Recombination of Similar Parents in EMO Algorithms

This paper examines the effect of crossover operations on the performance of EMO algorithms through computational experiments on knapsack problems and flowshop scheduling problems using the NSGA-II algorithm. We focus on the relation between the performance of the NSGA-II algorithm and the similarity of recombined parent solutions. First we show the necessity of crossover operations through computational experiments with various specifications of crossover and mutation probabilities. Next we examine the relation between the performance of the NSGA-II algorithm and the similarity of recombined parent solutions. It is shown that the quality of obtained solution sets is improved by recombining similar parents. Then we examine the effect of increasing the selection pressure (i.e., increasing the tournament size) on the similarity of recombined parent solutions. An interesting observation is that the increase in the tournament size leads to the recombination of dissimilar parents, improves the diversity of solutions, and degrades the convergence performance of the NSGA-II algorithm.

[1]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

[2]  Hisao Ishibuchi,et al.  A Similarity-Based Mating Scheme for Evolutionary Multiobjective Optimization , 2003, GECCO.

[3]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[4]  Yaochu Jin,et al.  A Critical Survey of Performance Indices for Multi-Objective Optimisation , 2003 .

[5]  Joshua D. Knowles,et al.  On metrics for comparing nondominated sets , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[6]  Tomoyuki Hiroyasu,et al.  SPEA2+: Improving the Performance of the Strength Pareto Evolutionary Algorithm 2 , 2004, PPSN.

[7]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[8]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[9]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[10]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithm test suites , 1999, SAC '99.

[11]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[12]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[13]  Piotr Czyzżak,et al.  Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization , 1998 .

[14]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[15]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[16]  Hisao Ishibuchi,et al.  Mating Scheme for Controlling the Diversity-Convergence Balance for Multiobjective Optimization , 2004, GECCO.

[17]  D. Corne,et al.  On Metrics for Comparing Non Dominated Sets , 2001 .

[18]  Hisao Ishibuchi,et al.  An Empirical Study on the Effect of Mating Restriction on the Search Ability of EMO Algorithms , 2003, EMO.

[19]  Prabhat Hajela,et al.  Genetic search strategies in multicriterion optimal design , 1991 .

[20]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[21]  Bernhard Sendhoff,et al.  A critical survey of performance indices for multi-objective optimisation , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[22]  Chien-Feng Huang,et al.  Using an Immune System Model to Explore Mate Selection in Genetic Algorithms , 2003, GECCO.

[23]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[24]  Hisao Ishibuchi,et al.  Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling , 2003, IEEE Trans. Evol. Comput..

[25]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[26]  Riccardo Poli,et al.  Genetic and Evolutionary Computation – GECCO 2004 , 2004, Lecture Notes in Computer Science.

[27]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[28]  Kalyanmoy Deb,et al.  Parallelizing multi-objective evolutionary algorithms: cone separation , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[29]  Andrzej Jaszkiewicz,et al.  On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment , 2002, IEEE Trans. Evol. Comput..

[30]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[31]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[32]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..