Introducing multiobjective complex systems |
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| Institution: | 1. Department of Mathematics, Technische Universität Kaiserslautern, Germany;2. School of Mathematics and Natural Sciences, University of Wuppertal, Germany;3. Department of Mathematical Sciences, Clemson University, SC, USA;1. College of Auditing and Evaluation, Nanjing Audit University, Nanjing, Jiangsu Province, 211815, China;2. Schulich School of Business, York University, Toronto, Ontario M3J 1P3, Canada;3. Foisie Business School, Worcester Polytechnic Institute, Worcester, MA 01609, USA;1. School of Economic Mathematics and Collaborative Innovation Center of Financial Security, Southwestern University of Finance and Economics, Chengdu 611130, China;2. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China;3. Department of Mathematics, Imperial College, London SW7 2BZ, UK;1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia;1. Instituto de Matemática y Ciencias Afines, Lima, Peru;2. Instituto de Telecomunicações and CIDMA, Universidade de Aveiro, Aveiro, Portugal;3. Laboratoire Informatique d’Avignon, Avignon Université, Avignon,France;1. Department of Logistics Management, School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China;2. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Special Administrative Region;1. Universidad Pontificia Comillas, ICADE. c/ Alberto Aguilera 23, 28015 Madrid, Spain;2. Department of Economics, Universidad Carlos III de Madrid. Calle Madrid, 126, Getafe, E-28903 Madrid, Spain |
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| Abstract: | This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multiple objectives, local constraints as well as local variables, and they are associated with an own, subsystem-dependent decision maker. On the other hand, these subsystems are interconnected to each other by global variables or linking constraints. Due to these interdependencies, it is in general not possible to simply optimize each subsystem individually to improve the performance of the overall system. This article introduces a formal graph-based representation of such complex systems and generalizes the classical notions of feasibility and optimality to match this complex situation. Moreover, several algorithmic approaches are suggested and analyzed. |
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