Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems View Full Text


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Article Info

DATE

2012-04-15

AUTHORS

Hiroyuki Sato, Hernán Aguirre, Kiyoshi Tanaka

ABSTRACT

In this work, we analyze variable space diversity of Pareto optimal solutions (POS) and study the effectiveness of crossover and mutation operators in evolutionary many-objective optimization. First we examine the diversity of variables in the true POS on many-objective 0/1 knapsack problems with up to 20 items (bits), showing that variables in POS become noticeably diverse as we increase the number of objectives. We also verify the effectiveness of conventional two-point and uniform crossovers, Local Recombination that selects mating parents based on proximity in objective space, and two-point and uniform crossover operators which Controls the maximum number of Crossed Genes (CCG). We use NSGA-II, SPEA2, IBEAϵ + and MSOPS, which adopt different selection methods, and many-objective 0/1 knapsack problems with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n=\{100,250,500,750,\mbox{1,000}\}$\end{document} items (bits) and m = {2,4,6,8,10} objectives to verify the search performance of each crossover operator. Simulation results reveal that Local Recombination and CCG operators significantly improve search performance especially for NSGA-II and MSOPS, which have high diversity of genes in the population. Also, results show that CCG operators achieve higher search performance than Local Recombination for m ≥ 4 objectives and that their effectiveness becomes larger as the number of objectives m increases. In addition, the contribution of CCG and mutation operators for the solutions search is analyzed and discussed. More... »

PAGES

197-224

References to SciGraph publications

  • 2004. Mating Scheme for Controlling the Diversity-Convergence Balance for Multiobjective Optimization in GENETIC AND EVOLUTIONARY COMPUTATION – GECCO 2004
  • 2012. A Study on Large Population MOEA Using Adaptive ε-Box Dominance and Neighborhood Recombination for Many-Objective Optimization in LEARNING AND INTELLIGENT OPTIMIZATION
  • 2007-01-01. Optimization of Scalarizing Functions Through Evolutionary Multiobjective Optimization in EVOLUTIONARY MULTI-CRITERION OPTIMIZATION
  • 2010. Self-Controlling Dominance Area of Solutions in Evolutionary Many-Objective Optimization in SIMULATED EVOLUTION AND LEARNING
  • 2007-01-01. Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization in EVOLUTIONARY MULTI-CRITERION OPTIMIZATION
  • 2011-09-03. Multi-objective Optimisation Using Evolutionary Algorithms: An Introduction in MULTI-OBJECTIVE EVOLUTIONARY OPTIMISATION FOR PRODUCT DESIGN AND MANUFACTURING
  • 2010. Alternative Fitness Assignment Methods for Many-Objective Optimization Problems in ARTIFICAL EVOLUTION
  • 2004. Indicator-Based Selection in Multiobjective Search in PARALLEL PROBLEM SOLVING FROM NATURE - PPSN VIII
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s10472-012-9293-y

    DOI

    http://dx.doi.org/10.1007/s10472-012-9293-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1000508369


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