A many-objective evolutionary algorithm with metric-based reference vector adjustment

To deal with the inconsistency of the distribution of reference vectors (RVs) and the shape of Pareto front in decomposition-based multiobjective evolutionary algorithms, many literatures proposed to adjust RVs in evolutionary process. However, most of the existing algorithms adjust RVs either in each generation or at a fixed frequency, not considering the evolving information of the population. To tackle this issue, we propose a many-objective evolutionary algorithm with metric-based reference vector adjustment named MBRA. To adjust RVs periodically and conditionally, we use the improvement rate of convergence degree of subproblems computed through d1 distance to reflect the whole convergence of the population. Only when the subproblems are considered convergent on the whole, are RVs allowed to be adjusted: delete the invalid RVs associated with no solutions and add new ones using the farthest solution in the subregion of the most crowded RVs for diversity. Besides, in mating selection and environmental selection, we adopt the sum of objectives and fitness-based sorting based on Iε+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{\varepsilon + }$$\end{document} as the secondary principles to promote convergence, respectively. Validated through extensive experiments, MBRA is effective and competitive on many-objective optimization problems, especially for problems with irregular Pareto fronts.