Discrete Optimization An empirical study on similarity-based mating for evolutionary multiobjective combinatorial optimization Hisao Ishibuchi * , Kaname Narukawa, Noritaka Tsukamoto, Yusuke Nojima Department of Computer Science and Intelligent Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan Received 14 February 2006; accepted 9 April 2007 Available online 19 April 2007 Abstract We have already proposed a similarity-based mating scheme to recombine extreme and similar parents for evolutionary multiobjective optimization. In this paper, we examine the effect of the similarity-based mating scheme on the performance of evolutionary multiobjective optimization (EMO) algorithms. First we examine which is better between recombining sim- ilar or dissimilar parents. Next we examine the effect of biasing selection probabilities toward extreme solutions that are dissimilar from other solutions in each population. Then we examine the effect of dynamically changing the strength of this bias during the execution of EMO algorithms. Computational experiments are performed on a wide variety of test prob- lems for multiobjective combinatorial optimization. Experimental results show that the performance of EMO algorithms can be improved by the similarity-based mating scheme for many test problems. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Multiple objective programming; Combinatorial optimization; Evolutionary computation; Genetic algorithms 1. Introduction Since Schaffer’s pioneering study (Schaffer (1985)), evolutionary algorithms have been applied to various multiobjective optimization problems for finding their Pareto-optimal solutions (e.g., see Deb (2001), Coello et al. (2002), and Coello and Lamont (2004)). Those algorithms are often referred to as evolutionary multiobjective optimization (EMO) algorithms. Recent EMO algorithms usually share some common ideas such as Pareto ranking, diversity preserving and elitism. While mating restriction has often been discussed in the literature, it has not been used in many EMO algorithms as pointed out in some reviews on EMO algorithms (e.g., see Fonseca and Fleming (1995), Zitzler and Thiele (1999), and Van Veldhuizen and Lamont (2000)). Mating restriction was suggested by Goldberg (1989) for single-objective genetic algorithms. Hajela and Lin (1992) and Fonseca and Fleming (1993) used it in their EMO algorithms. The basic idea of mating restriction is to ban the recombination of dis- similar parents from which good offspring are not likely to be generated. In the implementation of mat- ing restriction, a user-definable parameter r mating 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.04.007 * Corresponding author. Tel.: +81 72 254 9350; fax: +81 72 254 9915. E-mail address: hisaoi@cs.osakafu-u.ac.jp (H. Ishibuchi). Available online at www.sciencedirect.com European Journal of Operational Research 188 (2008) 57–75 www.elsevier.com/locate/ejor