Clusters of Non-dominated Solutions in Multiobjective Combinatorial Optimization: An Experimental Analysis

Abstract

This paper presents an analysis on the level of clustering of approximate non-dominated solutions for several instances of the Biobjective Travelling Salesman Problem and the Biobjective Quadratic Assignment Problem. The sets of approximate non-dominated solutions are identified by high performing stochastic local search algorithms. A cluster is here defined as a set of non-dominated solutions such that for any solution of the set there is at least one other that is at a maximum distance k for a given neighborhood function. Of Particular interest is to find k for which all approximate non-dominated solutions are in a single cluster. The results obtained from this analysis indicate that the degree of clustering depends strongly on the problem but also on the type of instances of each problem. These insights also suggest that different general-purpose search strategies should be used for the two problems and also for different instance features.KeywordsCombinatorial optimizationLocal searchMultiobjective programming