Pattern Identification in Pareto-Set Approximations

Abstract

In a multiobjective setting, evolutionary algorithms can be used to generate a set of compromise solutions. This makes decision making easier for the user as he has alternative solutions at hand which he can directly compare. However, if the number of solutions and the number of decision variables which define the solutions are large, such an analysis may be difficult and corresponding tools are desirable to support a human in separating relevant from irrelevant information. In this paper, we present a method to extract structural information from Pareto-set approximations which offers the possibility to present and visualize the trade-off surface in a compressed form. The main idea is to identify modules of decision variables that are strongly related to each other. Thereby, the set of decision variables can be reduced to a smaller number of significant modules. Furthermore, at the same time the solutions are grouped in a hierarchical manner according to their module similarity. Overall, the output is a dendrogram where the leaves are the solutions and the nodes are annotated with modules. As will be shown on knapsack problem instances and a network processor design application, this method can be highly useful to reveal hidden structures in compromise solution sets.