale-only models is that the outputs one can obtain from a model are very few compared to those from multiscale models. Results obtainable from the meso-scale of the multiscale model in the long-term simulations are depicted in Tables 1.9 and 1.10. These results can be useful for identification of how these changes affect power companies and their decision about what kinds of fuels to use. By comparing Tables 1.9 and 1.10, it is apparent how changes in prices of fossil fuels affect each area: after an increase in price, the share of LNG decreases drastically. This lack is covered by hydroelectric and nuclear generation. The most important point here is that those results are obtainable because of multiscale modeling and because of coupling of macro-scales and meso-scales.

6 Conclusions This work contributes to existing knowledge of social modeling and simulation. Particularly, an adaptation of MSMS to design social systems was described. Usage of MSMS was inspired by the fact that concepts such as Society 5.0 bring importance to the connection of heterogeneous social systems and to the proper management of social risk. Also, MSMS offers a broader view of important difficulties, allowing management of risks and possible changes within multiple levels. Two steps of a generic MSMS approach were analyzed and were tailored for social systems. Characteristic-based scale separation proved to be more consistent, compared to intuitive types. Scale connection was implemented based on sequential and concurrent information flow. It is worth mentioning that the direction of information is extremely important. Therefore, a connection between two scales should have two information flows (upwards and downwards). Furthermore, to evaluate the proposed approach, a hypothetical multiscale model of energy-economic interactions was created. The simulation included a case study with a mass smartmeter installation. Results of computational experiments demonstrated that the multiscale model of social systems is useful to gain results from multiple scales while avoiding usage of “black boxes.” An experiment with comparison of multiscale model and macro-scale-only model showed that multiscale modeling offers flexibility, giving the ability to affect a model from different perspectives. Additionally, multiscale modeling allows one to obtain much more output by connecting different models on different scales.

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Finally, limitations of this chapter must be considered. The current chapter described initial attempts at the application of MSMS to social systems. For additional and broader usage of MSMS in social simulation, the standardized theory is expected to be particularly useful. Additionally, one ever-existing limitation of simulation models is model validation. MSMS includes several models. Therefore, to ensure that the model offers consistent results, all aspects and submodels alongside with their connections must be validated. We would like to address these issues in our future work. Acknowledgments  This chapter is based on the research activity conducted at the “Research and Study Group for the Actual Development of New Systems Approach for the Smarter World” in the Society of Instrument and Control Engineers. The authors would like to thank all the research group members for our fruitful discussions and comments, both from a theoretical perspective and from practical viewpoints in terms of systems approaches. The authors also thank Ms. Sakamoto for her assistance with the organization of the figures and tables. This work is supported by JST-Mirai Program Grant Number JPMJMI20B3, Japan.

References Abar S, Theodoropoulos G, Lemarinier P, O’Hare G (2017) Agent-based modelling and simulation tools: a review of the state-of-art software. Comput Sci Rev 24:13–33 Ayton G, Noid W, Voth G (2007) Multiscale modeling of biomolecular systems: in serial and in parallel. Curr Opin Struct Biol 17:192–198 Bonabeau E (2002) Agent-based modeling: methods and techniques for simulating human systems. Proc Natl Acad Sci U S A 99:7280 A.  Borshchev 2013 Multi-method modeling, Proceedings of the 2013 Winter Simulation Conference. pp. 4089–4100. Brailsford S, Eldabi T, Kunc M, Mustafee N, Osorio A (2019) Hybrid simulation modeling in operational research: a state-of-the-art-review. Eur J Operational Res 278:721–737 Brookings (n.d.). https://www.brookings.edu/series/connected-­society-­internet-­of-­things-­ innovation/. Accessed May 2022 Japan Cabinet Office (n.d.). https://www8.cao.go.jp/cstp/english/society5_0/index.html. Accessed May 2022 Chopard B, Borgdorff J, Hoekstra AG (2014) A framework for multiscale modelling. Philos Trans R Soc A Math Phys Eng Sci 372(2021):20130378 CIA (n.d.). https://www.cia.gov/library/publications/the-­world-­factbook/fields/print\_2259.html. Accessed November 2019. T Eldabi, M Balaban, S Brailsford, N Mustafee 2016 Hybrid simulation: historical lessons, present challenges and futures, proceedings of the 2016 Winter Simulation Conference. 1388–1403. Electric Power Annual (n.d.). https://www.eia.gov/electricity/annual/. Accessed May 2022 Falcone J, Chopard B, Hoekstra A (2010) MML: towards a multiscale modeling language. Procedia Computer Science 1(1):819–826 Fish J (2009) Multiscale methods: bridging the scales in science and engineering. Oxford University Press, Oxford, UK Forrester J (1961) Industrial dynamics. MIT Press Gordon G (1978) The development of the general purpose simulation system, History of programming languages conference. 13(8):183–198 Heine B, Meyer M, Strangfeld O (2005) Stylised facts and the contribution of simulation to the economic analysis of budgeting, journal of artificial societies and social. Simulation 8(4)

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Hitachi (n.d.). https://www.hitachi.com/rev/archive/2020/r2020_01/01b05/index.html. Accessed May 2022 M.  Horstemeyer 2009 Multiscale modeling: a review. In: Practical Aspects of Computational Chemistry, Springer Science, Heidelberg, Germany. pp. 87–135. Kaihara T, Kita H, Takahashi S (eds) (2021) Innovative systems approach for designing smarter world. Springer Kansai Electric Power Inc., Annual report 2019, 2019 Maier MW (1998) Architecting principles for system of systems. Syst Eng 1(4):267–284 Multiscale ABSS Method for Social Policy Making (n.d.). https://www.jst.go.jp/mirai/en/uploads/ saitaku2020/JPMJMI20B3_summary_en.pdf. Accessed May 2022 Nikhanbayev N, Kaihara T, Fujii N, Kokuryo D (2019) Multiscale modeling of social systems: scale bridging via decision making, vol 567. Springer, IFIPAICT, Austin, pp 617–624 Society 5.0 (n.d.). https://www.keidanren.or.jp/en/policy/2018/095_booklet.pdf. Accessed May 2022 U.S. Energy Information Administration 2019 Annual Energy Outlook 2019. Weinan E, Li X, Ren W, Vanden-Eijnden E (2007) Heterogeneous multiscale methods: a review. Commun Comput Phys 2:367–450 Toshiya Kaihara  is a professor of Graduate School of System Informatics at Kobe University, Kobe, Japan. He received the BE and ME degrees in precision e­ ngineering from Kyoto University, Kyoto, Japan. After he worked for Mitsubishi Electric Corp. as senior researcher, he received the PhD in mechanical engineering from Imperial College London, UK. He is author of more than 250 publications. He is a member of IFIP, IFAC, IEEE, CIRP, ASME, and many others. He served as president of academic societies in Japan, such as Scheduling Society of Japan (SSJ), and the Institute of Systems, Control and Information engineers (ISCIE). He is a fellow member of the International Academy for Production Engineering (CIRP: College International pour la Recherche en Productique), the Japan Society of Mechanical Engineers (JSME), and the Institution of Electrical Engineers of Japan (IEEJ). His research interests include systems science, systems optimization theory, and their application into manufacturing, logistics, and social systems. Nikhanbayev Nursultan  received his master’s degree in 2018 from Graduate School of System Informatics, Kobe university. He withdrew his PhD course with credit in 2020 at Graduate School of System Informatics, Kobe University. He is currently working as AI technology team leader at Profield Co., Ltd. His research interests include Society 5.0, simulation modeling, and image processing.

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Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their Solution Strategies: A Risk-­Management Perspective in the Circulating and Spiral-up Systems Approach Eitaro Aiyoshi, Keiichiro Yasuda, and Kenichi Tamura

1 Introduction A new integrative system approach, the circulating and spiral-up systems approach, to the iterative multi-stage process of real-system implementation and operation → induction → abduction → deduction → real-system implementation and operation has been proposed (Kaihara 2021). The role played by system optimization within this multi-stage process is threefold. First, the induction stage corresponds to the process of using input–output data obtained from real systems to model input–output relationships in the form of equality constraints and to specify inequality constraints assessing the feasibility of input and output variables. Second, the abduction stage corresponds to formulating optimization problems with objective functions describing the goals of stakeholders concerned with the real system, as well as the value expected from the real system, and defining the solutions to be obtained. Third, the process of finding acceptable solutions to formulated optimization problems, and conducting simulations or experiments to prepare for implementing those solutions in real systems is the deduction stage. As a partial list of specific methods used in these processes, we note that the induction stage may use machine learning (Bishop 2006) to generate equality constraints representing input–output relationships and support vector machines (Vapnik 2008) to generate inequality constraints representing feasibility, while the abduction stage may apply the response-surface

E. Aiyoshi (*) · K. Yasuda · K. Tamura Tokyo Metropolitan University, Tokyo, Japan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 T. Kaihara et al. (eds.), Innovative Systems Approach for Facilitating Smarter World, Design Science and Innovation, https://doi.org/10.1007/978-981-19-7776-3_2

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method (Myers and Montgomery 1995) to numerical data quantifying the goals and values of stakeholders to create objective functions; finally, the deduction stage applies various optimization methods known as solvers to obtain solutions to optimization problems formulated at the abduction stage. Using these processes to implement and operate real systems gives rise to new data—from new environmental changes, from changes in the nature of real systems themselves, and from real-­ system operation in diverse environments—to which we respond by repeating the entire multi-stage sequence of processes, continuing thenceforth in iterative fashion. The notion that this procedure can yield a sustainable pattern of evolution for real systems is the basis of the circulating and spiral-up systems approach. In this paper, we begin in Sect. 2 by attempting to combine optimization problems formulated at the abduction stage of the circulating and spiral-up systems approach with modelling techniques used at the induction stage to construct approximate models of input–output relationships. In Sect. 3, we consider real systems in which uncertainty is present; by envisioning worst-case scenarios from a risk-­ management perspective, we combine the optimization of objective functions incorporating min-max criteria with the construction of approximate models satisfying robustness criteria to formulate modelling-driven optimization problems in the presence of uncertainty. Finally, as a solution strategy for such modelling-driven optimization problems in the framework of the circulating and spiral-up systems approach, we propose a constraint-relaxation method in which relaxation problems are solved sequentially while new approximate models are iteratively constructed as scenarios by anticipating values for uncertain variables.

2 Formulation of Modelling-Driven Optimization Problems We consider a static system in which an input variable u ∈ RL and the corresponding output x∈ RN are related by the function h : RL → RN: x = h ( u).



(2.1)

We treat this static system as a black box, with the function h unknown. For this real system, we construct an approximate model in which M basis functions Bm ( u;vm ) = b ( d ( u;vm ) ) , m = 1, …, M (2.2) are linearly coupled via coupling coefficients wnm, m = 1, …, M, n = 1, …, N: M



xn = ∑wnm b ( d ( u;vm ) ) , n = 1, …, N . m =1



(2.3)

In (2.2), the function d : RL → R1 used to construct the basis function Bm maps an L-dimensional input variable u to a 1-dimensional variable z based on the value of a parameter vm; Bm is defined as the composition of d, invoked with parameter value

2  Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their…

31

vm, with a function b : R1 → R1. We assume that the universal approximation theorem, as discussed in, e.g. (Hornik et  al. 1989; Hartman et  al. 1990; Girosi and Poggio 1990) holds for all basis functions Bm, m = 1, …, M defined in this way. For what follows, we will rewrite (2.3) in matrix-vector notation: x = Wb ( d ( u;V ) ) .



Here, W and V, respectively, denote the matrix of coupling coefficients and the matrix whose columns are the basis-function parameter vectors,  w1T   w11  w1M    W =    =      , V = [ v1  v M ] , T  w N   wN 1  wNM   

and the vector-valued function b(d(u; V)) is given by

 b ( d ( u;v1 ) )    b ( d ( u;V ) ) =   . b d ( u;v )  M )  ( 



We assume that we are given a training dataset consisting of S pairs (u(s), x(s)), s = 1, …, S,with u(s) and x(s),respectively, denoting the s th training input and the corresponding desired output. Because we evaluate output errors in accordance with the universal approximation theorem, the norm ‖x‖ that we choose for the output quantities x ∈ RN is the uniform norm: ||x|| = max { xn |n = 1,…,N }.



We also use the uniform norm for the output error in the S-dimensional data space (i.e. the distance between the output corresponding to the input data and the desired output data), where we define the output error to be

((

))

((

))

 ||Wb d u(1) ;V − x (1) ||      = max ||Wb d u( s ) ;V − x ( s ) |||s = 1,…,S ,     ||Wb d u( S ) ;V − x ( S ) ||    and we consider the problem of choosing the coupling-coefficient matrix W and basis-function parameters V to reduce this error below a tolerance ε. More specifically, our objective is to minimize the multimodality (i.e. maximize the smoothness) of the function defined by (2.3) while ensuring that the error remains within the prescribed tolerance, and to this end we seek to minimize the magnitudes of the elements of the coupling-coefficient matrix W, yielding the following inequality-­ constrained minimization problem:

||



{ ((

||

1 min ||W ||2

(V , W ) 2

))

}

(2.4)

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E. Aiyoshi et al. M

subj.to max max

s∈{1,…,S } n∈{1,…,N }

∑w m =1

nm

((

b d u ( ) ;v m s

) ) − x( ) ≤ ε , s n

(2.5)

where the norm ‖W‖ in (2.4) is the squared norm. We refer to the constrained optimization of (Eqs. 2.4 and 2.5) as the learning problem. Solving this learning problem to determine the optimal coupling-coefficient matrix W and the optimal basis-­function parameters V , and using these in (2.1) to construct an approximate model of the form

(

)

x = Wb d ( u;V ) constitutes the induction stage of the circulating and spiral-up systems approach. The notion of a multilayered neural network, which forms the basis of deep-­learning techniques, may be thought of as an extension of the above construction in which the function d used to define basis functions in (2.3) is itself approximated as a linear combination of basis functions, yielding a nested structure. This process is then recursively iterated through multiple nesting generations, producing basis functions that involve more complicated functional compositions and depend on a greater number of parameters; this has the effect of increasing the diversity of the basis set. Thus, the learning problem for multilayered neural networks may be interpreted as essentially equivalent to the learning problem of (Eqs. 2.4 and 2.5). Premised on the approximate model obtained by solving the induction-stage learning problem described above, we construct an objective function f(u, x) reflecting the goals and values of stakeholders, which may be minimized to determine the outputs desired by stakeholders and the inputs that produce those outputs. Thus, the abduction stage involves an optimization problem, which we formulate as follows:

min f ( u,x )

(2.6)

u

(

)

where x = Wb d ( u;V ) .

(2.7)

In practice, objective function f(u, x) itself is described by mathematical expressions involving data reflecting the goals and the values of stakeholders. However, to simplify the discussion, we here assume that the formulas defining the objective function are given in advance; we also assume that no inequality constraints are needed to represent feasibility for inputs u or outputs x, so that we have an unconstrained problem. Then using approximate model (2.7) to eliminate the output x from the objective function (2.6) yields an optimization problem for determining inputs likely to produce favourable results for stakeholders in the real system, which we formulate as

(

(

))

min f u,Wb d ( u;V ) . u

(2.8)

Solving this problem to determine the inputs whose implementation will be feasible in the real system constitutes the deduction stage of the process. Incorporating the induction-stage learning problem of determining the optimal

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33

coupling-­coefficient matrix W and the optimal basis-function parameter matrix V in the approximate model into the description of problem (2.8), we can rewrite it in two-­stage notation:

(

))

(



min f u,Wb d ( u;V ) u

(2.9) (2.10)



1 where (V ,W ) = argmin ||W ||2 (V ,W ) 2 M

subj.to max max

s∈{1,…,S } n∈{1,…,N

∑w }

nm

m =1

((

b d u ( ) ;v m s

) ) − x( ) ≤ ε s n

(2.11)

In this paper, we further combine (2.9) with (Eqs. 2.10 and 2.11) to yield the following problem formulation:

(

)

1 min cf u,Wb ( d ( u;V ) ) + ||W 2 || 2

(V ,W ,u )

M

subj.to max max

s∈{1,…,S } n∈{1,…,N

∑w } m =1

nm

((

b d u ( ) ;v m s

(2.12)

) ) − x( ) ≤ ε s n



(2.13)

We refer to the problem of (Eqs. 2.12 and 2.13), which combines distinct features of modelling and optimization problems, as a modelling-driven optimization problem. Whereas the input u is the decision variable in minimization function (2.12), constraint condition (2.13) ensures that the accuracy of the approximate model with respect to the S input–output data pairs (u(s), x(s)), s = 1, …, S is equivalent to that of (2.5). Also, the learning problem for modelling at the induction stage and the optimization problem solved at the deduction stage are coupled at the abduction stage to constitute a bi-objective problem, with the parameter c (>0) representing a weight coefficient that sets the balance between modelling and optimization. Viewpoints reminiscent of this formulation have also been proposed in (Haimes and Wismer 1972; McGrew and Haimes 1974; Roberts 1977), among other places; however, whereas in those cases the optimization problem was coupled to the identification of real-system model parameters, the optimization here is coupled to modelling via machine learning. A method for coupling modelling and optimization was also proposed in (Kitayama et al. 2008), but in that study the objective function was approximated as a response surface using evaluation data representing system properties with respect to sample points for design variables, and the method derived a computational procedure in which the generation of sample points was entrusted to updates of multiple search points for metaheuristics.

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3 Modelling-Driven Optimization with Uncertainty Tolerance 3.1 Formulation of Modelling-Driven Optimization with Uncertainty Tolerance We consider a system possessing both an input variable u ∈ RL for which data acquisition is possible and a separate exogenous input variable y  ∈  RI for which data acquisition is not possible. We refer to such variables y as uncertain variables and consider the coupling of modelling and optimization in the presence of uncertainty. As in the previous section, we consider a static real system with output variable x ∈ RN, whose unknown input–output function we denote by x = h ( u,y ) where h : RL × RI → RN. For this real system, we introduce basis functions

(2.14)

(2.15) b ( d ( u, y; vm ) ) , m = 1,…, M and consider an approximate model consisting of a linear combination of the basis functions with coupling coefficients wnm, m = 1, …, M, n = 1, …, N: M



xn = ∑wnmb ( d ( u, y; vm ) ) , n = 1,…, N . m =1

(2.16)

Here the function d : RL × RI → R1 used to construct basis functions in (2.15) accepts uncertain variable y together with the input variable u. As in the previous section, using the matrix-vector notation of (2.16) we can write

x = Wb ( d ( u, y;V ) ) .

We assume that the uncertain variable y takes values lying in a set Y, but that probabilistic information, such as distribution functions defined on this set, is not available. Then, with respect to a given set of input–output data pairs (u(s), x(s)), s = 1, …, S, we assume from a risk-management perspective that uncertain variable y will give rise to circumstances tending to maximize the output error, and we attempt to construct an approximate model in which the output error remains within the error tolerance ε. Using the uniform norm for the output error as in the previous section, and writing the left-hand side of inequality constraint (2.5) in terms of the result of an operation of the form max y∈Y , the tolerance criterion for the output error may be written as an inequality of the form M

max max max

y∈Y s∈{1,…,S } n∈{1,…,N

∑w } m =1

nm

((

b d u ( ) , y; v m s

)) − x( ) ≤ ε . s n

(2.17)

Then, formulating the learning problem of minimizing the entries of coupling-­ coefficient matrix W subject to this criterion yields

2  Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their…

1 min ||W ||2 W 2



M

subj.to max max max

y∈Y s∈{1,…,S } n∈{1,…,N



∑w } m =1

nm

((

35

(2.18)

b d u ( ) , y; v m s

)) − x( ) ≤ ε . s n

(2.19)

Incidentally, error tolerance condition (2.17) is equivalent to the following expression using the universal-quantification symbol ∀: M



∑w m =1

nm

((

b d u ( ) , y; v m s

)) − x( ) ≤ ε , n = 1,…, N , s = 1,…, S s n

∀y ∈ Y. (2.20)

Inequality-constrained optimization problems anticipating worst-case scenarios were formulated in Ref. (Shimizu and Aiyoshi 1982), but optimization problems with inequality constraints for all uncertain variables, equivalent to the above, were proposed in (Ben-Tal et  al. 2009) and termed robust optimization problems. Extending this terminology, we refer to inequality constraints anticipating the worst-case uncertain variable, or anticipating values for all uncertain variables equivalent thereto, as robustness criteria, and we refer to the learning problem of (Eqs. 2.18 and 2.19), which uses robustness criteria for output-error tolerances, as a robust learning problem. Similar notions of robust learning were proposed in (Xu et al. 2009; Takeda et al. 2013) in the context of support vector machines (SVMs), but SVMs, which use Gaussian functions as kernel functions, are essentially equivalent to learning problems in which radial basis functions are used as basis functions (2.15), and thus the notion of robust learning discussed in this paper may be interpreted as a generalization of the robust SVM philosophy. Additionally, for such robust learning problems, we may anticipate the use of radial basis functions in (2.15) and assume that values of basis-function parameter matrix V are given separately, whereupon V may be eliminated from the decision variables in the learning problem of (Eqs. 2.18 and 2.19). The process of solving this robust learning problem, taking the solution W as the optimal set of coupling coefficients, and constructing the approximate model in the presence of uncertainty in the form (2.21) x = Wb ( d ( u, y;V ) ) then constitutes the induction stage. We next formulate the optimization problem of determining inputs to yield specified outputs in a given system, taking uncertainty into account. More specifically, assuming that we have a formula for objective function f(u, x), an optimization problem using equality constraints for approximate model (2.21) of input–output relation (2.14) may be formulated as in (Eqs. 2.6 and 2.7) as follows:

min f ( u,x )

(2.22)

where x = Wb ( d ( u, y;V ) ) .

(2.23)

u

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E. Aiyoshi et al.

To simplify the discussion, we have here omitted inequality constraints for decision variables u and output variables x. Eliminating the output variables x from these equations reduces the problem description to

(

)

min f u,Wb ( d ( u, y ;V ) ) . u

(2.24)

This is the problem we consider below. Note that, because the value of uncertain variable y in (2.24) is unknown, the problem cannot be solved in practice. Thus, we must anticipate values for uncertain variable y based on some of criteria. If, by solving the optimization problem with these anticipated values, we succeed in determining the optimal value of input u, then this may be implemented in the real system. In situations where uncertainty is present, anticipating worst-cast scenarios is considered a reasonable risk-­ management strategy for ensuring safety and security. In other words, anticipating that uncertain variable y will take values that maximize the objective function being minimized, we consider adopting min-max criteria (Gilboa 2009) that seek to improve the objective-function value as much as possible given the output of the approximate model in the anticipated worst-case scenario. Introducing such risk-­ management-­motivated anticipated criteria into the abduction stage of the circulating and spiral-up systems approach, the optimization problem in the presence of uncertainty may be formulated as

(

)

min max f u,Wb ( d ( u, y;V ) ) . u y∈Y

(2.25)

Here, even for a y-independent objective function of the form f(u, x), output variable x still depends on uncertain variable y through approximate model (2.21), so it remains meaningful to introduce min-max criteria into the objective function in this case. Then, introducing a new variable σ representing an upper bound on the objective function,

(

)

max f u,Wb ( d ( u, y;V ) ) ≤ σ , y∈Y problem (2.25) may be rewritten in the equivalent form

min σ (σ ,u )

(

(2.26)

)

subj.to max f u,Wb ( d ( u, y;V ) ) ≤ σ . y∈Y

(2.27)

We refer here to such optimization problems in the presence of uncertainty as min-max optimization problems. Finally, in analogy to the modelling-driven optimization problem of (Eqs. 2.12 and 2.13), we may combine the robust learning problem of (Eqs.  2.18 and 2.19) with the min-max optimization problem of (Eqs. 2.26 and 2.27) to formulate a bi-­ objective problem:

1 min cσ + ||W ||2 2

(W ,σ ,u )

(2.28)

2  Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their…

(

)

subj.to max f u,Wb ( d ( u, y;V ) ) ≤ σ y∈Y



M

max max max

y∈Y s∈{1,…,S } n∈{1,…,N



∑w }

nm

m =1

((

b d u ( ) , y; v m s

37

(2.29)

)) − x( ) ≤ ε . s n

(2.30)

To simplify these formulas, we use the shorthand notation



(

)

F (W ,σ ,u ) = max f u,Wb ( d ( u, y;V ) ) − σ



y∈Y

M

G (W ) = max max max

y∈Y s∈{1,…,S } n∈{1,…,N }

∑w m =1

nm

((

b d u ( ) , y; v m s

)) − x( ) − ε . s n

Then the condition that (Eqs. 2.29 and 2.30) hold simultaneously is equivalent to the following condition: max {F (W ,σ ,u ) ,G (W )} ≤ 0.



By reversing the order in which the outermost max operation here and the max y∈ Y operations in the definitions of F(W, σ, u) and G(W) are applied, inequality constraints (Eqs.  2.29 and 2.30) may finally be expressed as a single inequality condition:

) { ( ∑w b ( d ( u( ) , y; v ) ) − x( ) − ε , n = 1,…, N , s = 1,…, S} ≤ 0 max max f u,Wb ( d ( u, y;V ) ) − σ , y∈Y

M

s

nm

m =1

s n

m

To summarize, we have combined the min-max criteria added to the objective function at the abduction stage with the robustness criteria added to the approximate model at the induction stage to yield a single inequality constraint. The problem of (Eqs. 2.28–2.30) may then be formulated in the final form 1 min cσ + ||W ||2 2



{ (

)

subj.to max max f u,Wb ( d ( u, y ;V ) ) − σ ,



y∈Y

M



(2.31)

(W ,σ ,u )

∑w m =1

nm

((

b d u ( ) , y; v m s

)) − x( ) − ε , n = 1,…, N , s = 1,…, S} ≤ 0. s n

(2.32)

We refer to this problem as a modelling-driven optimization problem with uncertainty tolerance. In the following section, we discuss a solution strategy for this problem and how it fits into the circulating and spiral-up systems approach.

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E. Aiyoshi et al.

3.2 Constraint-Relaxation Method for Modelling-Driven Optimization Problems with Uncertainty Tolerance As a strategy for attacking the modelling-driven optimization problem with uncertainty tolerance of (Eqs. 2.31 and 2.32), we apply the constraint-relaxation approach. Inequality constraint (2.32) is equivalent to the following inequality involving the universal-quantification symbol:

) { ( ∑w b ( d ( u( ) , y; v ) ) − x( ) − ε , n = 1,…, N , s = 1,…, S} ≤ 0, max f u,Wb ( d ( u, y;V ) ) − σ ,

M



s

nm

m =1

s n

m

∀y ∈ Y. (2.33)



When the set of values Y anticipated for the uncertain variable y contains uncountably many elements, the problem of (Eqs. 2.31 and 2.32) involves an uncountable infinitude of inequality constraints, making it difficult to solve in practice. Even if set Y is of finite but extremely large order, the problem is not easy to solve. A practical remedy is to restrict the set of values anticipated for uncertain variable y to a smaller number of possibilities and replace the problem of (Eqs. 2.31 and 2.32) with a constraint-relaxation problem involving a reduced number of inequality constraints (2.33). Denoting the anticipated values by y(p) ∈ Y, p = 1, …, P, the constraint-­ relaxation problem corresponding to the modelling-driven optimization problem with uncertainty tolerance of (Eqs. 2.31 and 2.32) is written as 1 min cσ + ||W ||2 2

(W ,σ ,u )



{( (

M



(

subj.to max f u,Wb d u, y ( p ) ;V

∑w m =1

nm

((

b d u ( ) , y ( ) ;v m s

p

(2.34)

))) − σ ,

)) − x( ) − ε , n = 1,…, N , s = 1,…, S} ≤ 0, s n

p = 1, …, P. (2.35)

We test whether the solution to the constraint-relaxation problem of (Eqs. 2.34 and 2.35) is the optimal solution to the original modelling-driven optimization problem with uncertainty tolerance of (Eqs.  2.31 and 2.32). If not, we add new constraints to the problem of (Eqs. 2.34 and 2.35) and repeat the process. This is the constraint-relaxation method of (Blankenship and Falk 1976; Shimizu and Aiyoshi 1980). A new approximate model is generated, corresponding to new anticipated values for uncertain variables y, and inequality constraints are added to represent the ^ ^ ^ associated output-error tolerances. First, denoting by (W , σ, u) the solution of the

2  Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their…

39

constraint-relaxation problem of (Eqs. 2.34 and 2.35), to check whether this solution solves the problem of (Eqs.  2.31 and 2.32), we check whether it satisfies inequality constraint (2.32). That is, we consider the maximization problem for uncertain variables y ∈ Y of anticipating the worst-case scenario,



 max max  f y∈Y 

M

∑ w^

nm

m =1

((

b d u ( ) , y; v m s

^ ^  ^  ^ ,  u ,W b  d  u , y;V    − σ    

)) − x( ) − ε , n = 1,…, N , s = 1,…, S}, s n

(2.36)

and, denoting the y value that maximizes this expression by ^y ∈ Y and the maximal value by ^

^ ,u ^ ) φ (W , σ

 = max  f 

M



∑ w^

nm

m =1

 ^ ^   ^ ^  ^  u ,W b  d  u , y ;V    − σ,    

  s  s b  d  u( ) , ^y ;vm   − xn( ) − ε , n = 1,…, N , s = 1,…, S },,   

we check whether ^ ^ ^ φ (W , σ , u) ≤ 0 ^ ^ ^ holds. If so, (W , σ , u) satisfies the inequality constraint and is the solution to the modelling-driven optimization problem with uncertainty tolerance of (Eqs. 2.31 and 2.32). If instead we have ^ ^ ^ φ (W , σ , u) > 0,

then among inequality constraints (2.33), the inequality constraint corresponding to the maximizer ^y ∈ Y ,



 max  f 

     u,Wb  d  u, ^y ;V    − σ ,     M   s  s wnmb  d  u( ) , ^y ;vm   − xn( ) − ε , n = 1,…, N , s = 1,…, S } ≤ 0, ∑  m =1   ^

(2.37)

^ ,u ^ ). In this case, we take ^ to be a new (P + 1)-th is maximally violated by (W , σ y (P + 1) entry y  in a sequence of anticipated values for uncertain variable y; we add corresponding tolerance condition (2.37) for the new approximate model to the set of inequality constraints (2.35), and then repeat the above procedure starting with this

40

E. Aiyoshi et al.

newly constraint-relaxation problem. Maximization problem (2.36) can be described as the result of anticipating a new worst-case scenario upon solving the constraint-­ relaxation problem of (Eqs.  2.34 and 2.35). After formulating the constraint-­ relaxation problem during the abduction stage and obtaining its solution during the deduction stage, we return once again to the abduction stage, anticipating the worst-­ case scenario for the solution to the constraint-relaxation problem, constructing a new relaxation problem, and repeating the entire procedure. The single constraint (2.35) made possible by the max operation may be separated, so the constraint-relaxation problem of (Eqs. 2.34 and 2.35) is equivalent to min cσ +



(W ,σ ,u )

(

((

1 || W ||2 2

subj.to f u,Wb d u, y ( p ) ;V



M

∑w



m =1

nm

((

))) ≤ σ , p = 1,…, P

b d u ( ) , y ( ) ;v m s

p

(2.38) (2.39)

) ) − x( ) ≤ ε , s n

n = 1, …, N , s = 1, …, S , p = 1, …, P. (2.40)



Equation (2.40) is the condition that the output error of the approximate model remains less than ε for all possible combinations of input-data values u(s), s = 1, …, S and uncertain-variable samples y(p),p = 1, …, P. These approximate models may be interpreted as scenarios within the scenario approach of (Campi et  al. 2009). Equation (2.39) is the condition giving the coupling coefficients of an approximate model that uniformly minimizes the objective-function values obtained in all possible scenarios corresponding to anticipated values of the uncertain variable, together with the value of the input variable for that model. In modelling-driven optimization problems with uncertainty tolerance, we again refer to the problem of (Eqs. 2.38–2.40) for such scenarios as a constraint-relaxation problem. Considering this constraint-relaxation problem, we find that, in maximization ^

^ ,u ^ ) and the maximizing input ^y ∈ Y problem (2.36), the maximum value φ (W , σ may be obtained as the overall maximum value and maximizing input for the following set of 1 + N × S maximization problems:

^ ^  ^  ^ max f  u W b  d  u, y;V    − σ y∈Y    



M

max

y∈Y

∑ w^ m =1

nm

((

b d u ( ) , y ;v m s

)) − x( ) − ε , n = 1,…, N , s = 1,…, S s n

(2.41) (2.42)

Thus, the worst-cast scenario due to problem (2.42) may be separately anticipated for each input–output data pair (u(s), x(s)), s = 1, …, S and for all components s xn( ) , n = 1, …, N of each output-data value xs.

2  Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their…

41

Summarizing the above, the procedure for applying constraint-relaxation methods to the modelling-driven optimization problem with uncertainty tolerance of (Eqs. 2.31 and 2.32), including the task of problem formulation, may be outlined as follows. Step 1: Select basis functions (2.15) for approximate model (2.16), obtain input– output data pairs (u(s), x(s)), s = 1, …, S for constructing the approximate model, and choose error tolerance ε (>0). Step 2: Select an initial anticipated uncertain-variable sample y(1) ∈ Y and set P(1) = 1 and k = 1. Step 3: Construct the constraint-relaxation problem of (Eqs.  2.38–2.40) with P = P(k). ^ ^ (k ), u ^ ( k )) . Step 4: Solve the problem of Step 3 and denote the solution by (W (k ), σ ^

Step 5: Solve the 1 + N × S maximization problems of (Eqs. 2.41 and 2.42) with ( 0)

^

^ =σ ^ k ,u W = W (k ), σ ( ) ^ = u^ ( k ) . Denote the maximizer of (2.41) by ^y ( n, s )

(k )

and

the maximizers of (2.42) by ( k ) , n = 1,…, N , s = 1,…, S . Let ∮(k), ∮ (k), n = 1, …, N, s = 1, …, S be the corresponding maximal values. Denote the maxi^ ^ k ,u mum of these values by ϕ ((W ( k ) , σ ( ) ^ ( k ))) and let ^y ( k ) be the maximizing ^y

(n, s)

input that produces this maximum in (Eqs. 2.36).  ^ ^ ( k ), u ^ ( k )   ≤ 0, then terminate the procedure and take Step 6: If ϕ   W (k ), σ    ^ ^ k , u (W ( k ) , σ ( ) ^ ( k )) to be the solution of the modelling-driven optimization prob ^ ^ ( k ), u ^ ( k )   > 0, lem with uncertainty tolerance of (Eqs. 2.31 and 2.32). If ϕ   W (k ), σ    ( P( k +1) ) ^ then set P ( k + 1) = P ( k ) + 1, y = y ( k ) , k ← k + 1, and return to Step 3. Relating this procedure to the process of the circulating and spiral-up systems approach, we see that Step 1 corresponds to the induction stage, Steps 2 and 3 correspond to the abduction stage, and Step 4 is the deduction stage. The result is returned to the abduction stage, and a new anticipated value ^y ( k ) for the uncertain variable, corresponding to the worst-case scenario, is generated in Step 5. If the evaluation of the abduction stage in Step 6 determines that the process may termi^ k determined in the deduction stage may be implenate, then the optimal input u ( ) mented in the real system. If instead the evaluation of Step 6 requires further iterations of the procedure, a new sample y ( P( k +1)) (= ^y(k )) giving a new worst-case scenario is added to the set of anticipated y values and a new relaxation problem is generated by Step 3 in the abduction stage.

3.3 Computational Techniques for Constraint-Relaxation Methods In this section, we discuss specific computational techniques for constraint-­ relaxation methods. In the constraint-relaxation procedure, new uncertain-variable

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samples corresponding to anticipated worst-case scenarios are added as input data. Thus, to maintain the precision of the new approximate model, the increase in the number of uncertain-variable samples must be matched by an increase in the number of basis functions. To this end, an effective strategy is to use radial basis functions, for which the correspondence between input data and basis-function parameters is straightforward and basis-set expansion is automatic. Using a set of S × P(k) radial basis functions in the (u, y)-space

(

B( s ,p ) u, y;vu( ) ,v (y



s

p)

) = b ( d ( u, y;v ( ) ,v ( ) )) , u

s

y

p

s = 1, …, S , p = 1, …, P ( k ) ,



(2.43)

the approximate model is expressed as S P( k )

(

xn = ∑∑wnsp B( s ,p ) u, y;vu( ) ,v (y



s =1 p =1

s

p)

) , n = 1,…, N .

(2.44)

In the definition of the radial basis functions in (2.43), function d is the Euclidean s p distance from point vu( ) ,v (y ) in the (u, y)-space and b is a Gaussian function:

(

)

(

d u, y;vu( ) ,v (y

s

p)

)

(s)  u   vu  =   −  ( p)   y   v y 

b ( d ) = exp ( −d 2 / r 2 ) .



Parameters vu( ) ,v (y ) in the radial basis function are simply the s-th data point for the input variable and the p-th anticipated sample of the uncertain variable: s

p

vu( ) = u( ) ,v (y p ) = y ( p ) . Consequently, whereas the number of input-variable data points S is fixed, the set of anticipated samples y(p) of the uncertain variable, which grows on each update of the constraint-relaxation method, directly furnish values for basis-function parameters v (y p ) , thus automating the task of creating new basis functions. As the number P(k) of anticipated y samples grows, the number of basis functions (2.43) grows as well, increasing the size of the three-dimensional coupling-­coefficient array W = {wnsp} and modifying the structure of approximate model (2.44) itself. Thus, to ensure that the constraint-relaxation problem of (Eqs. 2.38–2.40) with P = P(k) in Step 3 is described accurately when using radial basis functions, we add an iteration-count argument k to the array variable as W(k) and the basis-function parameter variable as Vy(k), yielding the following formulation: s



s

min cσ +

(

(W ( k ),σ ,u )

((

2 1 W (k ) 2

subj.to f u,W ( k ) B d u, y ( p ) ;Vu ,Vy ( k )

))) ≤ σ , p = 1,…, P ( k )

(2.45) (2.46)

2  Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their… S P( k )

∑∑w ( k ) b ( d ( u( ) , y ( ) ;u( s ′=1 p ′=1



s

ns ′ p ′

p

s ′)

, y(

p ′)

)) − x( ) ≤ ε , s n

n = 1, …, N , s = 1, …, S , p = 1, …, P ( k ) .



43

(2.47)

Here W(k) of (Eqs. 2.45 and 2.46) is an array variable of dimensions N × S × P(k) with components wns ′ p′(k), n = 1, …, N, s′ = 1, …, S, p′ = 1, …, P(k), and Vu, Vy(k) are given by P(k ) S Vu =  u(1)  u( )  , Vy ( k ) =  y (1)  y ( )  .  

Additionally,

(

)

B d ( u, y;Vu ,Vy ( k ) )



(

 b(d u, y;u(1) , y (1)  =   b(d u, y;u( S ) , y (1) 

(



(

) 

)

 b(d u, y;u(1) , y (

)

  P( k )  b(d u, y;u( S ) , y ( )  

(

(

P( k ) )



)

)

W ( k ) B d ( u, y;Vu ,Vy ( k ) )



 S P( k ) ( s ′) ( p ′)  ∑∑w1s ′ p ′ ( k ) b d u, y;u , y  s ′=1 p ′=1  =  P( k ) S  ( s ′) ( p ′)  ∑ ∑wNs ′ p ′ ( k ) b d u, y;u , y  s ′=1 p ′=1





((

)) 

((

))

     

Note that the constraint-relaxation problem of (Eqs. 2.45–2.47) is a constrained problem whose global solution may not be easy to find due to the multimodality of the radial basis functions. Instead, we may use the penalty method to convert it to an unconstrained problem: min cσ +

(W ( k ),σ ,u )

P( k )

( {

})

 +γ ∑  max f (u,W (k ) B (d (u, y ( p ) ;Vu ,Vy (k )))) − σ , 0 p =1 



P( k )   S s p s p + ∑∑  max  ∑∑wns ′ p ′ ( k ) b d u( ) , y ( ) ;u( ′) , y ( ′)  s =1 n =1 s ′= 1 p ′= 1    S



2 1 W (k ) 2

N

((

)) − x

(s)

n

2

  − ε ,0    

2

  .(2.48)  

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In particular, because the number of anticipated samples of uncertain variable P(k) grows on each iteration of the constraint-relaxation method and that dimension of the array variable W(k) increases accordingly, in solving problem (2.48), it is desirable to use metaheuristics capable of controlling global convergence. Also, ^  ^ k ,u denoting the solution of the constraint-relaxation problem by  W ( k ) , σ ( ) ^ (k ) ,   the maximization problem of (Eqs. 2.41 and 2.42) solved in Step 5 for uncertain variable y is expressed using radial basis functions as ^



^ k ,W ( k ) B (d ( u ^ ( k ), y;V ,V ( k )))) − σ ^ (k ) max f (u ( ) u y y∈Y

S P( k )

max

y∈Y

∑∑ w^ ( k ) b(d (u( ) , y; u( s

ns ′ p ′

s ′)

s ′=1 p ′=1

, y ( ′) )) − xn( ) − ε s

p



n = 1, …, N , s = 1, …, S .



In this case as well the application of metaheuristics is desirable in view of the multimodality and non-differentiability of the functions to be maximized. The multimodality of the function in the unconstrained problem (2.46) stems primarily from the multimodality of the approximate functions. The shape of the multimodality of these functions, in turn, is affected by the magnitude of the r parameter in the Gaussian function used to construct the radial basis functions. An empirical formula for this parameter that has been reported to yield good results (Kitayama et al. 2008) is r = d max /



(

)

D DT ,

( ) ( ) ( ) ( ) where D denotes the number of basis-function parameters (vu ,v y )(= (u ,y )), T s

p

s

p

denotes the total number of input data points (samples), and dmax denotes the maximum distance between any two input data points (samples). For the radial basis functions used in the constraint-relaxation problem of (Eqs.  2.45–2.47), we have D = L + I, T = S × P(k). For dmax, assuming that the values of the input variables and uncertain variables lie in finite ranges,

U = {u|ullow ≤ ul ≤ ulupper , l = 1,…, L}



Y = { y| yilow ≤ yi ≤ uiupper , i = 1,…, I } ,

a convenient choice is d max =

L

∑ (u l =1

upper l

I

− ullow ) + ∑ ( yiupper − yilow ) . 2

i =1

2



2  Modelling-Driven Optimization Problems with Uncertainty Tolerance and Their…

45

4 Conclusions In the present study, working within the circulating and spiral-up systems approach, we embedded induction-stage modelling into the formulation of abduction-stage optimization problems. For modelling, we envision using machine-learning methods based on input–output data, not to construct approximate models based on squared-error minimization but rather as inequality constraints for error tolerances to be embedded into optimization problems within the framework of the universal approximation theorem. This viewpoint may also be applied to the problem of learning for the multilayered neural networks considered in deep-learning schemes. We believe that the idea of embedding learning problems within optimization problems may itself yield new value and utility in the field of machine learning. Additionally, creating inequality constraints for error tolerances allows the construction of approximate models satisfying robustness criteria, even when uncertainty is present in the target system; further combining with the min-max criteria added to objective functions in the presence of uncertainty allows problems to be formulated as modelling-driven optimizations. We also noted that, in the constraint-­ relaxation methods used to solve these problems, radial basis functions are useful for increasing the number of basis functions when reconstructing new approximate models as scenarios by anticipating values of uncertain variables. Increasing the number of basis functions in a constraint-relaxation method is also a familiar strategy for boosting (Freund and Schapire 1997) in machine learning, again suggesting the possibility of conceptually extending this solution method to the field of machine learning.

References Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press Bishop CM (2006) Pattern recognition and Machine learning. Springer, NewYork, p 738 Blankenship JW, Falk JE (1976) Infinitely constrained optimization problems. J Optim Theory Appl 19(2):261–281 Campi MC, Garatti S, Prandini M (2009) The scenario approach for systems and control design. Annu Rev Control 33(2):149–157 Freund Y, Schapire RE (1997) A decision-theoretic generation of on-line learning and application to boosting. J Comput Syst Sci 55(1):119–139 Gilboa I (2009) Theory of decision under uncertainty. Cambridge University Press Girosi F, Poggio T (1990) Networks and the best approximation property. Biol Cybern 63(3):169–176 Haimes YY, Wismer DA (1972) A computational approach to the combined problem of optimization and parameter identification. Automatica 8(5):337–346 Hartman EJ, Keeler JD, Kowalski JM (1990) Layered neural networks with Gaussian hidden units as universal approximations. Neural Comput 2(2):210–215 Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

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Kaihara T (2021) New trends in systems approaches to realized smarter world. In: Kaihara T, Kita H, Takahashi S (eds) Innovative systems approach for designing smarter world. Springer, Singapore, pp 1–15 Kitayama S, Yasuda K, Yamazaki K (2008) The integrative optimization by RBF network and particle swarm optimization. IEEJ Trans Electron Inf Syst 128(4):636–645. (in Japanese) McGrew DR, Haimes YY (1974) Parameter solution to the joint system and optimization problem. J Optim Theory Appl 13(5):582–605 Myers RH, Montgomery DC (1995) Response surface methodology: process and product optimization using designed experiments. Wiley Interscience Roberts PD (1977) Multilevel approaches to the combined problem of system optimization and parameter identification. Int J Syst Sci 8(3):273–299 Shimizu K, Aiyoshi E (1980) Necessary conditions for min-max problems and algorithms by relaxation procedure. IEEE Trans Autom Control 25(1):62–66 Shimizu K, Aiyoshi E (1982) A new solution to optimization-satisfaction problems by a penalty method. Automatica 18(1):37–46 Takeda A, Mitsugi H, Kanamori T (2013) A unified classification model based on robust optimization. Neural Comput 12(3):759–804 Vapnik V (2008) The nature of statistical learning theory. Springer Xu H, Caramanis C, Mannor S (2009) Robustness and regularization of support vector machine. J Mach Learn Res 10(51):1485–1510 Eitaro Aiyoshi  received the Doctor of Engineering degree from Keio University and joined the Faculty of Science and Technology, Keio University in 1980. From 1996 to 2016, he was a professor, and since 2016, he is an emeritus professor at Keio University. He was a visiting professor at the Institute of Statistical Mathematics from 2017 to 2021, and he is a visiting professor at Tokyo Metropolitan University from 2021. His research interests are systems optimization methods and machine learning methods. Keiichiro Yasuda  received PhD degree from Hokkaido University, in 1989. The same year, he became an assistant professor in the Faculty of Engineering at the Tokyo Metropolitan University. In 1991, he became an associate professor in the Faculty of Engineering at the Tokyo Metropolitan University and, since 2006, he has been a professor in the Graduate School of Systems Design at the Tokyo Metropolitan University. He is engaged in research on systems optimization and power systems engineering. Kenichi Tamura  received the BE degree in system design engineering and the ME and PhD degrees in integrated design engineering from Keio University in 2003, 2005, and 2008, respectively. Since 2008, he has been with Tokyo Metropolitan University, where he is currently an assistant professor with Faculty of Systems Design Engineering. His research interests include system control and optimization.

3

Issues of System Cooperation from a Viewpoint of System Structure Hajime Kita

1 Introduction The outbreak of COVID-19 became a global pandemic in 2020 and has given a large impact on society. As well as the pandemic, we, especially in Japan, have very difficult social problems such as global warming and other environmental issues, large-scale disasters, depopulation and aging, and widening disparity. At the same time, the progress of information and communication technologies (ICT) is quite rapid, and utilization of the Internet of Things (IoT) where various objects will be connected to the network, and application of artificial intelligence technologies such as the deep learning are expected. The experience of telework and online education under the pandemic gave people opportunities of thinking about digital transformation (DX). Assuming utilization of ICT, construction of Cyber-Physical-System, CPS which combines physical world consisting of material processes, and cyber world consisting of information processes, and System of Systems (SOS) which combines various systems to achieve higher functions attract attention to solve the aforesaid problems. We need to develop science and technology of systems under such vision. This paper discusses the cooperation of systems from a viewpoint of its structure to think SOS.  In cooperation with social systems, we have to consider an economical aspect of it and the will of the organization that operates each system. In the following, first, this paper gives an overview of the economical aspect of

H. Kita (*) Institute for Liberal Arts and Sciences, Kyoto University, Kyoto, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 T. Kaihara et al. (eds.), Innovative Systems Approach for Facilitating Smarter World, Design Science and Innovation, https://doi.org/10.1007/978-981-19-7776-3_3

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systems and value creation with them. Then, the author tries to list typical structures of cooperating systems and discusses points to be considered in each structure.1

2 Value and Economy of Systems 2.1 System Size and Economy In thinking of society-level systems and their cooperation, we have to consider the structure of the systems and their economic characters. Here we see the change of benefits and costs by changing the system in size. Current systems use computer software largely, and hence we have to consider that software requires large fixed cost for development on the one hand, and on the other hand, additional costs in expanding its unit usage, which is called the “marginal cost” in economics, are quite low (Rifkin 2014).2 Due to such characteristics, average cost including fixed cost decreases rapidly according to the increase in use. Typical economies of the system relating to its sizes are as follows. The first two items relate to the cost needed at the producer side, but the third item relates to the benefit generated at the user side. Economy of scale: Economy of scope: Network externality:

Reduction of average production cost along the increase in the amount of use Reduction of average production cost along the increase in types of uses Increase in benefits along with the increase in the number of users (Kats and Shapiro 1985)

2.2 Symbiotic Man-Machine Systems and Value Creation The value of artificial systems is created by the users of the systems. If we don’t include humans explicitly in systems, values obtained by constructing systems are recognized as goals given exogenously or costs needed by the systems. In thinking about value creation, we have to consider that values are created in various meanings. There may exist trade-offs among values and conflicts among stakeholders of the systems. Various characteristics of the systems relate to values brought about by the systems. In de Weck et al. (2011), life cycle characteristics of engineering systems are  Adapted from Hajime Kita “System and Information. A Viewpoint toward a Novel Systems Approach (written in Japanese),” Journal of Society of Control and Instrument Engineers, Vol 55, No. 8 (2016). Partly translated by permission of The Society of Instrument and Control Engineers. Section 3 is newly added in this article. 2  We can understand it by comparing the cost to produce one automobile and that to produce one software additionally. The former needs a big cost for the material. Contrary to it, the latter, e.g., additional production of an operating system or a set of office tools, it is just cost to copy files. 1

3  Issues of System Cooperation from a Viewpoint of System Structure

49

called “-ilities.” It is because terms for such characteristics often include “-ility” as a suffix. In their book, the following terms are shown with their frequencies appearing in scientific literature and results of the search on the internet. Quality, reliability, safety, flexibility, robustness, durability, scalability, adaptability, usability, interoperability, sustainability, maintainability, testability, modularity, resilience, extensibility, agility, manufacturability, repairability, evolvability.

To think of systems as symbiotic man-machine systems is important as a viewpoint to find values created by the systems. By seeing the use cases of the systems by humans, we can find opportunities for value creation through expanding or shrinking system boundaries, and cooperating relating systems. Discussions by Kawakami (2021) and Shimohara (2021) give important points concerning it. Further, self-driving cars attract attention as innovative transportation. For utilization of such technology, we have to think not only about technologies for self-­driving but also cooperation among users and autonomous systems operating in complex environments and failure of it, and responsibilities in such cases.

3 Cooperation of Two Similar Systems There are cases of trying to cooperate with two similar systems for various reasons. The followings are typical examples: • In merging two organizations, they want to unify services and products provided by organizations, or they want to unify the internal systems for organizational management. • They want to increase in connectivity of their services through cooperation. For example, mutual operations of railway companies (Uzuka 2020) (See also the article by Tetsuo Uzuka in this book.) have been conducted in Japan. Even organizations provide similar services and products, the detail of system design is different. Hence there can be taken various strategies in cooperation: • So as to minimize changes in both systems, cooperation is taken only in the necessary part. • Adjust only the smaller system common to the larger one. • Construct a new system and move both old systems to the new one.

4 Structure of Cooperating Systems There may be various structure types of cooperating systems. Here we would like to think about the following six types (Kita 2017a) as shown in Fig. 3.1 from viewpoints of social systems.

50

H. Kita

a

b

Layer Type Platform

c

Interaction Type Platform

d

Leyered System

e

Serial System

f

Autonomous Decentrarized System

System Integration

Fig. 3.1  Structures of system cooperation ((a), (b) is taken from Kita (2021) and translated)

4.1 Platforms Recently, “platforms” or “platformers” that provide this type of services as organizations are attracting attention because of the emergence of big players such as GAFA.  Based on the study by Negoro et  al. (Negoro and Kato 2010; Negoro and Ajiro 2012), structure types (a) and (b) in Fig. 3.1 shown in Kita (2021) are platforms of the “layer type” and “interaction type,” respectively. As characteristics of platforms, the network externality (Kats and Shapiro 1985) and two-sided markets are discussed. Due to the network externality, a platform

3  Issues of System Cooperation from a Viewpoint of System Structure

51

having large customers attracts more customers, and hence it tends to grow monopolistic as the winner-take-all.

4.2 Layered Systems A layered structure is a structure that several platforms stack as layers as shown in Fig.  3.1c. One example is communication protocols used on the internet. The IP protocol transfers IP packets globally as a bottom layer, and the TCP layer supports connection-oriented communication stacks on it. Further, various protocols are employed on these layers. The upper layer conceals the difference of the lower layer, for example, TCP/IP conceals a difference of types of the lower physical layer such as wired LAN and wireless LAN.

4.3 Serial Systems We often see a structure that systems are connected in series as shown in Fig. 3.1d. It may seem just a rotating structure of the layered system. However, in the layered systems, layers work in parallel. Contrary to this, in a serial systems, usage moves forward. Supply chain form material to parts and parts to assembled products is of this type. In supply chains, it is know a characteristic called the Bullwhip effect (Lee et al. 1997) where fluctuation of demand at the downstream propagates with amplification to the upstream. School education systems from preschool education to higher education via elementary and secondary education are also systems of this type (Kita 2019). In Japanese school systems, social demands for education are shown and planned as council reports and national course of studies. Then the government asks implementation to organizations of each educational level. However, the interests of each school are securing enrolled students and their promotion to the next level. Social demands shown in the reports, and the course of studies tend to be taken as the constraints rather than the objectives.

4.4 Autonomous Decentralized Systems There proposed the Sustainable Development Goals (UNDP 2022) to solve various social problems. Toward this, in Japan, there are movements that try to develop regions facing the problems of depopulation and aging utilizing their regional resources (Motani 2020; Hiroi 2019). We can consider this situation as an autonomous decentralized system of autonomously working regions cooperating in wide areas. See Fig. 3.1e. The next section discusses it as “systems close to and far from us.”

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4.5 System Integration System integration as Fig. 3.1f integrates various platforms for a particular user or organization. We also discuss it in the later section with a trend in educational information systems as a hint.

5 Systems Close to and Far from Us 5.1 Distance to Systems Yukiko Kada, a previous governor of Shiga Prefecture, Japan, discussed “Chikai-­ Mizu, Thoi-Mizu”3 in her invited talk (Kada 2016). The former means the local circulation system of water resources before modernization, and the latter means the modern water and sewage services operated in a wide area. Recognizing the necessity of the latter one in an urbanized area, she said the former one was negated because it was not modern as well as inconvenient. Kita (2017a) pointed out that Kada’s idea of “close to us” and “far from us” gave a viewpoint applicable to various social systems such as foods, energy, farms, government, and education.4 In the contemporary society, on the one hand, globalization is sought, and on the other hand, we also face a problem of declination of rural areas. Through generalization of Kada’s idea of “close to us” and “far from us,” to social systems, and comparing them, we would like to discuss it as a hint to think novel social systems beyond dichotomy. Kita (2017b) compared “systems close to us” and “systems far from us” as shown in Table 3.1, and discussed dichotomy is caused by difference of norms and criteria in various viewpoints.

5.2 Importance of Human Resources, Knowledge, and Learning Rifkin discussed the impact of the internet and renewable energy in his book (Rifkin 2014). Currently, utilizing various services of platform types, we can support small-­ scale “systems close to us.” It gives a view of cooperating autonomous systems via platforms. Now, various autonomous activities are actually taken in regional areas in Japan, it is said that knowledge and human resources are important for them (Motani 2020). In Laloux and Wilber (2014), the importance of organizations that can learn  in Japanese, it means “Water close to Us and Water far from us.”  There are systems that connect distant suppliers and consumers such as tourism. Even though tourism planned by the destination side attracts attention, it can be said tourism that is close to us for the region that accepts tourists. 3 4

3  Issues of System Cooperation from a Viewpoint of System Structure

53

Table 3.1  Comparison of systems close to and far from us Viewpoint Norm of rationality Governing mechanisms Redistribution Capacity building and improvement Participation Convenience Quality Attitude to user Attitude to expansion Risk

Systems close to us Regional circulation and sustainability Sympathy, mutual benefit, autonomous norm formation Averaging Bottom-up, lack of knowledge in small community Inclusive, connected demand and supply Low Unstable but understood Own matters Continuity and fulfilling Movement to systems far from, vulnerability in external pressure, free riders, decrease in participation and declination, conflict with neighbors

Systems far from us Division of work and economy of scale Law and market Centralize Centralized, large investment in research and development Exclusive, separation of demand and supply High Stable without understanding Matters of someone else Growth for profit Environmental disruption, large-scale impairment, over investment, international risks, and market risks

and evolve is discussed. Online education taken widely under the COVID-19 pandemic showed that we can relax the constraint of coming to campus in learning activities, and it shows a possibility of providing human resources, knowledge, and learning opportunities to autonomous activities in regional areas. Thus, understanding the aforesaid situation, we may be able to design novel social systems beyond the dichotomy of “systems close to us” and “systems far from us,” and we have to construct a vision of such social systems.

6 User-Centric System Construction 6.1 Users as a Field of Value Creation While platforms attract attention, system integration (SI) that combine various services provided by the platform to meet users’ requirement is important for users. In large organizations, they integrate information services for the management of finance, human resources, and production on the infrastructure of authentication, network, servers, and terminals as well as systems for communication such as e-mail. In such organizations, information systems are planned and operated by information system divisions with experts. In Japan, however, the number of IT engineers at the user side is small (Information Technology Promotion Agency 2017), and it is often managed by operators outside the organization, which is called system integrators (SIers). Such a way may not sufficiently efficient and effective for customer organizations.

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6.2 Proposal of Home System Integration Considering SI is directly connected creation of value at the user side, downsizing of SI would be the issue to be challenged. Here, the author proposes SI in-home, i.e., HSI (Home System Integration), as an ultimate goal of SI. It is a kind of digitization of housekeepers while housekeepers are rarely used in Japan because of increase in the household of single or of a few members. In such a sense, HSI is not a new concept. However, life in the contemporary society is very complex. Home has relations with lifelines, local and national governments, schools, medical services, postage and delivery services, maintenance of the house and its facilities, finance such as saving, loan, insurance and tax. It takes important roles in childcare, education, health care, nursing. Move and evacuation in disaster or death of household member may occur. Further, there are trends in subscription services and sharing economy. In reality, various services get more complicated and come to home separately. HSI is to integrate these for household members. In this sense, it should be designed differently from home energy management systems or integration of control of home appliances. It also should be designed considering management of personal data and its usage in the society (Atsumenai Big Data Consortium 2015). We should consider stakeholders such as organizations providing services and the people using services via HSI.

6.3 System Integration and Standardization, from a Case of Educational Systems As a hint in thinking downsizing of system integration such as HSI, there is a discussion of Next Generation Digital Learning Environment (NGDLE) by Educause (Brown 2017). Many universities operate “learning management systems (LMS)” to support education with ICT. In university, many functions are needed in LMS to support classes of wide varieties. Before, as an LMS, all-in-one types supporting various functions have been pursued. One of the key ideas of NGDLE is to treat an LMS as a hub to integrate various educational services. With Learning Tools Interoperability (LTI) (IMS Global 2020) as a standard interface, educational systems are integrated by connecting various educational services to the LMS. With such architecture, educational organizations can easily construct systems along their requirements. At the same time, by supporting many universities as users, education service providers can be platformers that integrate use, and they can provide services in better quality with cheaper costs.

7 Conclusion In this paper, the author shows six types of system structures in cooperation with social systems as a viewpoint of System of Systems (SOS). Additionally to the platform discussed in Kita (2021), issues are pointed out with a background of recent trends and systems for the future in autonomous decentralized systems and system integration. The author will try to think of novel systems approaches to attack various problems of the societies.

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References Atsumenai Big Data Consortium (2015, in Japanese) Atsumenai big data consortium Seika-Houkokusho Brown M (2017) The NGDLE: we are the architects. Educ Rev 52(4) de Weck OL, Roos D, Magee CL (2011) Engineering systems meeting human needs in a complex technological world. MIT Press, Cambridge Hiroi Y (2019, in Japanese) Jinko Genshou Shakai no Design. Toyokeizai, Tokyo IMS Global (2020) Learning tools interoperability. http://www.imsglobal.org/activity/learning-­ tools-­interoperability. Accessed 27 Aug., 2020 Information Technology Promotion Agency (2017, in Japanese) IT Jinzai-Hakusho 2017 Kada Y (2016, in Japanese) Shiga-ken ni okeru Bunri-Renkei no Chiiki-Kenkyu to sono Ouyouteki-­Seisaku ni tuite, invited talk, SICE, systems and information division. Annual Conference SSI 2016, Munich Kats ML, Shapiro C (1985) Network externalities, competition, and compatibility. Am Econ Rev 75(3):424–440 Kawakami H. (2021) Growing systems in smarter world. In: Kaihara T, Kita H, Takahashi S. (eds.), Innovative systems approach for designing smarter world. Springer, Singapore Kita H (2017a, in Japanese) Cho-smart-Shakai heno systems approach ni Tuite no Kosatsu. SICE SSI2017 Kita H (2017b in Japanese) Systems close to us and systems far from us, discussions on studies of design. vol. 9, pp. 19–21 Kita H (2019, in Japanese) Education of informatics in Japan. Syst Control Inform 62(7): 242–247 Kita H (2021) System and information. A viewpoint toward a novel systems approach. In: Kaihara T, Kita H, Takahashi S. (eds) Innovative systems approach for designing smarter world. Springer, Singapore Laloux F, Wilber K (2014) Reinventing organization: a guide to creating organizations inspired by the next stage of human consciousness. Lightning Source Inc., La Vergne Lee HL et al (1997) The bullwhip effect in supply chains. Sloan Manag Rev 38(3):93–102 Motani K (2020, in Japanese) Shinka suru Satoyama Shihonshugi. The Japan Times Publishing, Tokyo Negoro T, Ajiro S (2012) An outlook of platform theory research in business studies. Waseda Bus Econ Stud 48:1–29 Negoro T, Kato K (2010) A strategic model of non-technological advantage between platforms– mechanism of winner-take-all and countermeasures in software products. Waseda Bull Int Manag 41:79–94. (in Japanese) Rifkin J (2014) The zero marginal cost society: the internet of things, the collaborative commons, and the eclipse of capitalism. Palgrave Macmillan, London Shimohara K (2021) Interpenetration of system borders mediated by human activities: weaving trees with rhizome. In: Kaihara T, Kita H, Takahashi S. (eds.), Innovative systems approach for designing smarter world. Springer, Singapore Uzuka T (2020, in Japanese) System of systems in railway. J Soc Instrum Control Eng 59(12):953–956 UNDP (2022) United Nations development programme: sustainable development goals. https:// www.undp.org/sustainable-­development-­goals. Accessed 12 Feb 2022 Hajime Kita  received his B.E., M.E., and D. E. degrees all from Kyoto University. Currently he is Professor of Institute for Liberal Arts and Sciences of Kyoto University. He also serves as Director General of Institute of Information Management and Communication of Kyoto University. His research interests are social simulation and general education of informatics in universities.

4

Boundary and Relationality Perspective Systems Approach: Towards Its Development Yasuaki Kuroe

1 Introduction In recent years with the remarkable development of computer science and information technology, it has become possible to easily acquire, store, process, and use a wide variety of large amounts of data, and we are now entering the so-called Internet of Things (IoT) era in which everything is directly connected and exchanged via networks. Meanwhile, systems in the real world have become larger and more complex, and the purposes of the systems have become more demanding and increasingly diverse. It is, therefore, urgent to build a new systems approach that can deal with various problems in the systems in a flexible manner (Kuroe 2016). To summarize boldly the underlying concepts of systems engineering/science and systems approach, systems are to be considered as systems and their problems are to be solved. In other words, what kinds of perspective or viewpoint should be utilized to grasp and understand the systems and solve their problems. For this purpose, it was pointed out that it is important to take boundaries and relationalities as perspectives in order to build a systems approach that can deal with the situations and issues surrounding recent real systems. Under the perspectives, the research committee named “Boundary and Relationality Perspective Systems Approach” was established in the

Adapted from Y. Kuroe “ Boundary and Relationality Perspective Systems Approach –Towards Its Development – (written in Japanese),” Journal of The Society of Instrument and Control Engineers, Vol. 59, No. 12, pp. 906-909 (2020). Partly translated by permission of The Society of Instrument and Control Engineers. Y. Kuroe (*) Doshisha University, Kyoto, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 T. Kaihara et al. (eds.), Innovative Systems Approach for Facilitating Smarter World, Design Science and Innovation, https://doi.org/10.1007/978-981-19-7776-3_4

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Systems and Information Division of SICE in 2019 and started its activities. In this chapter, the author considers what it means to think of a system from the viewpoint of boundaries and relationalities, and what it brings about, and also looks forward to a path towards the construction of a systems approach that takes these perspectives.

2 Challenges Related to Boundary and Relationality for Systems Approaches The systems approach has been discussed from various points of view and is usually summarized as the following steps. This chapter begins the discussion based on these steps. STEP 1: In the real world, determine the ranges and boundaries of things (systems) that you want to realize or those of problems that you want to solve and extract them. This extracted system or the extracted problem to be solved are called the target system. STEP 2: Build a model (often a mathematical model) for the target system (modeling). The constructed model is equated with the target system. STEP 3: By using various methods that have been developed so far, or by developing new methods, develop measures to realize the system or to solve the problem for the constructed mode. STEP 4: In the real world, implement the system or solve the problem you want to solve by using the developed measures. If you are satisfied with the result, finish it. If you are not satisfied with the result, return to Step 1 and repeat the procedure. Or if a new problem arises or is excavated, return to Step 1 and repeat the procedure. In the above approach, there are several possible issues related to boundaries and relationalities. In Step 1, a problem arises how to determine the ranges and boundaries of the target system or problem, which requires systems thinking and in-depth knowledge of the target field in the real world. Recently, in particular, the problem that the boundary cannot be determined or the boundary changes has become one of important issues, and it is necessary to develop a new system approach which enables to deal with it. In addition, when extracting the system to be realized and the problem to be solved and deciding the boundaries, it is necessary to fully consider the relationality between the target system and the world outside it. In addition, not only in Step 1, but also in modeling of Step 2 and in analysis and design of the system based on the modeling of Step 3, there are the following issues related to boundaries and relationalities. The systems we should deal with are becoming larger and more complex, and not only engineering systems, but also extending to life, energy, environment, economy, and society, and it is necessary to handle them not individually, but multiple of them at the same time. In dealing with them, one of the issues is that elements and

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subsystems with greatly different temporal and spatial scales coexist, that is, the micro and macro coexisting problem. Therefore, it becomes a problem how to handle those boundaries and relationalities. There are also relationalities concerning the structure of each element or subsystem. For example, if it is regarded as a hierarchical structure, there are relationalities among the boundaries of each layer and their relationalities, as well as relationalities where the hierarchical structure cannot be defined, or where there are penetrations among the layers and these become essential. In all those cases how to handle such boundaries and relationalities also becomes a challenge. In Step 4, the measures constructed for the model which is abstract world are mapped and implemented for the target system or problem in the real world, which also requires knowledge of systems thinking and in-depth knowledge of the target field. In addition, the consistency of these results with the ranges and boundaries of the target system or problem determined in Step 1 may become an issue. Furthermore, it may also become a problem whether the relationalities between the implemented system and its outside is consistent with those assumed in Step 1, 2, and 3. And the relationalities between thus implemented system and its outside determine values of the implementation, and moreover values emerge in the real world. Therefore, development of a systems approach that can take such values creation into account is strongly desired. The problems mentioned above can be found everywhere in engineering systems, social systems, life systems, environmental systems, and so on. Consider, for example, the case where a systems approach is used to deal with the problem of diseases such as heart disease in a human living system. The biological system has multiple layers from the cellular level to the organ level and the individual level of humans and is a system in which the musculoskeletal system, cerebral nervous system, blood circulation system, immune system, etc. are intricately intertwined. Therefore, the question is how to grasp the boundaries and relationalities among these elements and subsystems, and it is very difficult to build a model and the solve the problems such as heart disease by deciding the boundaries and relationalities. In physical systems, the following example is also found. The International Fusion Experimental Reactor (IFR) is being constructed to realize magnetic fusion plasmas, and there is an urgent need to develop modeling and simulation methods for plasma phenomena in order to predict performance, establish control methods, and optimize operation scenarios. However, plasma phenomena include a wide variety of physical phenomena with very wide discrepancies in time and spatial scales, and the boundaries and relationalities among these physical phenomena are complex, making their handling extremely difficult. Moreover, the boundaries of the plasma cannot be directly measured, and the boundaries also change, which makes the determination of these boundaries an important problem (Beghi and Cenedese 2005). Another example is as follows. The IoT, in which everything including things, data, humans, and so on are directly connected via the Internet, is expanding explosively. The IoT is also a system, and when dealing with this, the problems of boundaries and relationalities mentioned above also appear.

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Furthermore, in considering the systems approach, how to treat humans becomes a problem at each stage of the steps described above. There are three positions or situations for humans in the relationalities with the system, the first is the human as a component of the system, the second is the human as the object that views and handles the target system, and the third is that these roles are changed and also is the human who takes both positions. Another important concept in dealing with humans is the handling of values. In the conventional systems approach, it is usual to set objectives for the target system and design the system to achieve those objectives, and it is usual to incorporate values into the objectives. However, the objectives change as the boundaries of the system, the relationalities among internal elements and subsystems, and the relationalities with the outside change, and in many cases, values cannot be set in advance. Therefore, it is necessary to consider incorporating mechanisms that enable to create new values.

3 Various Kinds of Boundaries and Relationalities In the previous section, we have mainly focused on issues related to the boundaries of the ranges of the target system or problem, the boundaries and relationalities among elements and subsystems within the system, and those with the outside of the system. In recent years, Cyber Physical System (CPS) (Lee 2006) and System of Systems (SoS) (Jamshidi 2009) have attracted a great deal of attention as a way to understand systems, and it is very important to consider the boundaries and relationalities mentioned above when taking such perspectives. However, the boundaries and relationalities that should be considered when thinking about systems are not only those described in the previous section, but also the following should be considered. One of the fundamental properties of a system is emergent property. This means that the system as a whole has new characteristics that are not possessed by individual elements, due to the relationalities (interaction) of its elements. This emergent property is very important when considering systems, and it is sometimes said that systems science is the study that investigates systems and clarifies the mechanism of emergent property, while systems engineering is the study of developing methodology that constructs systems with desirable emergent properties. This concept was further developed and the concept of “emergent systems” was proposed in the 1990s, in which the development of design methodologies that enables to create emergent phenomena in a system is aimed. In other words, the system and the interaction between the lower and upper levels of the system is designed so as to create desired emergent properties of the system. This effort has not yet been resolved, and discussions are underway from various perspectives. In the efforts, the key is how to determine the boundaries and relationalities between the lower level and the upper level of the system, or those between micro and macro, and to model the boundaries and relationalities, which implies the importance of boundary and relationality perspective systems approach. In addition, each of the elements and subsystems that make up a system has its own unique function, and there are the boundaries and

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relationalities among those functions. Therefore, it is also important to consider system design methodologies from these perspectives, and in particular, it may be indispensable in constructing a design methodology that brings about emergence with desirable characteristics. The following also becomes important when dealing with systems. Step 2 in the previous section is modeling, and models of systems can take several forms of representation. The most typical form of models is a mathematical model, but there are several other forms of models. For example, there are models represented in terms of rules, models expressed in terms of algorithms, system simulators are regarded as models, and data are also regarded as models. It is necessary to consider the boundaries and relationalities among these different forms of models and to develop methodologies of system analysis and synthesis that integrate these different forms of models. In Step 3 of the previous section, we need to make full use of various systems methodologies that have been developed so far: systems theory and engineering, control theory and engineering, OR, optimization theory, simulation methods, and various methodologies in machine learning and computational intelligence (Kuroe 2015). In addition, we also need to develop new methodologies if necessary. There are boundaries and relationalities among these methodologies, and it is necessary to apply each methodology from the boundary and relationality perspectives, and these perspectives are also important when building new methodologies. The systems approach described in the previous section basically repeats modeling, analysis, and synthesis for the system under study until satisfactory results are obtained. Boundaries and relationalities exist among modeling, analysis, and synthesis, and by taking these boundaries and relationalities as perspectives, it is possible to further develop them or to create new methodologies. It is also possible to remove the boundaries among them and to integrate modeling, analysis, and synthesis into a methodology that carries them out simultaneously.

4 Possible Systems Approaches Up to the previous section, we have looked at various boundaries and relationalities related to systems. By looking at systems from these perspectives, we can find clues that will enable us to solve problems in systems that were not visible or could not be handled until now, and to construct a new systems approach. In this section, we look towards this direction from some perspectives.

4.1 Relationality Oriented Systems Approach As mentioned earlier, in the conventional systems approach, the boundaries of the system to be realized or the problem to be solved are usually determined first, and then the target system or problem is modeled. However, there are many cases where the boundaries cannot be determined in advance or they even change. In order to

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deal with such problems, the following approaches can be considered, especially orienting to relationalities. This approach first focuses on the elements or subsystems of interest, and by considering their relationalities, linkages or interactions, and even interpenetration among them, conversely, the characteristics and roles of the constituent elements and subsystems in the overall system are then determined, and as a result the boundaries of the overall system are also determined. Consider, for example, the interconnection of urban transportation systems. In this case, for example, by investigating the regional, economic, and cultural relationalities among cities, as well as the relationalities between different transportation systems and the dynamics of human mobility, and by designing them in some appropriate way. As a result, for example, which city plays the role of a hub is determined, and the boundaries of the entire system is determined, which we call relationality-oriented systems approach. There may be many other fields that require this perspective. Another example is that deals with the problem of diseases of the biological system. In this case, it is considered that, by investigating the relationalities among the diseased part and other tissues and controlling those relationalities, the boundaries in the living body are determined in dealing with the disease as a result. One successful example of such perspectives is the Internet system that is now spread throughout the world. This Internet itself may not necessarily be designed by the systems approach discussed here; however, it is a good example that should be referred for building a relationality-oriented systems approach. In any case, in order to elevate such an approach to concrete system design theory, it is indispensable to introduce a framework of evolution and learning, as will be discussed later. In order to further advance such a relationality-oriented systems approach, or to abstract and model this approach, category theory (Awodey 2015) is considered to be a powerful tool. Category theory is said to be a theoretical system that gives a bird’s-eye view of mathematics (i.e., modeling activities in mathematics), and its applications are expanding not only to mathematics but also to physics, computer science, and cognitive science. Applications of category theory to system science and engineering has also begun (Minamizono et al. 2003). A category is a system that consists of objects and arrows called morphisms that represent the relationality among the objects and is represented as a network that connects the objects. In addition to object and morphism, category theory also includes a functor, which expresses the relationality between categories, and also a natural transformation, which expresses the relationality between functors. Although it is beyond the scope of this chapter to describe category theory in detail, in conventional mathematics based on set theory, the properties of objects are determined by the properties of the elements inside the set and their relationships, whereas in category theory, the properties of objects are determined by the network of objects and arrays, that is, the relationalities with the outside. Therefore, category theory can be a powerful tool for modeling the framework of the relationality-­oriented systems approach, in which relationalities determine the properties of a system and also determine the boundaries of the system.

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4.2 Systems Approach Integrating Heterogeneous Models and Co-evolving with Real Systems As mentioned in the previous section, the first step in the systems approach is modeling the target. Various forms of models can be considered, including mathematical models, rules, algorithms, simulators, data, and so on. Considering the boundaries and relationalities of all these models, an approach that integrates them to analyze and design the system can be considered. A promising approach to achieve this is to use the framework of reinforcement learning (Sutton and Barto 1998) in computational intelligence (Kuroe 2015, 2016). Reinforcement learning is a learning method in which an agent with a task acquires optimal policy by trial and error, using the rewards obtained through its interactions with the environment as a clue, the general framework of which is shown in Fig. 4.1. This learning method is a framework in which an agent learns to maximize the profit that it will receive from the present to the future and has attracted much attention because it can solve problems in unknown and complex environments with simple procedures. In reinforcement learning, the main task of the system designer is to design the rewards, which allows the agent to learn autonomously. We call a model that integrates different forms of models such as mathematical models, algorithmic models, simulators and data an integrated model, and the framework of reinforcement learning is used as follows. We consider an agent as an entity that analyzes and designs a system or solves a problem in the system and call it an analysis and design agent. Consider the framework shown in Fig. 4.2, in which the environment in reinforcement learning is replaced by the integrated model of the target system. In this framework, the analysis and design agent acquire analysis and design methods by learning through interactions with the integrated model. That is, the agent applies the analysis and design method currently obtained to the integrated model as an action, and it receives the result, that is, reward or evaluation, and uses

Fig. 4.1 General framework for reinforcement learning

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Fig. 4.2  Systems approach based on reinforcement learning in Computational Intelligence

it as a clue to improve the current analysis and design method. By repeating the above, the agent learns to acquire the optimum analysis and design method. The approach shown in Fig.  4.2 does not explicitly depict interactions with the real world and real systems, but a learning model that takes these into account can be considered, as shown in Fig. 4.3. In this figure, in addition to the analysis and design agent, agents responsible for modeling, wisdom of clinic, and wisdom of practice are also depicted. There are other possible agents as well, that is, agents are not limited to these, but other agents can be considered. This learning model is a model that enables modeling, analysis, and design methods to co-evolve with real systems. Furthermore, the wisdom of clinic here includes the concept of wisdom of clinic as defined and proposed by the philosopher Yujiro Nakamura (Nakamura 1992). This is a framework that aims to develop a systems approach that can introduce the wisdom of clinic and wisdom of practice (Sawaragi 2015). In other words, it is a learning model that attempts to co-evolve the wisdom of clinic and wisdom of practice with real systems. This learning model also executes modeling, analysis, and synthesis at the same time and enables to consider or remove the boundaries and relationalities among them. Another important approach related to boundaries and relationalities is to analyze and design systems by fusing and integrating different fields of studies in consideration of their boundaries and relationalities. There are various possible fields of studies to be fused and integrated. In recent years, data science has been attracting a great deal of attention since it has become possible to acquire, store, process, and use a large number of various types of data. The methods and possibility of fusing data science and systems science are discussed in (Kuroe 2020).

5 Conclusion In this chapter, the author discussed what it means to think about systems from the perspectives of boundaries and relationalities, and what is newly brought about by them. The chapter also looked at the path towards the construction of a new systems

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Fig. 4.3  Computational Intelligence-based systems approach interacting with real systems

approach from these perspectives. There are several terms for systems-related concepts, such as systems science, systems engineering, systems approach, systems thinking, and so on. It is also important to consider the boundaries and relationalities among them in order to further develop this field. Furthermore, it is necessary to remove the boundaries among these and integrate and fuse them into “systemics” to further consider systems-related problems, and such efforts are underway.

References Awodey S (2015) Category theory. Oxford University Press Beghi A, Cenedese A (2005) Advances in real-time plasma boundary reconstruction. IEEE Control Systems Magazines 25(5):44–64 Jamshidi M (ed) (2009) System of systems engineering: innovation for the 21st century. John Wiley & Sons Kuroe Y (2015) Computational intelligence–present status and prospect. J Soc Instrum Control Eng 54(8):553–560

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Kuroe Y (2016) Viewing systems from boundary and evolution–towards developing new systems approaches. J Soc Instrum Control Eng 55(8):657–664 Kuroe Y (2020) Data science and systems science–considering both perspectives. J Soc Instrum Control Eng 59(9):659–664 Lee, EA (2006) Cyber-physical systems–are computing foundations adequate? In NSF workshop on cyber-physical systems: research motivation, techniques and roadmap, vol. 2, pp. 1–9 K. Minamizono, O. Katai, T. Shiose and H. Kawakami (2003) Analyses of design processes based on category theory and channel theory. In SICE Annual Conference in Fukui 2003, vol. 1, pp. 3239–3244 Yujiro Nakamura (1992) What is wisdom of clinic? Iwanamisyoten Sawaragi T (2015) An aspect of design study as wisdom of practice. J Soc Instrum Control Eng 54(7):455–461 Sutton RS, Barto AG (1998) Reinforcement learning. MIT Press, Cambridge, MA Yasuaki Kuroe  received the Ph.D. degree from Kobe University, Kobe, Japan, in 1982, he joined the Department of Electrical Engineering, Kobe University, as an Assistant Professor. In 1991, he moved to Kyoto Institute of Technology, Kyoto, Japan, and became a professor. Since 2016, he has been a Professor Emeritus with Kyoto Institute of Technology, a Research Fellow with Doshisha University, Kyoto, Japan, and a Visiting Professor with Kansai University, Osaka, Japan. His current research interests include computational intelligence, control and system theory and its applications, and computer-aided analysis and design.

5

Relationality Design Emphasizing Clinical Aspects of System of Systems in Local Community Katsunori Shimohara

1 Introduction In designing, operating, and managing a System of Systems (SoS), human factors cannot be disregarded. Postulating that the hints for achieving an SoS are naturally embedded and concealed in people’s daily lives, we should set human activities and lives as the origin for system design. Starting from the reality of people’s activities and daily lives in a local community, we investigate a possibility to create a mechanism through which people are naturally self-motivated to be involved in the process of generating, operating, and managing an SoS. Specifically, we envision promoting behavioral changes in the real world through a mechanism in the cyberspace, correlated with people’s behaviors in the real world, and utilizing data accumulated by circulating such movement for prevailing and spreading an SoS that should naturally be embedded in their lives, in a local community (Shimohara 2020a, b). A community is not only a system, where “Hito,” “Mono,” and “Koto” are the main elements, and their relationality determines its functionality, but also a system in which people have to be involved on an unprompted basis. “Hito,” “Mono,” and “Koto” in Japanese mean a person or resident, a tangible and physically perceived thing or entity, and an intangible and cognitively conceived thing or entity, respectively. The term relationality is used here to include direct or indirect interactions, relations or connections over time and space, and relationships. People in a

Adapted from Shimohara (2020a). Partly reprinted by permission from the Society of Instrument and Control Engineers. K. Shimohara (*) Department of Information Systems Design, Doshisha University, Kyoto, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 T. Kaihara et al. (eds.), Innovative Systems Approach for Facilitating Smarter World, Design Science and Innovation, https://doi.org/10.1007/978-981-19-7776-3_5

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community not only have diverse ways of thinking and sense of value but are also different in age, occupation, family composition, and human relations. To promote people’s self-motivated involvement in community activities, designing and forging relationality among “Hito,” “Mono,” and “Koto” are indispensable for the community to function as a system. At present, we are handling a system design of community toward an SoS in a local community, for which, we have devised relationality assets as a concept for quantifying and visualizing relationality that results from people’s daily lives with interactions between “Hito,” “Mono,” and “Koto” in a local community (Shimohara 2020b). Subsequently, we implemented mechanisms to activate the generation, circulation, and benefit-sharing of relationality assets. However, when quantifying relationality assets, we employed the so-called equality-based method in which the quantified value should be the same and equal for everyone. In other words, we were inclined to “Science Wisdom,” and thus, neglected the “Clinical wisdom” of diversity and difference, inherent in a community despite understanding such properties. Here, we propose to employ the equity-based method to displace the equality-­ based method. Focusing on the premise of “Clinical Wisdom (Nakamura 1992),” which emphasizes identity or locality, multiplicity, and experience or embodiment as opposed to the “Science Wisdom” which is based on universality, logicality, and objectivity, it is inevitable to take a clinical approach to create an SoS in a local community.

2 Relationality-Driven System Design of Community for SoS in Local Community Before moving on to relationality design with a clinical approach, we summarize the relationality-driven system design of community for an SoS in a local community that we have conducted along with the field experiment, for a decade.

2.1 Research Perspective We pursue two scientific questions in this research. One is on people’s behavioral principles, that is, whether or not the proposed mechanism through which people’s selfish behavior gives rise to awareness in their relationships with others, and eventually derives an altruistic effect (Shimohara 2020b) could result in well-being in a community. The other is on various and diverse boundaries that exist in our society explicitly or implicitly, and intentionally or unintentionally, for example, gender, generation, economic status, religion, nationality, race, thought, ideology, sense of value, whether infected, whether vaccinated, and so forth, that is, whether it is feasible to devise a cyber-physical-system mechanism to enable people to cross such boundaries and to promote their behavioral changes doing that (Shimohara 2016, 2019, 2020c).

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The viewpoints we have introduced here are as follows: (1) The relationality created by people in their daily lives should be the assets that have social and economic values, anticipated to benefit the community in the future, although it vanishes if not stored or accumulated, let alone that people are unconscious about it. (2) No intersystem coordination and cooperation with individual systems so that they function as a system in a community. Here individual systems in a community include habitable systems such as homes, towns, education, medicine, caregiving, and disaster prevention; public infrastructure such as garbage collection, water, sewerage, energy utility, telecommunications, traffic; and business sectors such as selling, manufacturing, logistics, sightseeing, and other services. Based on the above perspective, we have worked on quantifying and visualizing the relationality that people naturally generate while living in a community. In addition, we have proposed the gift & circulation model (G&CM) as a cyber-physical system mechanism for the generation, circulation, and benefit-sharing of relationality assets (RAs), pursuing the following research objectives: we aim to make people aware of the significance and meaning of relationality in a community to lead their behavioral changes through the G&CM, and eventually create effective cooperation between individual systems that provide various services with a community, as shown in Fig. 5.1. Specifically, spatial and physical resources, such as places and facilities, and invisible social customs and events, such as town meetings and community gatherings, are included in “Mono” and “Koto,” respectively.

Fig. 5.1  Relationality-driven system design

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2.2 Gift & Circulation Model (G&CM) as Mechanism for Generation, Circulation, and Communization of Relationality Assets (RAs) We have proposed the G&CM as a cyber-physical system mechanism for the generation, circulation, and benefit-sharing of relationality assets that people naturally produce through living in the real world (Tanaka et al. 2019; Yonezaki et al. 2019). The aims are to make them elicit awareness in their relationships with others, to lead their behavioral changes and natural movement for communication and community activities in the real world, and to eventually generate an altruistic effect in a community. People, in general, are likely to take the so-called Give & Take principle of behavior that brings in equal and immediate exchange efficiently. The basic idea of the G&CM is to make an effect different from the Give & Take. When we give a gift to someone, we are likely to put diverse feelings and values such as love, gratitude, respect, or trust toward the person, thinking of how and what they feel. Also, in a sense, not asking for direct and immediate returns by exchange, the G&CM incorporates a role to drive circulations of relationality by introducing the similar mechanism to local exchange trading systems as explained below. Figure 5.2 shows a mechanism and basic features of the G&CM: • Earnings: Relationality Assets (RAs) that a resident acquires while living in a community. • Personal Account A and B for storing RAs that resident A and B earn, respectively. • Leakage to decrease RAs in personal accounts for prompting residents to gift some RAs rather than losing them. • Gift: transferring of RAs from one person to another.

Fig. 5.2  Gift & circulation model

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• Public account to virtually pool and accumulate the same amount of RAs gifted. • Redistribution to distribute some of the accumulated RAs to everyone in a given period. From a psychological perspective, it is normal for people to try and increase their RAs as a selfish act. Contrarily, the leakage mechanism would urge everyone to gift some RAs, and hence pay attention to others around them to whom they can gift. In addition, people can check the amount in their personal account as the record of giving RAs to someone, RAs gifted from someone, and the record of decreased RAs as daily leakage and redistribution from the public account. Monitoring the public account also allows people to know the global situation in their community, for example, how actively they interact through gifting and being gifted (Tanaka et al. 2020).

2.3 Applications Provided in Field Experiment To verify whether the proposed mechanisms, including the G&CM, work in reality in a community and to what extent, we have conducted field experiments for almost 10 years in Makishima area, Uji, Kyoto, Japan. For this purpose, we have implemented smartphone applications that provided participants with the following services: (1) “Kizuna” service: “Kizuna” means emotional ties or human bond; (2) Area Map services; and (3) “Jingori” game service: “Jingori” means PokeMon like turf war (Tanaka et al. 2019; Shioya et al. 2019). Figure 5.3 shows snapshots of these applications.

Fig. 5.3  Snapshots of the smartphone applications

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“Kizuna” service is designed for people to involve and function the G&CM of RAs, and to evaluate how well it works to enrich and activate communications and interactions in a community, and subsequently, promote people’s self-motivated involvement in community activities. Table 5.1 shows “Kizuna” point system that allocates RA points to peoples’ daily actions. Area map services are designed to share common interests in a community, for example, walking course recommendations and sharing the awareness of problems, as shown in Figs. 5.4 and 5.5, respectively. The “Jingori” game service is designed Table 5.1  “Kizuna” Point System Actions Post a photo to the Regional map Add "Like" to Regional map posts Participation in “Jintori” game Steps (counts by using Omron's activity monitor) Add a comment when gifting Passing with residents Visit to community center

Point 30P 5P 30P 1P in 10 steps 20P 50P 50P

Fig. 5.4  Walking course recommendation: blue pins represent places that are posted by residents so that they can share nice seasonal spots and events in a community

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Fig. 5.5  Sharing awareness of problems: orange pins represent places that are posted by residents so that they can share problems concerning the peace and safety in a community

to promote people to walk and interact with each other through playing a sort of game where two teams compete in taking special spots on the map by walking those spots faster than the other.

3 Relationality Design with Emphasis on Clinical Aspects This chapter describes the current situation as we recognize it, and the reasons for why we need to emphasize the clinical aspects. Few attempts have been made to rebuild a local community so far using the technological approach to introduce ICT (Information and Communications Technology). Attempts that employed only externally driven incentives, however, have revealed that they had limited effects and worked well only in the short term. It is well understood that using only a technological approach, we cannot cope with the risks inherent in human relationships, such as mutual misunderstandings, avoidance, conflict, alienation, and ignorance, in a community.

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To rebuild and activate a local community confronting the problem of super-­ aging, it is imperative for people to embrace internally driven incentives. Moreover, it is crucial to inspire their consciousness and psychology to encourage self-­ motivated behavioral changes that lead to mutual understanding and tolerance between them. It is almost impossible to solve any problem of the human society only through technology; we need to take a human-centric approach for the technology to embed some mechanism that reflects people’s consciousness and psychology. Hence, taking a “Clinical Wisdom” approach, focusing on individuals’ clinical aspects such as identity as an individual, their locality, and difference in situations, we aim to create a mechanism to secure equity and reciprocity as a social community. A scientific question is how to achieve a balance, clinically and dynamically, between individual and social benefit through this mechanism.

3.1 Relationality Assets Adapted for an Individual’s Clinical Aspects As expected, there exist differences and disparities among people living in a community: (1) personal attributes such as age, gender, family composition including living alone, and health and physical conditions; (2) social and private attributes such as relationship with friends and other associations; and (3) social and public attributes such as occupation, official position, or role in private/public organization. From a clinical perspective, the meaning or value of the same behavior should be different, depending on the differences and disparities between people. For example, the meaning of taking a 5000-step walk for the elderly is different from what it may mean to the young. The value of conversation across-generations or between people who have a different way of thinking should be more significant than between similar groups (Aso et al. 2021). Esteeming diversity in a community, we therefore, employs not equality-based but equity-based point allocation corresponding to personalized and situated RAs for an individual. A key issue is to devise methodologies for incentive design and to verify the usefulness, through conducting field experiments. As a trigger to ignite people’s psychology, we consider “Nudge” as a method of the libertarian paternalism, advocated in behavioral economics, and utilize “fun” to motivate them to take part in activities in a community. For instance, when focusing on health, we apply a method of gamification to embed some game elements (but non-related games) in activities and events useful for health (Shiozu et al. 2018, 2019).

3.2 Introduction of Proactive Functions for Leadership Commission in Community To promote peoples’ self-motivated involvement in community activities more than ever, we also consider introducing proactive functions into a current system that

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passively gathers, analyzes, and visualizes data concerning relationality that people generate through interactions between “Hito,” “Mono,” and “Koto.” Differences and disparities in people naturally generate differences and disparities in community activities. A point to be emphasized is that we can acquire that data through the G&CM as a mechanism for generation, circulation, and communization of RAs, and analyze and utilize them. For example, the following data are available: (1) the number of people who give gifts, its frequency and the amount; (2) the number of people who are given gifts, its frequency and the amount; (3) the point ranking in steps based on an activity monitor; (4) the ranking in the number and frequency of photo posting; (5) the ranking in the number and frequency of participation in “Jintori (PokeMon like turf war)” game; (6) various properties in a network such as betweenness centrality, in-degree centrality, page rank, and so on. Based on successive analysis of the data, the system makes the person who leads in such rankings aware of being in a leader-like position and then promotes the person to play a sort of leadership. We postulate relational leadership to view leadership as the communication processes by which relational realities are made, and social order is constructed and changed (Uhl-Bien 2006). To achieve proactive functions for leadership commission, we introduce a computer agent to intermediate communication between a leadership candidate and possible collaborators (Ohara et al. 2021).

3.3 Diverse Development of Gift & Circulation Model to Incorporate Clinical Aspects Corresponding to personalized and situated RAs for the emphasis on clinical aspects of individuals, it is vital to maintain the equity and reciprocity in the G&CM as a mechanism for generation, circulation, and communization of RAs from a macroscopic viewpoint. That is, it is essential to adjust and balance personal and public benefits. One way to adjust G&CM to incorporate clinical aspects is to achieve equity by introducing progressive leakage, postulated as a sort of tax to earnings as income as well as assure reciprocity by introducing adaptable redistribution from the public account (Shimohara 2020a). To make the mechanism function, it is necessary to incorporate spatio-temporal factors such as the size and demographic composition of a community, their temporal changes as well as situation-specific changes to a given region, season, climate, and weather into the mechanism. In addition, we should investigate how to utilize the mechanism for spurring or constraining a behavior appropriate to their age and situations such as stay-at-home and congestion avoidance in a pandemic. The following diverse models can be developed and investigated for how they work through simulations: (1) gift & circulation model with progressive leakage (Fig. 5.6); (2) gift & circulation model with exemption for gift (Fig. 5.7); (3) gift & reinforced circulation model (Fig. 5.8); and (4) enhanced gift & circulation model (Fig. 5.9).

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Fig. 5.6  G&CM with progressive leakage: The more the earnings, the more the leakage, like a tax

Fig. 5.7  G&CM with exemption for gift: Leakage for gifted is exempted

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Fig. 5.8  G& Reinforced CM: Leakage is pooled in the public account to be redistributed

Fig. 5.9  Enhanced G&CM: Virtually pooled amount of RAs is multiplied by X times depending on the situation or the number of participants in this world

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Conducting field experiments and various simulations on these models, we elucidate their functionality as the mechanisms of generation, circulation, and communization of RAs, and its influence on people’s behavioral changes.

4 Conclusion To create an SoS through community system design in a community, it is crucial to embrace internally driven incentives by people so that the community, as well as the SoS, can function as a system. While it is almost impossible to achieve it only through technology, what it takes to make it possible is a technology that embeds mechanisms to naturally reflect people’s consciousness and psychology to encourage their self-motivated behavioral changes. Grounded in the premise of “Clinical Wisdom,” we take a clinical approach to focus on individuals’ clinical aspects such as identity as an individual, their locality, and situational differences, aiming to create a mechanism to secure equity and reciprocity as a social community. We have introduced the following research issues that we tackle in this article at present: relationality assets adapted for an individual’s clinical aspects, proactive functions for leadership commission in the community, and diverse development of the gift & circulation model to incorporate the clinical aspects. We continue to work on achieving a balance, both clinically and dynamically, between individual and social benefits through the investing mechanisms that we have proposed here. Acknowledgment  The author wishes to thank Mizuki Tanaka, Ryo Shioya (ex-post-graduation students), Satoko Yoshida, Yuto Ohara, and Hiromu Aso (post-graduation students) for their contribution, and Prof. Yurika Shiozu, Kyoto Sangyo University, Prof. Kazuhiko Yonezawa, Taisho University, and Prof. Ivan Tanev, Doshisha University for their help as research collaborators.

References Aso H, Ohara Y, Yoshida S, Shiozu Y, Yonezaki K, Tanev I, Shimohara K (2021) Individuality-­ oriented community system design. Proc SICE Annual Conf 2021:509–513 Yujiro Nakamura, What is clinical wisdom Iwanami-shoten, 1992 Ohara Y, Aso H, Yoshida S, Shiozu Y, Yonezaki K, Tanev I, Shimohara K (2021) Community system Design to elicit functionality as leader. Proc SICE Annual Conf 2021:514–517 Shimohara K (2016) Interpenetrative model of system borders based on human activity–weaving trees with rhizome. J Soc Instrum Control Eng 55(4):680–685 Shimohara K (2019) Boundary and relationality in systems design: toward designing system of systems. In: 2019 IEEE Asia-Pacific Conf on Computer Science and Data Engineering. https:// doi.org/10.1109/CSDE48274.2019.916242 Shimohara K (2020a) Relationality-driven system design for System of Systems in local community. J SICE 59(12):910–913 Shimohara K (2020b) System design of community toward Wellbeing. HCII, LNCS 121185:254–263

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Shimohara K (2020c) Interpenetration of system borders mediated by human activities: weaving trees with rhizome. In: Kaihara T et al (eds) Innovative systems approach for designing smarter world, pp 95–108 Shioya R, Tanaka M, Yonezaki K, Shiozu Y, Tanev I, Shimohara K (2019) Self-motivated information sharing in communities for promoting regional revitalization. In: 2019 IEEE Asia-Pacific Conf. on computer science and data engineering. https://doi.org/10.1109/CSDE48274.2019.9162394 Y. Shiozu, K. Kimura, K. Shimohara, K. Yonezaki, Case study about the visualization of GPS data as the nudge and place attachment. In: Proceedings SICE Annual Conf. 2018, pp. 666–669 (2018). Y. Shiozu, K. Kimura, R. Shioya, K. Shimohara, K. Yonezaki, Relationship between difference of motivation and behavior change caused by visualization, HCII 2019. In: Proceedings of HIMI, Part I, LNCS11569, pp. 489–499 (2019). Tanaka M, Shioya R, Yonezaki K, Shiozu Y, Tanev I, Shimohara K (2019) Multi-agent simulation of relationality assets to enable community vitalization. 2019 IEEE Asia-Pacific Conf. on Computer Science and Data Engineering. https://doi.org/10.1109/CSDE48274.2019.9162353 Mizuki Tanaka, Ryo Shioya, Katsuhiko Yonezaki, Yurika Shiozu, Ivan Tanev and Katsunori Shimohara, Simulations for Gift & Circulation Model of relationality assets toward rebuilding community. Prod SICE Annual Conf 2020, pp. 1946–1951 (2020). Uhl-Bien M (2006) Relational leadership theory: exploring the social processes of leadership and organizing. Leadersh Q 17:654–676 K.  Yonezaki, K.  Ogita, K.  Kimura, Y.  Shiozu, R.  Shioya, K.  Shimohara, On the relationality assets and gift-and-circulation model in community problem. In Human Interface and the Management of Information. Visual Information and Knowledge Management: Thematic Area, HIMI 2019, Part I, LNCS11569, pp. 638–647 (2019). Katsunori  Shiomohara He received the BE and ME degrees in Computer Science and Communication Engineering and the Doctor of Engineering degree from Kyushu University, Fukuoka, Japan, in 1976, 1978, and 2000, respectively. He was Director of the Network Informatics Laboratories and the Human Information Science Laboratories, Advanced Telecommunications Research Institute (ATR) International, Kyoto, Japan. He is currently a professor at the Department of Information Systems Design, Faculty of Science and Engineering, ant the Graduate School of Science and Engineering, Doshisha University, Kyoto, Japan. His research interests include community system design, human communication mechanisms, evolutionary systems, human–system interactions, and socio-informatics.

6

Black-Box Optimization and Its Applications Wataru Kumagai and Keiichiro Yasuda

1 Introduction Super Smart Society (Society 5.0) (Cabinet Office 2021) and Bioeconomy (European Commission 2021) get attention recently as smarter or more advanced concept to realize pre-symptomatic state, healthy life expectancy, circular economy, and energy efficiency and conservation. To adapt to this trend, industry transformation is required, such as product design has more efficiency or manufacturing process is fundamental reformed by smart cells or genetics. Conversely, many systems become more large-scale and complex according to an appearance of System of Systems (SoS), which is a new kind of system consisting of connected various systems with operational autonomy and control autonomy (e.g., distribution system, medical system, power and energy system, or railway system). From this background, the need for practical optimization is growing more urgent. Achieving this needs an integrated methodology by combination of not only on optimization theory but also surrounding technologies, such as simulation,

Adapted from Keiichiro Yasuda and Wataru Kumagai. “Black-Box Optimization and Its Applications (written in Japanese).” Journal of The Society of Instrument and Control Engineers, 59–12, 914/917 (2020). Partly translated by permission of The Society of Instrument and Control Engineers. W. Kumagai Innovation Center, Marketing Headquarter, Yokogawa Electric Corporation, Tokyo, Japan e-mail: [email protected] K. Yasuda (*) Graduate School of Systems Design, Tokyo Metropolitan University, Tokyo, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 T. Kaihara et al. (eds.), Innovative Systems Approach for Facilitating Smarter World, Design Science and Innovation, https://doi.org/10.1007/978-981-19-7776-3_6

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artificial intelligence-based (AI) modeling, and computing technologies; e.g., general-­purpose graphics processing units (GPGPU). This type of optimization is data-driven approach using online data obtained from simulator or sensor, called black-box optimization (BBO). BBO uses only design-variable value and its objective-­function value because the objective function is black-box or expensive function with its unknown landscape. Mathematical programming, which is a classical optimization algorithm’s class using analytical information about the objective function (e.g., gradient or Hessian matrix) and its properties (e.g., convexity or variable dependency), cannot be applied to BBO. Therefore, BBO technology with an ability to adapt to quickly change of the environment surrounding optimization is required. This article focuses some representative approaches of BBO especially metaheuristics (Yang 2010). This article reviews its overview, desirable properties, constraint handling techniques, and its applications based on recent research trends. Mathematical notations used in this article are as follows; ℝ denotes the set of real numbers, ℕ denotes the set of natural numbers, ∅ denotes the empty set, respectively. [a, b], (a, b) denote the closed interval and the open interval between a and b, where a, b ∈ ℝ (a  0 denotes the scale parameter. ES lacks similarity and scale invariance, so it is typically used with an adaptive parameter-tuning rule called one-fifth success rule, tuning the scale parameter σ according to the improvement frequency of the search point. Conversely, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) has been developed as a multi-point ES and various versions of CMA-ES have been proposed; e.g., (μ/μw, λ)-CMA-ES (Hansen et al. 2015). A search steps of a typical CMA-ES using weighted recombination, covariance matrix adaptation (CMA), and step-size adaptation (SSA) is the following:

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1. Step 1: sampling the next position of search points from the normal distribution according to Eq. (6.3), which has a covariance matrix C(k) ∈ ℝN × N and a scale parameter σ(k) > 0. 1

x i ( k + 1) = m + σ ( k ) AΛ2 s i

(6.3) 2. Step 2: deriving a mean vector m  ∈  ℝN using weighted recombination of the search points with superior objective-function value f(xi(k + 1)). 3. Step 3: updating the parameters C(k) and σ(k) according to the search state using CMA and SSA. Here, si ∈ ℝN denotes a random vector distributed according to the multi-variable standard normal distribution  , A = (a1, a2, …, aN) ∈ ℝN × N denotes the basis transformation matrix, and Λ =  diag (λ1, λ2, …, λN) ∈ ℝN × N denotes the eigen matrix, respectively. {(a1, λ1), (a2, λ2), …, (aN, λN)}(λ1 ≥ λ2 ≥ … ≥ λN) are pairs of the eigenvector and eigenvalue of the covariance matrix C(k). CMA-ES has the following meaningful features for BBO: • To have affine transformation invariance and monotonic invariance of the objective function f. • To realize intensification and diversification-based search strategy by adaptive parameter-tuning rules, the search points move to a superior region obtained through the search process. • To provide recommended values for all parameters. Parameter-tuning rules of ES following the design guideline B in Subsection 3.1 give an equivalent effect of adding affine invariance to ES; e.g., the one-fifth success rule, CMA, and SSA.  It is expected that CMA-ES has high search performance according to the fact that an advanced version of it is highly ranked in BBO competitions called Black-Box Optimization Benchmarking workshop (BBOB) (The Black-box Optimization Benchmarking (BBOB) n.d.).

3.2.2 Adaptive Particle Swarm Optimization with Rotational Invariance Particle swarm optimization (PSO) (Yang 2010) is a metaheuristic algorithm inspired by swarm intelligence in biology. The update rules of PSO are expressed by the following equations:

υ i ( k + 1) = wυ i ( k ) + c1 R1 ( p i ( k ) − x i ( k ) ) + c2 R2 ( p g ( k ) − x i ( k ) ) x i ( k + 1) = x i ( k ) + υ i ( k + 1)



{

pi ( k ) = argmin f ( x i (κ ) ) |κ = 1, 2, , k x i (κ )

(6.4) (6.5)

}

(6.6)

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p g ( k ) = argmin f ( pi ( k ) ) pi ( k )∈ ( k )

(6.7)



 ( k ) = { pi ( k ) |i = 1, 2,, m}

(6.8)

Here, w, c1, c2 > 0 denote PSO’s parameters, R =  diag (Rℓ1, Rℓ2, …, RℓN) ∈ ℝN × N (ℓ = 1, 2) denotes a random number matrix, and Rℓn(n = 1, 2, …, N) denotes random number distributed according to the uniform distribution  ( 0,1) , respectively. Especially, pi(k)  ∈  ℝN denotes a personal-best solution called p-best, pg(k)  ∈  ℝN denotes the group-best solution called g-best. PSO has room for improvement in both of adaptability and robustness to various conditions. Yasuda et al. (2008) have proposed the swarm activity P as a metrics of the search state in terms of intensification and diversification, and derived accurately the stable and unstable regions in the PSO’s parameter space using it. The swarm activity P is expressed by Eq. (6.9).

P (k ) =

1 m

m

∑||v ( k )|| N i

(6.9)

i =1

Moreover, the activity feedback PSO (AFPSO) is proposed as a new-type PSO with an adaptive parameter-tuning rule to control the swarm activity P during the search process (Yasuda et al. 2008). The update rule of AFPSO consists of PSO and a tuning rule for the inertia parameter w. The tuning rules for w(k) are expressed by Eqs. (6.10) and (6.11).

w ( k + 1) = w ( k ) + sgn ( P ( k ) − Pt ( k ) ) ∆w

(6.10)

k

Pt ( k ) =

ε start  ε end  kmax   ||γ max − γ min || N  ε start 

(6.11)

Here, γmax, γmin ∈ ℝN denote the vectors determined from the initial search points, kmax ∈ ℕ denotes the iteration counter max, and sgn : ℝ → {−1, 1} denotes the sign function, respectively. After updating w(k) with Eq. (6.10), we revise it so that w(k) ∈ [wmin, wmax]. This tuning rule adjusts w(k) so that the swarm activity P(k) follows a target value Pt(k). It is shown that AFPSO has better search performance than PSO with various parameter-tuning rules (Yasuda et al. 2008). However, Kumagai and Yasuda (2017, 2019) have pointed out that AFPSO has scale invariance, translation invariance, and monotonic invariance of f, but lacks rotational invariance such as PSO with various parameter-turning rules through mathematical proofs and numerical simulations. On that point, the adaptive PSO with rotational invariance using correlativity (adaptive CRI-PSO) has proposed as a new-type PSO with both of rotational invariance and the adaptive parameter-tuning rule (Kumagai and Yasuda 2019). The update rules of the adaptive CRI-PSO are basically the same as that of AFPSO, except that Eq. (6.4) is revised to Eq. (6.12). v i ( k + 1) = w ( k ) v i ( k ) + c1 AR1 AT ( pi ( k ) − x i ( k ) ) + c2 AR2 AT ( p g ( k ) − x i ( k ) ) (6.12)

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Here, A = (a1, a2, …, aN) ∈ ℝN × N denotes the basis transformation matrix, and {a1, a2, …, aN} are the eigenvectors of the covariance matrix based on the p-best distribution  ( k ) . In the tuning rules for w(k) of the adaptive CRI-PSO, parameters Δw, εstart, εend, wmin, wmax > 0 are added.3 The adaptive CRI-PSO controls the swarm activity P(k) while determining the perturbation direction from the p-best distribution  ( k ) . In the above the parameter-­ tuning rule, controlling the search state according to the ideal ensures that the intensification and diversification-based search strategy is realized. This strategy is expected to give the adaptive CRI-PSO highly adaptation. Additionally, the adaptive CRI-PSO consists of Eq. (6.12) and the above parameter-tuning rule; and has similarity, rotational, and translation invariance in the solution space and monotonic invariance of f. But, because adding parameter-tuning rule preserves these invariances, this satisfies the design guideline A in Sect. 3.1. Thus, it is expected to have high robustness and adaptability. In fact, the search performance of the adaptive CRI-PSO is shown to be superior to that of PSO and AFPSO through numerical experiments (Yasuda et al. 2008). CMA-ES and the adaptive CRI-PSO are common in the following points: 1. They get transformation invariance by using the covariance matrix based on the solution set obtained in the search process. 2. They get adaptability by parameter tuning according to the intensification and diversification-based search strategy.

4 Constrained Black-Box Optimization The direct-search method including metaheuristics is considered to be unconstrained optimization problems, but we need to consider constraints in real-world use. This section describes classes of constraints in BBO and methods for handling them.

4.1 Classes of Constraints in BBO This section focuses on constrained optimization problem in BBO. A solution satisfying all constraints is called feasible solution, and a solution not satisfying a constraint is called infeasible solution or constraint-violating solution. The notation  denotes the set of feasible solutions called feasible region.

 Kumagai and Yasuda (2019) given the following recommended values to for these parameters. γmax, γmin are determined by the region for initial search points. wmax, wmin should be to across the boundary line between stable and unstable regions in PSO’s parameter space. It is pointed out that the boundary line is located inside the region w ∈ [0.5,1.0] while c1 = c2 = 1.4955 through parameter analysis. 3

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Constraints can be classified according to their analytic properties and formal properties. In terms of analytic properties, we can classify constraints as either linear constraints including non-negative constraints and upper/lower bound constraints, or non-linear constraints.4 In terms of formal properties, we can classify constraints including simulation-based optimization or BBO based on the form. QRAK (Digabel and Wildy 2015) is a taxonomy rule with the four following perspectives: • Quantifiable (Q)/Nonquantifiable (N): whether the degree of constraint violation can be quantified; • Relaxable (R)/Unrelaxable (U): whether a constraint-violating solution can be evaluated; • A priori (A)/Simulation-based (S): whether a simulation is needed to evaluate a solution; • Known (K)/Hidden (H): whether the existence of constraints is known. Constraints can be classified into 16 types according to the QRAK rule.5 This includes situations such as when constraint-violating solutions cannot be evaluated due to reasons on simulator’s side, or when the simulation does not have completed successfully. In practical use, many cases are QRAK or QRSK constraints. The reason for this is that a binary constraint meaning whether a solution is feasible or infeasible can be quantified as numerical constraint violation, or constraint-­violating solutions can be evaluated in some reasonable way. It would be meaningful to know classes of constraints in BBO more broadly and to consider handling methods matching them. Sections 4.2 and 4.3 will explain methods for handling QRAK or QRSK constraints.

4.2 Classical Method for Constraint Handling Classical method for constraint handling is a type of problem-transformation method called the penalty-function method. If the class and properties of objective or constraint functions are clear, you can apply a method for constraint handling that matches the class of problem. For example, if the objective function and constraint functions are convex, a convex optimization method that uses analytic information about their functions (gradient or Hessian matrix) can solve this problem by constructing a new convex objective function introduced penalty function; and converting the problem to an unconstrained optimization, which called the augmented Lagrangian function. Equation (6.13) shows the augmented Lagrangian function L : ℝN → ℝ with a penalty function.  Besides linear constraints and non-linear constraints, there are discrete constraints and level-sets constraints determined by objective-function values. 5  Actually, the QRAK rule classifies constraints into nine types because it is not possible to calculate or quantify numerical constraint violation value if the existence of them is unknown. 4

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L ( x ) = f ( x ) + λφ ( x )

k

φ ( x) = ∑ k =1 Ω k ( x)

(6.14)



Ωκ ( x ) = max { g κ ( x ) ,0}

(6.15)

(6.13)

Here, f : ℝN → ℝ denotes the objective function, ϕ : ℝN → ℝ denotes the penalty function, and λ > 0 denotes the penalty coefficient, respectively. Many definitions for penalty function ϕ are possible, but a typical definition is formulated as Eqs. (6.14) and (6.15).



An amount of constraint violation v(x), which amount of violating a constraint or all constraints, is basically defined by v(x) = ϕ(x) and vκ(x) = Ωκ(x).

4.3 Methods for Constraint Handling in BBO 4.3.1 Constraints Handling Techniques The classical penalty-function method is not effective for constrained optimization problem including the black-box or non-convex objective function and constraint functions. Difficulties in this class of problem are the following: 1. Because there are multiple local optimal solutions in the feasible region  being non-convex or disconnected, it needs a global search capability. 2. Typically, because the global optimal solution is located on the boundary of the feasible region  , it needs an efficient search on this boundary. The constraint handling techniques (CHTs) have been developed as methods expanding the applicable scope of metaheuristics to this class of problems and cope with the above issues (Coello 2002; Mezura-Montes et  al. 2011). Metaheuristic algorithm searches the global optimal solution by selection superior solutions. The selection operation evaluates and compares solutions obtained through multi-point search according to a metrics called fitness function S(x). While the selection for unconstrained optimization uses the fitness S defined by the objective-function value f, CHTs use the fitness S defined by the objective-function value f and amount of constraint violation v. Additionally, it has been pointed out that using constraint-­ violating solutions is important for improving search efficiency in constrained BBO (Ray et al. 2009). According to the above discussion, CHTs can be largely classified depending on the following viewpoint: 1. CHTs can be categorized as penalty-based, separatist-based, or multi-objective-­ based method depending on the definitions of fitness S. 2. CHTs can be categorized as “none,” “inexplicit,” or “explicit” class depending on degree of utilization of constraint-violating solutions.

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Table 6.1  Summary of studies on constraint handling techniques − None

Inexplicit

Explicit

Penalty-based CHT Death penalty (Mezura-Montes and Coello 2011) Static penalty (Homaifar et al. 1994), Dynamic penalty (Joines and Houck 1994), Adaptive penalty (Lemonge and Barbosa 2004) ASCHEA (Hamida and Schoenauer 2000)

Separatist-based CHT − Feasibility rule (Mezura-­ Montes and Coello 2011), Stochastic ranking (Runarsson and Yao 2000), ε constraint method (Takahama and Sakai 2005), GCR (Runarsson and Yao 2003), HSR (Ho and Shimizu 2007), MCR (Garcia et al. 2017) MCODE (Liu et al. 2007), TNSDM (Miyakawa et al. 2013)

Multi-objective-based CHT − −

Two-phase framework (Venkatraman and Yen 2005), IDEA (Ray et al. 2009), DeCODE (Wang et al. 2021), Adaptive Weighted MOEA/D (Yasuda et al. 2022)

Table 6.1 shows summary of studies on CHTs categorized based on these criteria. We will provide a description of each approach in next subsection and beyond.

4.3.2 Penalty-Based CHT The penalty-based CHT uses the augmented Lagrangian function L defined in Eq. (6.13) as the fitness, but it differs from classical penalty functions in terms of the way it treats the penalty coefficient λ. The death penalty (Mezura-Montes and Coello 2011), static penalty (Homaifar et al. 1994), and dynamic penalty (Joines and Houck 1994) have been proposed as the penalty-based CHT. The death penalty assigns an extremely bad value (or an infinitely large value) to the penalty coefficient λ for constraint-violating solutions, and searches only using feasible solutions. The static penalty assigns a constant to λ and the dynamic penalty increases λ according to a given schedule during the search process. However, the search performance is deteriorated, and a feasible solution cannot be obtained without a properly set or tuning for the penalty coefficient λ. For example, the fitness function L highly depends on scale differences between constraint functions because of lacking monotonic invariance of the objective function and constraint functions if the amount of constraint violation v is defined in Eq. (6.14). On that point, the adaptive penalty (Lemonge and Barbosa 2004) and ASCHEA (Hamida and Schoenauer 2000) have been proposed as the penalty-based CHT for adaptively tuning the penalty coefficient during the search process. In the adaptive penalties, a fitness function S of a constraint-violating solution x in a solution set  is formulated as Eqs. (6.16), (6.17), and (6.18).

6  Black-Box Optimization and Its Applications ^



S ( x ) = f ( x ) + ∑ κ =1 λκυκ ( x ) f ( x ) = max f ( x ) , f λκ = f



K

{

^



93

υk

∑

K

2

υ κ =1 k

}

(6.16) (6.17) (6.18)

Here, the notations f , υκ denote the mean objective-function value f and the mean amount of constraint violation vκ, respectively; and their mean values are averaged of f and vκ of solutions in the solution set  . Thus, it is possible to mitigate the above deficiency by assigning different penalty coefficients for each constraint function and adaptively tuning in response to the objective-function value and each amount of constraint violation obtained in the search process. However, because many penalty-based CHTs do not make use of the order relationship between the amount of constraint violation of solutions, it is thought that the usefulness of constraint-violating solutions be low.

4.3.3 Separatist-Based CHT The separatist-based CHT separates objective-function values f and amount of constraint violation v, and evaluates and compares solutions; they can be classified as either switching-based or ranking-based CHT.  The switching-based CHT selects and uses either of the objective-function value or the amount of constraint violation as a fitness S. Feasibility rule (Mezura-Montes and Coello 2011), stochastic ranking (Runarsson and Yao 2000), ε constraint method (ε CM) (Takahama and Sakai 2005), and MCODE (Liu et al. 2007) have proposed in this category. In ε CM, when comparing two solutions x and y, the order relation of fitness S is defined in Eq. (6.19).  f ( x ) ≤ f ( y ) ; v ( x ) , v ( y ) < ε (6.19) S ( x) ≤ S ( y) ⇔  v x ≤ v y otherwise ; ( ) ( )   Here, ε > 0 denotes a threshold parameter for the amount of constraint violation and decreases to almost 0 gradually during the search process, since the search points improve the objective-function value after they move to near the feasible region early on. The ranking-based CHT uses a fitness S based on a total rank in a solution set. The total rank consists of rank based on objective-function values and rank based on amount of constraint violation. Global competitive ranking (GCR) (Runarsson and Yao 2003), Ho-Shimizu ranking (HSR) (Ho and Shimizu 2007), multiple constraint ranking (MCR) (Garcia et  al. 2017), and TNSDM (Miyakawa et  al. 2013) have proposed in this category. In MCR, the fitness function S(x) of a solution x in a solution set  is formulated as Eq. (6.20).

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 Rn + ∑ K Rυ ; F ∩ X = ∅  κ κ =1 S ( x) =  K  R f + Rn + ∑ κ =1 Rυκ ; otherwise

(6.20)

Here, R f , Rvκ , Rn denote a rank of objective-function value f, ranks for each amount of constraint violation vκ, and a rank of constraint violation count, respectively; and their ranks are determined from an order relation in the solution set  . Because the separatist-based CHTs make use of the order relation between the amount of constraint violation, it is thought that they make better use of constraint-­ violating solutions than penalty-based CHT.

4.3.4 Multi-Objective-Based CHT The multi-objective-based CHT converts a single-objective constrained optimization problem into a two-objective (objective-function value f and amount of constraint violation v) unconstrained optimization problem and uses evaluations and comparisons of the solution in multi-objective optimization. The terms of multi-­ objective optimization in the multi-objective-based CHT are explained below. Multi-objective optimization finds a Pareto optimum set in the objective-function space considering trade-off relationship between each objective function while the multi-objective-based CHT finds a feasible global optima in the space (f, v). Superiority relation (Pareto dominance) gives superiority or inferiority relation between two solutions in the space (f, v). When two solutions x, y satisfy Eq. (6.21), an order relation between x and y is called “dominates y” or “x is superior to y.”

( f ( x ) ≤ f ( y ) ∧ v ( x ) ≤ v ( y )) ∧ ( f ( x ) < f ( y ) ∨ v ( x ) < v ( y ))

(6.21)

In a solution set  , a solution x ∈  to be not dominated by all other solutions y ∈  is called non-dominated solution or Pareto solution. A set of non-dominated solutions in the solution space is called Pareto optimum set or Pareto frontier. A feasible solution is located on the f-axis in the space (f, v) and means weakly Pareto solution. Note that the multi-objective-based CHT aims to find the only feasible global optima located on the intersection of the Pareto frontier and the f-axis in the space (f, v), not the entire of this region. The multi-objective-based CHT can be classified as either the Pareto ranking-­ based or decomposition-based CHT in the viewpoint of multi-objective optimization approaches. Pareto ranking gives candidate solutions a rank-based fitness constructed by superiority relation and crowded distance in the objective-function space and is used in NSGA-II (Deb et al. 2002) for multi-objective optimization. The Pareto ranking-based CHT uses the fitness based on Pareto ranking in the space (f, v). However, even if feasible solutions are obtained in the search process, they are easily eliminated because they are weakly Pareto solutions. On that point, as the Pareto ranking-based CHT preserving some feasible solutions during the search process, the two-phase framework (Venkatraman and Yen 2005) and the

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infeasibility driven evolutionary algorithm (IDEA) (Ray et al. 2009) have been proposed. IDEA preserves both of feasible solutions and constraint-violating solutions in the search points and assigns two-types fitness for each solution set. One fitness of feasible solutions is the objective-function value f, and the other fitness of constraint-­violating solutions is a rank Rp based on Pareto ranking. In IDEA, when comparing two feasible solutions or two constraint-violating solutions, the order relation of fitness S is defined in Eq. (6.22).  f ( x ) ≤ f ( y ) ; x , y ∈  (6.22) S ( x) ≤ S ( y) ⇔   R p ( x ) ≤ R p ( y ) ; x , y ∉  Decomposition decomposes a multi-objective optimization problem into a set of single-objective optimization subproblems and solves them in parallel by a scalar-­ based fitness function with a different weight parameter wi ∈ [0, 1] assigned for each search point xi; and is used in MOEA/D (Zhang and Li 2007) for multi-objective optimization. The decomposition-based CHT uses the above problem decomposition in the space (f, v). The scalarizing function S of the weighted sum is formulated as Eq. (6.23).

S ( x;w ) = wf ( x ) + (1 − w ) v ( x )

(6.23)

Note that MOEA/D for multi-objective optimization assigns the weights to constant value during the search process and distributes them uniformly in the objective-­ function space to find the entire of the Pareto frontier, but this is not effective of constrained optimization to find the only feasible global optima finally. On that point, as the decomposition-based CHT with weight-tuning rule dynamically during the search process, DeCODE (Wang et  al. 2021), and the adaptive weighted MOEA/D (Yasuda et al. 2022) have been proposed. DeCODE uses a weight-tuning rule dynamically so that the search region is limited from the violation region to the feasible region gradually. The adaptive weighted MOEA/D uses a weight-tuning rule adaptively so that the search region is balanced to cover the boundary of the feasible region  , and the tuning rules for wi are expressed by Eqs. (6.24) and (6.25).



wi ( k ) = α ( k )

i −1 m −1

γ α ( k ) ; x t ( k ) ∈  α ( k + 1) =  u  γ dα ( k ) ; otherwise

(6.24) (6.25)

Here, α ∈ [0, 1] denotes a variable parameter for controlling the distribution of weights wi in the space (f, v), xt(k) denotes the search point having t-th weight wt. γu  >  1, γd  ∈  (0, 1) denote an increasing coefficient and a decreasing coefficient, respectively. After updating wi with Eq. (6.24), we revise it so that wi(k) ∈ [δ, 1], and after updating α by Eq. (6.25), we revise it so that α(k) ∈ [0, 1].6  Yasuda et al. (2022) given the following recommended values to for these parameters; α(1) = 1.0, t = ⌊0.8m⌋, γu = 1.001, γd = 0.999, δ = 10−15.

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The multi-objective-based CHT makes the most utilization of constraint-­ violating solutions than the penalty-based and the separatist-based CHTs because an effective search works on trade-off regions between objective-function value f and amount of constraint violation v by superiority relation. The Pareto ranking-­ based and the decomposition-based CHTs have the following advantages and disadvantages: • Pareto ranking-based CHT: –– Advantage: it is possible to search the trade-off region while not being affected by a difference between f and v scales; or a shape of the Pareto frontier because the fitness S is determined only from ranks in the space (f, v). –– Disadvantage: it is difficult to gain feasible solutions if the Pareto frontier is large in the solution space, which the feasible region is narrower than the violation region, because it searches the entire of the region uniformly. • Decomposition-based CHT: –– Advantage: it is possible to improve an ability to gain feasible solutions by weight tuning so that the search region is limited to a part of the Pareto frontier because solutions converge almost surely and the weights corresponds to the Pareto solutions basically. –– Disadvantage: it is difficult to maintain the limitation in the space (f, v) as ideal and the corresponding relation between the weights and the Pareto solutions if the difference between f and v scales is large (Ishibuchi et al. 2017); or a scalarization function S does not match the shape of the Pareto frontier near the optimal solution.7 Both approaches are complementary, but there is a difference in effectiveness on constrained optimization. The Pareto ranking-based CHT preserves some feasible solutions in the search process, but it is relatively disadvantaged in finding the only feasible global optima because the search region cannot be limited to the part of the Pareto frontier. In contrast, the decomposition-based CHT can search the limited region, and its disadvantage is considered less serious than the Pareto ranking-based CHT according to the following reasons: 1. The difference between f and v scales can be suppressed by normalization or standardization (Ishibuchi et al. 2017). 2. Even if the uniformity of approximation to the Pareto frontier is reduced a little, there is some effectiveness. In fact, Yasuda et al. (2022) confirmed that the adaptive weighted MOEA/D is superior to the separatist-based CHT and the Pareto ranking-based CHT in terms of both of convergence on a feasible solution and global optimization performance through numerical simulation. From the above, the decomposition-based CHT is  The scalarizing function of the weighted sum cannot approximate the Pareto frontier uniformly, whose shape is not convex (non-convex or disconnected) (Zhang and Li 2007). 7

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considered advantageous in constrained optimization in terms of the ability to gain feasible solutions.

4.3.5 General Comment According to the above review, because CHTs use the order relation in the solution set obtained in the search process, they have a high affinity for metaheuristics with multi-point and direct-search method. As shown in Table 6.1, CHTs can be largely classified based on the viewpoint of definition of fitness function and degree of utilization of constraint-violating solutions; and especially the multi-objective-based CHT makes the most utilization of them. But the fitness function S in CHTs is deeply related to intensification and diversification-based search strategy, and transformation invariance; e.g., the monotonic invariance of objective function f and each constraint function gκ. In the future research, it is desirable to develop and combine metaheuristic algorithms and CHTs for constrained BBO considering the above strategy or property totally.

5 Application of BBO This section reviews three important examples of BBO applications. First example is online operation optimization or configuration design for SoS. SoS consists of connected various systems with operational autonomy and control autonomy (e.g., distribution system, medical system, power and energy system, or railway system). This needs total and data-driven optimization using obtained online and uncertain data from sensor and state of each system in real time. Demand response maintains the supply-demand balance efficiently by providing people with data and financial incentives to indirectly change their behavior and demand, such as dynamic pricing in energy management systems (Yasuda and Tokoro 2020). Even if a state of SoS involves uncertainly such as potential to change people’s behavior or demand, BBO can be applied to it. And there is an approach to find and design configuration system of SoS (Agarwal et al. 2015). These problems are formulated as constrained BBO. Second example is hyperparameter tuning or optimization for expensive machine learning models. Automated machine learning (AutoML) frameworks and deep learning (deep neural networks) have many tunable hyperparameters such as very complex parameter architecture (Feurer and Hutter 2019). On that point, parameter-­ tuning techniques have proposed for automating their engineering process. It is shown that these techniques are superior to manually tuning or engineering by human in the viewpoint of performance and time comsuming (Snoek J et al. 2012; Bergstra et al. 2011); especially neural architecture search is the most successful example (Elsken et al. 2019). Hyperparameter tuning problem is formulated as constrained BBO. Third example is material discovery, design, and optimization for multi-range application. Design of new and highly functional material including raw material or chemical compounds can change all manufacturing areas, such as healthcare, medical care, and energy. Industrial biotechnology can realize the production of

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renewable biological resources and the conversion of these resources and waste streams into value added products, which alternative energy sources, biopharmaceutical, and high-quality food, by smart genetics and cells. The bio-industry subcommittee of Ministry of Economy, Trade, and Industry (METI) in Japan shows the following examples as their use cases (Ministry of Economy, Trade, and Industry (METI) n.d.): 1. Regenerative medicine or gene therapy may cause radical treatments for diseases. 2. In manufacturing process, redesign of cell’s function may improve efficiency of industrial production; e.g., transformation from glucose to raw material for high-­ quality plastics. Material discovery problem for these processes is formulated as constrained BBO (Terayama et al. 2021).

6 Conclusion This article reviewed the main approaches to BBO, especially metaheuristics and constraint handling techniques, and provided some applications of BBO.  As we shift toward Super Smart Society (Society 5.0) or Bioeconomy, real-world systems will grow in scale and complexity such as SOS. Conversely, practical system optimization will realize to combine surrounding technologies advancing rapidly. It is desirable to develop BBO with an ability to adapt all of these changes. Given these trends, we believe that SMBO for constrained BBO will be increasingly important, and these technologies should be able to adapt to various applications such as SOS in the future.

References Agarwal S, Pape LE, Dagli CH, Ergin NK, Enke D, Gosavi A, Qin R, Konur D, Wang R, Gottapu RD (2015) Flexible and intelligent learning architectures for SoS (FILA-SoS): architectural evolution in systems-of-systems. Procedia Computer Sci 44:76–85 Bergstra J, Bardenet R, Bengio Y, Kégl B (2011) Algorithms for hyper-parameter optimization. Adv Neural Inf Proces Syst 24:2546–2554 Cabinet Office, Government of Japan (2021) Society 5.0. https://www8.cao.go.jp/cstp/english/ society5_0/index.html. Accessed 15 May 2022 Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11–12):1245–1287 Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197 Digabel SL, Wildy SM (2015) A taxonomy of constraints in simulation-based optimization. Les cahiers du GERAD, technical report G-2015-57. https://doi.org/10.48550/arXiv.1505.07881

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Elsken T, Metzen JH, Hutter F (2019) Neural architecture search, Automated machine learning. In: Hutter F, Kottohoff L, Vanschoren J (eds) The Springer series on challenges in machine learning, Cham, Springer, pp 63–77 https://doi.org/10.1007/978-3-030-05318-5_3 European Commission (2021) What is the Bioeconomy. https://ec.europa.eu/research/bioeconomy/policy/bioeconomy_en.htm. Accessed 15 May 2022 Feurer M, Hutter F (2019) Hyperparameter optimization. In Hutter F, Kotthoff L, Vanschoren J (eds): Automated machine learning. In: The Springer series on challenges in machine learning. Cham, Springer, pp. 3–33 https://doi.org/10.1007/978-3-030-05318-5_1 Garcia R, Lima B, Lemonge A, Jacob B (2017) A rank-based constraint handling technique for engineering design optimization problems solved by genetic algorithms. Comput Struct 187:77–87 Hamida SB, Schoenauer M (2000) An adaptive algorithm for constrained optimization problems. In: Proceedings of the International Conference on Parallel Problem Solving from Nature. pp. 529–538 Hansen N, Ros R, Mauny N, Schoenauer M, Auger A (2011) Impacts of invariance in search: when CMA-ES and PSO face ill-conditioned and non-separable problems. Appl Soft Comput 11(8):5755–5769 Hansen N, Arnold DV, Auger A (2015) Evolution strategies. In: Kacprzyk J, Pedrycz W (eds) Springer handbook of computational intelligence, Springer, vol 44, Berlin, Heidelberg, pp 871–898 https://doi.org/10.1007/978-3-662-43505-2_44 Ho PY, Shimizu K (2007) Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme. Inf Sci 177(14):2985–3004 Homaifar A, Qi CX, Lai SH (1994) Constrained optimization via genetic algorithms. Simulation 62(4):242–253 Ishibuchi H, Doi K, Nojima Y (2017) On the effect of normalization in MOEA/D for multi-objective and many-objective optimization. Complex Intell Sys 3(4):279–294 Joines J, Houck C (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA’s. In: Proceedings of the First IEEE Conference on Evolutionary Computation. pp. 579–584 https://doi.org/10.1109/ICEC.1994.349995 Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492 Kanemasa M, Aiyoshi E (2014) Algorithm tuners for PSO methods and genetic programming techniques for learning tuning rules. IEEJ Trans Electr Electron Eng 9(4):407–414 Kawarabayashi M, Yasuda K (2008) Integrated optimization method using particle swarm optimization and Modeling (written in Japanese). Trans Soc Instrum Control Eng 44(11):855–862 Kumagai W, Yasuda K (2017) Making rotational invariance of particle swarm optimization based on correlativity. IEEJ Trans Electr Electron Eng 12(S2):S131–S132 Kumagai W, Yasuda K (2019) Adaptive particle swarm optimization with rotational invariance (written in Japanese). Trans Inst Electr Eng Japan Part C 139(10):1201–1214 Lemonge A, Barbosa H (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59(5):703–736 Liu B, Ma H, Zhang X, Zhou Y (2007) A memetic Coevolutionary differential evolution algorithm for constrained optimization. In: Proceedings of the 2007 IEEE congress on evolutionary computation. pp. 2996–3002 https://doi.org/10.1109/CEC.2007.4424853 Mezura-Montes E, Coello CAC (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput 1(4):173–194 Ministry of Economy, Trade, and Industry (METI) (n.d.), Bio-Industry Subcommittee’s Report (2021) Fifth industrial revolution. Cultivated with Biotechnology. https://www.meti.go.jp/english/press/2021/0202_001.html. Accessed 2 May 2022 Miyakawa M, Takadama K, Sato H (2013) Two-stage nondominated sorting and directed mating for solving problems with multi-objectives and constraints. In: proceedings of the 2013 genetic and evolutionary computation conference. pp. 647–654 https://doi.org/10.1145/2463372.2463449 Ray T, Singh HK, Isaacs AA, Smith W (2009) Infeasibility driven evolutionary algorithm for constrained optimization. In: Mezura-Montes, E. (eds) Constraint-handling in evolutionary opti-

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mization. Studies in Computational Intelligence, vol 198. Springer, Berlin, Heidelberg. pp. 145–165 https://doi.org/10.1007/978-3-642-00619-7_7 Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294 Runarsson TP, Yao X (2003) Constrained evolutionary optimization-the penalty function approach. In: Sarker R, Mohammadian M, Yao X (eds) Evolutionary optimization. International series in Operations Research & Management Science, vol 48. Springer, Boston, MA, pp 87–113 Snoek J, Larochelle H, Adams RP (2012) Practical Bayesian optimization of machine learning algorithms. Adv Neural Inf Proces Syst 25(2):2951–2959 Takahama T, Sakai S (2005) Constrained optimization by ε constrained particle swarm optimizer with ε-level control. In: Proceedings of the 4th IEEE International Workshop on Soft Computing as Transdisciplinary Science and Technology. pp. 1019–1029 Terayama K, Sumita M, Tamura R, Tsuda K (2021) Black-box optimization for automated discovery. Acc Chem Res 54(6):1334–1346. https://doi.org/10.1021/acs.accounts.0c00713 The Black-box Optimization Benchmarking (BBOB) (n.d.) Workshop. http://numbbo.github.io/ workshops/index.html. Accessed 29 March 2022 Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9(4):424–435 Wang B, Li H, Zhang Q, Wang Y (2021) Decomposition-based multiobjective optimization for constrained evolutionary optimization. IEEE Transact Sys Man Cybernet: Syst 51(1):574–587 Yang XS (2010) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver Press Yasuda K, Tokoro K (2020) Smartification of social infrastructure for efficient power and energy use. In: Kaihara T, Kita H, Takahashi S (eds) Innovative systems approach for designing smarter world. Springer, Singapore, pp 133–145 Yasuda K, Iwasaki N, Ueno G, Aiyoshi E (2008) Particle swarm optimization: a numerical stability analysis and parameter adjustment based on swarm activity. IEEJ Trans Electr Electron Eng 3(6):642–659 Yasuda Y, Kumagai W, Tamura K, Yasuda K (2022) An extension of MOEA/D to constrained optimization and adaptive weight adjustment (written in Japanese). Trans Inst Electr Eng Japan Part C 142(1):108–109 Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731 Wataru Kumagai Born in 1991, Wataru Kumagai  completed his doctoral program in Electrical and Electronic Engineering at the Graduate School of Science and Engineering, Tokyo Metropolitan University, Japan, in 2020. Since 2016, he has been working at Yokogawa Electric Corporation, Japan. He is engaged in research on systems optimization (evolutionary computation), machine learning, and energy optimization. He holds a Doctor of Engineering and is a member of The Institute of Electrical Engineers of Japan. Keiichiro Yasuda Born in 1960, Keiichiro Yasuda  completed his doctoral program in Electrical Engineering at the Graduate School of Engineering, Hokkaido University, in 1989. The same year, he became an assistant professor in the Faculty of Engineering at the Tokyo Metropolitan University. In 1991, he became an associate professor in the Faculty of Engineering at the Tokyo Metropolitan University and, since 2006, he has been a professor in the Graduate School of Science and Engineering. He is engaged in research on systems optimization and power systems engineering. He holds a Doctor of Engineering and is a member of societies such as The Society of Instrument and Control Engineers, The Institute of Electrical Engineers of Japan, The Japanese Society for Evolutionary Computation, and the IEEE.

7

Estimation of Objective Functions: Modeling of Problems and Understanding of Decision-Making Processes Towards the Spiral-up Systems Approach Ryohei Funaki and Junichi Murata 1 Introduction The spiral-up systems approach (Kaihara et al. 2020) considers systems to evolve through cycles of analysis and synthesis, or cycles of induction, deduction, and abduction (hypothesis generation) (Fanni 2020), and it designs, constructs, and operates systems following these cycles. Optimization plays a significant role in system synthesis. An optimization problem is formulated as a set of decision variables, objective functions, and constraints. The formulated problems correspond to the models that represent functionality and objectives of the target systems. Determination or estimation of the objective functions, among others, is an essential part of the analysis in the spiral-up systems approach and leads to abduction. Decision-making by humans plays a key role in systems involving humans. The decision-making process can be regarded as optimization; however, the objective functions used by humans for decision-making are not always explicitly defined. In this chapter, the authors describe their proposed and other techniques of objective function estimation, which leads to modeling and understanding of the decision-­ making processes towards the spiral-up systems approach.

R. Funaki (*) · J. Murata Kyushu University, Fukuoka, Japan e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 T. Kaihara et al. (eds.), Innovative Systems Approach for Facilitating Smarter World, Design Science and Innovation, https://doi.org/10.1007/978-981-19-7776-3_7

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2 Formulation of Optimization/Decision-Making The optimization/decision-making problems in this chapter are formulated as follows:



Maximize f1 ( x ) , …, f p ( x ) , s.t. x ∈ X ,

(7.1)

where x is a vector of decision variables and fi(x), i = 1, …, p are objective functions, sometimes called attributes. The number of the objective functions p may be 1. The symbol X denotes the feasible region of the decision variables.

3 Estimation of Objective Functions The objective functions measure the goodness of target systems or decision-making processes; however, defining them correctly is not always easy. Determination of the objective functions for some optimization problems, especially some decision-­ making problems, is not straightforward. For example, the priority among multiple objective functions cannot be objectively determined because it depends on the decision-maker’s judgment. We call, in this chapter, establishing objective functions that approximate the true objective functions, which are not always obvious, “estimation of objective functions.” Estimating the objective functions requires data and information. They include (A) the values of the objective functions at multiple x, (B) the order among the objective function values at a number of x, and (C) the optimal value x∗ of the decision variable. The use of data type (A) is equivalent to the function approximation of the objective functions, for example, estimation and use of surrogate models (Lin 2011). Here we focus on types (B) and (C) which contain less information than type (A). The following sections present several methods for estimation of objective functions.

3.1 Estimation of Weight Coefficients on Multiple Objective Functions Among the optimization/decision-making problems shown in Eq. (7.1), those with p equal to two or higher are called multi-objective optimization problems or multi-­ attribute decision-making problems. A commonly used solution technique is to solve a single-objective problem with the objective function given by p



F ( x ) = ∑wi f i ( x ) , i =1



(7.2)

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which is a sum of fi(x) multiplied by its importance weight wi. The value of the weight wi depends on decision-makers. Estimating/setting wi corresponds to estimating the objective function. Typical estimation methods of wi are Analytic Hierarchical Process (AHP) (T. L. 1977) and Analytic Network Process (ANP) (Saaty and Vargas 2006). In these methods, a human compares the importance of two evaluation criteria. The pairwise comparisons are less burdensome than the simultaneous comparisons of many elements or their quantitative evaluations. The information and data obtained by pairwise comparisons are of type (B) above. In AHP, for every pair (fi, fj) of objective functions, the human selects the relative importance aij of fi to fj from several predetermined values. If they are equally important, aij = 1. We set aji = 1/aij. Values of w = [w1…wp]T are obtained as the principal eigenvector of the matrix whose elements are aij. ANP treats the cases where elements have inter-dependencies. For example, the mass of a vehicle affects both its safety and its fuel efficiency; however, the mass has different importance when compared with other elements from the safety perspective and when compared from the fuel economy viewpoint. Therefore, all pairwise comparisons among the objective functions are performed from the perspective of each of the objective functions fi, i = 1, …, p, and AHP calculates each of the weight vectors wi, i = 1, …p. Then the matrix W is formed by vectors wi, i = 1, …, p. The importance of an objective function affects the importance of other objective functions through dependencies. Since this transitive relationship is expressed as a power of W, limk → ∞Wk determines the weights. Pairwise comparisons of objective functions are easy for humans, but comparing actual alternatives, x, is even easier. When xa1 is found to be better in a pair (xa1, xb1), the following inequality for the weights wi, i = 1, …, p holds from Eq. (7.2): p

∑ { f ( x ) − f ( x )} w



i

i =1

a1

i

b1

i

> 0.

(7.3)



When we obtain similar inequalities for other pairs (xak, xbk),   k = 2, ⋯, K, the region where the weight vector w can exist is obtained as a p-dimensional polytope that is a solution to these K simultaneous inequalities. A representative point, such as the center of the polytope, is used as the weight vector (Murata et al. 2010). When the pairwise comparisons give, in addition to the better ones, the difference in goodness in each pair, the additional information can also be utilized. For example, when the difference is large, the left-hand side of inequality Eq. (7.3) should be much larger than 0. To reflect this, the equality can be replaced by



1 αk

p

∑ { f ( x ) − f ( x )} w i =1

i

ak

i

bk

i

> 0,

k = 1, …, K .



(7.4)

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When the difference is large, we set a large value for αk. Since αk reflects human judgment, it is sufficient for it to take one of several distinct values. The weight vector is derived as the solution to the min-max optimization problem Eq. (7.5): 1 k ∈{1,…,K } α k

Minimize max

w1 ,…, w p

p

∑ { f ( x ) − f ( x )} w . i =1

i

ak

i

bk

i

(7.5)

3.2 Estimation in Interactive Evolutionary Computation Interactive evolutionary computation (IEC) replaces the objective functions of evolutionary computation (EC) with human evaluations. The optimization system randomly generates Np solutions. A human (user) evaluates them, and the system generates new solutions based on the evaluations. EC and IEC repeat the cycle (called a generation in the EC field) of evaluations and renewals of solutions to obtain the solution that satisfies the user. The primary issue in IEC is user fatigue caused by repetitive evaluations. In order to reduce the fatigue, the pairwise comparison has recently become the mainstream evaluation method, which dramatically reduces the burden compared to the conventional methods that use simultaneous comparisons and evaluations of many solutions (Takagi and Pallez 2009). If it is possible to estimate the objective functions that a user has internally, utilization of these functions further reduces his or her fatigue. Although the information obtained from the pairwise comparison evaluations is the type (B) shown in Sect. 3, most of the solutions are located in the region of high objective function values in some advanced stages of a search, and their distribution is valuable information. This section introduces methods to estimate parts of properties of an objective function from the values of decision variables only. The properties are the contribution of decision variables (the elements xj, j = 1, …, D of x) to the objective function and the strength of interactions between decision variables. The contribution of decision variables to the objective function is their influence on the goodness of the evaluation. The interaction between decision variables is the dependence of a decision variable value on the goodness of another decision variable value. In this section, the decision variables take real values.

3.2.1 Estimation of the Contribution of Decision Variables to the Objective Function The contribution of decision variables to the objective function is estimated from the scattering of values of the decision variables. Consider the optimization problem consisting of two variables, x1 with a high contribution to the objective function and x2 with a low contribution. Since initial solutions are generated randomly, the solutions in the early stages of the search are widely distributed within the feasible region, regardless of their evaluation. However, as the search progresses, the

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solutions with low evaluation are discarded, and the other surviving solutions converge to the region with high evaluation. Since the value of x2 has little effect on the evaluation, x1 converges preferentially. Thus, the variables that converge more quickly and have smaller scatter are estimated to have a higher contribution to the evaluation (Funaki et al. 2018) (Fig. 7.1). The scatter of values of the decision variable is calculated using entropy. Compared to other measures, entropy is less sensitive to locally optimal solutions. The entropy of the decision variable xj is calculated using a probability density function in Eq. (7.6) that is approximated by a linear combination of Gaussian distributions based on the values of Np decision variables:  ( x − u )2  ij   exp − (7.6) , ∑ 2 2 2σ i =1 2πσ   where uij is the value of xj of the i th solution out of Np solutions, and σ is the standard deviation. The smaller the entropy is, the higher the contribution to the objective function is. 1 p j ( x) = Np

Np

1

3.2.2 Estimation of the Interaction Between Decision Variables The interaction between two decision variables is estimated from eigenvalues and eigenvectors calculated from their covariance matrix. The eigenvalues and eigenvectors indicate the spread and direction of distribution of solutions, respectively. As the search progresses and the solutions converge to regions of high evaluation, the solutions are distributed approximately along the contour lines of the objective function values. Therefore, it is possible to estimate the hem extent of the objective function and the angle to the axis from the eigenvalues and eigenvectors. Figure 7.2 shows the solutions projected onto the plane of the two variables x1 and x2 and the eigenvectors calculated from the covariance matrix for the two variables. Note that the eigenvalues correct the magnitude of the eigenvectors. In the left side of Fig. 7.2, the long eigenvector extending from the lower left to the upper right indicates a strong interaction between x1 and x2. On the other hand, on the right side

Fig. 7.1  Distribution of solutions in the early (left) and middle (right) stages of a search

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Fig. 7.2  Distribution of solutions and their eigenvectors in the middle stage of a search (Left: with interaction, Right: without interaction)

of Fig. 7.2, there is no correlation between x1 and x2, and the interaction is small; however, the eigenvectors incline against the axes. In such cases, it is necessary to note that there is no difference in the distribution spread in each eigenvector direction. The spread of distribution can be measured from the magnitude of the eigenvalues. The indicator of the strength of the interaction, which takes these factors into account, is defined below. The interaction strength dlm between xl and xm is calculated by d lm =

λ1lm s1lm + λ2lm s2lm , λ1lm + λ2lm

(7.7)

where let λklm , k = 1, 2 and vklm be, respectively, the eigenvalues and eigenvectors of the covariance matrix of the two variables xl and xm, and sklm , −1 ≤ sklm ≤ 1 is the slope between the xl-axis and vklm . The closer dlm is to 1 or −1, the stronger the interaction between xl and xm is, and the closer dlm is to 0, the weaker the interaction is. Because of the weighted average of sklm according to magnitudes of the eigenvalues, dlm will be smaller if the magnitudes of the two eigenvalues are close, even if the eigenvectors incline. dlm is calculated for each pair of D decision variables.

3.3 Inverse Optimization and Inverse Reinforcement Learning The results of decisions are the optimal solutions to the optimization problems solved by decision-makers. Estimating the objective function from the optimal solution is an inverse operation of an optimization problem, i.e., an inverse optimization problem. This is estimation of objective functions based on the information of type (C).

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Reinforcement learning (RL) solves multi-stage decision-making problems in Markov decision processes. The evaluation of a state at time t is the reward rt obtained in the state st at that time. The expected value of the sum, over the whole time, of the rewards multiplied by the discount factor γ, 0