Working principles, behavior, and performance of MOEAs on MNK-landscapes Herna ´n E. Aguirre * , Kiyoshi Tanaka Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan Available online 18 September 2006 Abstract This work studies the working principles, behavior, and performance of multiobjective evolutionary algorithms (MOEAs) on multiobjective epistatic fitness functions with discrete binary search spaces by using MNK-landscapes. First, we analyze the structure and some of the properties of MNK-landscapes under a multiobjective perspective by using enu- meration on small landscapes. Then, we focus on the performance and behavior of MOEAs on large landscapes. We orga- nize our study around selection, drift, mutation, and recombination, the four major and intertwined processes that drive adaptive evolution over fitness landscapes. This work clearly shows pros and cons of the main features of MOEAs, gives a valuable guide for the practitioner on how to set up his/her algorithm, enhance MOEAs, and presents useful insights on how to design more robust and efficient MOEAs. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Evolutionary computations; Multiobjective evolutionary algorithms; Multiobjective combinatorial optimization; MNK-land- scapes; Epistasis; Non-linear multiobjective fitness functions; Discrete binary search spaces; Selection; Drift; Mutation; Recombination 1. Introduction Epistasis in the context of evolutionary algo- rithms (EAs) describes non-linearities in fitness functions due to changes in the values of interacting bits. Epistasis is recognized as an important factor that makes a problem difficult for optimization algorithms and its influence on the performance of single objective EAs is being increasingly investi- gated (Davidor, 1991; Manderick et al., 1991; Alten- berg, 1994; De Jong et al., 1997; Altenberg, 1997; Merz and Freisleben, 1998; Heckendorn et al., 1999; Smith and Smith, 1999; Mathias et al., 2001; Aguirre and Tanaka, 2003). Particularly, Kauff- man’s NK-landscapes model of epistatic interac- tions (Kauffman, 1993) has been the center of several studies, both for the statistical properties of the generated landscapes and for their EA-hard- ness. Studies on the behavior of single objective EAs on NK-landscapes have proved useful to advance our understanding of EA’s working princi- ples and served to design robust and better algo- rithms (see Section 2.1). Contrary to the single objective case, studies con- cerning epistasis within the context of multiobjective optimization are quite few and its effects are still far from being well understood. Due to the characteris- tics and requirements particular to multiobjective 0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2006.08.004 * Corresponding author. E-mail addresses: ahernan@shinshu-u.ac.jp (H.E. Aguirre), ktanaka@shinshu-u.ac.jp (K. Tanaka). European Journal of Operational Research 181 (2007) 1670–1690 www.elsevier.com/locate/ejor