Reference-lines-steered memetic multi-objective evolutionary algorithm with adaptive termination criterion

Multi-objective evolutionary algorithms (MOEAs) have been the choice for generating a set of Pareto-optimal (PO) solutions in one run. However, these algorithms sometimes suffer slow and poor convergence toward the PO front. One of the remedies to improve their convergence is to couple global search of MOEAs with local search. However, such coupling brings other implementation challenges, such as what, when, and how many solutions can be chosen for local search with MOEAs? In this paper, these challenges are addressed by developing a local search module that can choose solutions for local search using a set of reference lines. The heuristic strategies are also developed with the module for determining the frequency of executing local search and for terminating MOEA adaptively using a statistical performance indicator. The proposed algorithm, which is referred to as RM2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {RM}}^2$$\end{document}OEA, is tested on 2-objective ZDT and 3-objective DTLZ test problems. Results demonstrate faster and improved convergence of RM2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {RM}}^2$$\end{document}OEA over a benchmark MOEA from the literature.