A Multi-Objective Evolutionary Algorithm With Hierarchical Clustering-Based Selection

Abstract

This paper proposes an evolutionary algorithm with hierarchical clustering based selection for multi-objective optimization. In the proposed algorithm, a hierarchical clustering is employed to design the environmental and mating selections, named local coverage selection and local area selection, respectively, for multi-objective evolutionary algorithm. The local coverage selection strategy aims to preserve well-distributed individuals with good convergence. While, the local area selection strategy is devised to deliver a balanced evolutionary search. This is achieved by encouraging individuals for exploration or exploitation according to the $I_{\epsilon }+$ indicator. In both strategies, a hierarchical clustering method is employed to discover the population structure. Based on the clustering results, in local coverage selection, the individuals of different clusters will be retained according to their coverage areas and crowding distances, such that distributing as evenly as possible in the Pareto front. In local area selection, the individual(s) with the best value of $I_{\epsilon }+$ indicator in each cluster will be selected to perform mating, with the purpose of achieving a balanced exploration and exploitation. The proposed algorithm has been evaluated on 26 bench-mark problems and compared with related methods. The results clearly show the significance of the proposed method.

Keywords

• Multi-objective evolutionary algorithm
• multi-objective optimization problem
• hierarchical clustering