Localized Constrained-Domination Principle for Constrained Multiobjective Optimization

Abstract

The constrained-domination principle (CDP) is one of the most popular constraint-handling techniques (CHTs), since it is simple, nonparametric, and easily embedded in unconstrained multiobjective evolutionary algorithms (MOEAs). However, the CDP overly emphasizes the importance of feasibility, which may lead to the search getting stuck in some locally feasible regions or locally optimal, especially when encountering problems with discontinuous and/or narrow feasible regions. This article seeks to capitalize on the strengths of the CDP while overcoming its weaknesses. Accordingly, we propose a novel constrained MOEA (called MOEA/D-LCDP), in which the CDP is applied in a local manner. Unlike most CHTs that emphasize feasibility, which use the feasibility rule in the whole search space, the proposed localized CDP only adopts the CDP within the niche. That is, to maintain the diversity of the population, only solutions within the niche are compared based on the localized CDP. The niche radius is determined a priori by the acute angle between the current subproblem and its nearest subproblem. Additionally, a population-based status detection strategy is developed to allocate computing resources more rationally, and a diversity-enhanced CDP is designed to enhance the exploitation of the search. Comprehensive experiments conducted on four benchmark test suites with a total of 34 problems and three real-world applications demonstrate that MOEA/D-LCDP is very competitive with representative algorithms.