A Pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation

Abstract

Evolutionary algorithms (EAs) have shown to be efficient in dealing with many-objective optimization problems (MaOPs) due to their ability to obtain a set of compromising solutions which not only converge toward the Pareto front (PF), but also distribute well. The Pareto-based multi-objective evolutionary algorithms are valid for solving optimization problems with two and three objectives. Nevertheless, when they encounter many-objective problems, they lose their effectiveness due to the weakening of selection pressure based on the Pareto dominance relation. Our major purpose is to develop more effective diversity maintenance mechanisms which cover convergence besides dominance in order to enhance the Pareto-based many-objective evolutionary algorithms. In this paper, we propose a Pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation, abbreviated as SPSAT. The space partitioning selection increases selection pressure and maintains diversity simultaneously, which we realize through firstly dividing the normalized objective space into many subspaces and then selecting only one individual with the best proximity estimation value in each subspace. To further enhance convergence and diversity, the angle-based truncation calculates the angle values of any pair of individuals in the critical layer and then gradually removes the individuals with the minimum angle values. From the comparative experimental results with six state-of-the-art algorithms on a series of well-defined optimization problems with up to 20 objectives, the proposed algorithm shows its competitiveness in solving many-objective optimization problems.