A novel two-phase evolutionary algorithm for solving constrained multi-objective optimization problems

Abstract

It is challenging to balance convergence and diversity in constrained multi-objective optimization problems (CMOPs) since the complex constraints will disperse the feasible regions into many diverse, small parts of the entire search region. Although there has been some research on CMOPs, existing evolutionary algorithms still cannot cause the evolutionary population to converge a diversified feasible Pareto-optimal front. In order to solve this problem, we propose a novel two-phase evolutionary algorithm for solving CMOPs, named DTAEA. DTAEA divides the population’s coevolutionary process into two phases. In the first phase, the dual population weak coevolution is combined with the complementary environmental selection strategy to improve the algorithm’s exploration under constraints, which makes the evolutionary population quickly traverse the infeasible regions and search for all of the feasible regions. When the proportion of feasible solutions in the population reaches a certain threshold or the convergence of feasible solutions reaches a certain level, the population’s evolutionary process enters the second phase, that is, the progressive phase. In the second phase, a feasibility-oriented method guides a single population to distribute itself widely in the feasible regions explored in the first phase. Comparative experiments show that the DTAEA is more competitive than other algorithms on CMOP benchmarks. • A novel two-phase evolutionary algorithm for solving constrained multi-objective optimization problems is proposed. • The first phase combines dual-population weak coevolution and complementary environmental selection to improve the algorithm’s exploration under constraints. • The second phase adapts a feasibility-oriented method to ensure the diversity of the population in the feasibility regions. • Experiments verify that our proposed algorithm can achieve better all-around performance on several new constrained multi-objective benchmarks.