Insights on properties of multiobjective MNK-landscapes

The influence of epistasis on the performance of evolutionary algorithms (EAs) is being increasingly investigated for single objective combinatorial optimization problem. Kauffman's NK-landscapes model of epistatic interactions, particularly, has been the center of several studies and is considered as a good test problem generator. However, epistasis and NK-landscapes in the context of multiobjective evolutionary algorithm (MOEAs) are almost unexplored subjects. In this work we present an extension of Kauffman's NK-landscapes model of epistatic interactions to multiobjective MNK-landscapes. MNK-landscapes present several desirable features and hold the potential of becoming an important class of scalable test problems generator for multiobjective combinatorial optimization. In order to meaningfully use MNK-landscapes as a benchmark tool we first need to understand how the parameters of the landscapes relate to multiobjective concepts. This paper is a first step towards understanding the properties of MNK-landscapes from a multiobjective standpoint.