A reference direction and entropy based evolutionary algorithm for many-objective optimization

Abstract

Evolutionary algorithms have been successfully applied in dealing with multi-objective optimization problems with two or three objectives. However, when solving the problem with more than 3 objectives (also called as many-objective optimizing problem), most multi-objective evolutionary algorithms perform poorly due to the ineffectiveness of Pareto dominance relationship in a high-dimensional space, and the diversity maintenance mechanism usually leads the population to be far from the true Pareto front. In this paper, a novel approach is proposed to handle the challenges in the many-objective optimization problem. Firstly, a grid-based approach is adopted to eliminate dominance resistant solutions which are non-dominated solutions with excellent diversity while incur the dominance resistance and lead the population far from the true Pareto front. Secondly, a new diversity maintenance mechanism based on reference directions is proposed, which not only enhances the diversity but also takes the convergence into consideration. For a domination- relationship based MOEA hardly has enough convergence capability for a high-dimension optimizing problem, our approach embeds convergence capability into the diversity maintenance process, and balances the convergence and diversity capability according to evolutionary states and Pareto entropy. The proposed algorithm is evaluated on a number of standard benchmark functions, i.e., DTLZ1-7 and WFG1-9 with 3-, 4-, 5-, 8-, 10-objective and compared with 5 state-of-the-art Many-Objective Evolutionary Algorithms (MaOEAs). Experimental results demonstrate the proposed algorithm’s competitiveness in both convergence and diversity in solving Many-Objective Optimization Problems.