An analysis of decomposition approaches in multi-objectivization via segmentation |
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| Affiliation: | 1. Air Force Research Laboratory, Area B, 2800 Q Street, Building 824, WPAFB, OH 45433, USA;2. BIE Department, Wright State University, 3640 Colonel Glenn Highway, Dayton, OH 45435, USA;1. British Geological Survey, Edinburgh, EH14 4AP, UK;2. School of GeoSciences, University of Edinburgh, EH9 3FE, UK;1. School of Mathematical Sciences, Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China;2. School of Science, Huaihai Institute of Technology, Lianyungang, Jiangsu 222005, PR China;1. Key Laboratory of Condition Monitoring and Control for Power Plant Equipment, Ministry of Education, North China Electric Power University, Changping District, Beijing 102206, China;2. Institute of Engineering Thermophysics, Chinese Academy of Sciences, Haidian District, Beijing 100190, China;1. Department of Electronics and Communication Engineering, St. Joseph''s College of Engineering, Anna University, Chennai, India;2. Department of Computer Science and Engineering, Anna University, Chennai, India;1. PRESAD Research Group, SEED Research Group, IMUVA, Universidad de Valladolid, Valladolid, Spain;2. Centre for Computational Intelligence, Faculty of Technology, De Montfort University, Leicester, UK;3. DMU Interdisciplinary Group in Intelligent Transport Systems, Faculty of Technology, De Montfort University, Leicester, UK |
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| Abstract: | Multi-objectivization via Segmentation (MOS) has been shown to give improved results over other previous multi-objectivization approaches. This paper explores the mechanisms that make different segmentations in MOS successful in the context of the Traveling Salesman Problem (TSP). A variety of new segmentation methods are analyzed and theories regarding their performance are presented. Spatial segmentation methods are compared with other adaptive and static decomposition methods. Insight into why previous adaptive methods performed well is provided. New decomposition methods are proposed and several of these methods are shown to attain better performance than previously known methods of decomposition. The convergence of various degrees of multi-objectivization is examined leading to a new, more general segmentation algorithm, Multi-Objectivization via Progressive Segmentation (MOPS). MOPS combines the single-objective genetic algorithm with multi-objectivization in a general form. In a given run MOPS can progress from a more traditional single objective method to a strong multi-objectivization method. MOPS attempts to improve the ratio of fitness improvements to fitness decrements, signal-to-noise ratio (SNR), over the course of an evolutionary optimization based on the principle that often fitness improvements are generally easier to find early in the run rather than late in the run. It is shown that MOPS provides robust performance across a variety of problem instances and different computational budgets. |
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| Keywords: | Multi-objectivization Via Decomposition (MVD) Multi-Objectivization via Segmentation (MOS) Multi-Objectivization via Progressive Segmentation (MOPS) Traveling Salesman Problem (TSP) |
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