Many-Objective Evolutionary Algorithm with Vector Angle Selection and Indicator Deletion

Abstract

Given that the challenge for evolutionary algorithms when solving many-objective optimization problems lies in balancing the convergence and diversity, a many-objective evolutionary algorithm based on vector angle selection and indicator deletion (MOEA/AS-ID), is proposed. In this algorithm, a coordinated mechanism that includes two strategies is designed in the environmental selection process to delete the solutions with poor convergence and diversity one by one, retaining the elitist to participate in the evolution process for the next generation. To be specific, the former strategy based on vector angle selection is used to select a pair of solutions with a similar search direction in the objective space, and the latter indicator-based deletion strategy which uses the [ISDE+] indicator (indicator shift-based density estimation) that takes into account the convergence and diversity of a single solution, is employed to compare the selected pair of solutions and delete the solution with a smaller indicator value, then encourage the population to converge to the Pareto optimal front toward all directions. Finally, the balance between convergence and diversity of the solution set is achieved. On DTLZ (Deb-Thiele-Laumanns-Zitzler), SDTLZ (scaled DTLZ), and MaF (many-objective function) three benchmark test suites with various characteristics，MOEA/AS-ID and six recently proposed many-objective evolutionary algorithms covering all current types perform extensive comparative simulation experiments and numerical results analysis. Simulation results and numerical analysis show that MOEA/AS-ID has strong competitiveness in balancing the convergence and diversity when solving many-objective optimization problems with various characteristics.

Keywords

• evolutionary algorithm; many-objective optimization; vector angle selection; indicator deletion; conver-gence; diversity