A Dual-Population-Based Evolutionary Algorithm for Constrained Multiobjective Optimization

Abstract

The main challenge in constrained multiobjective optimization problems (CMOPs) is to appropriately balance convergence, diversity and feasibility. Their imbalance can easily cause the failure of a constrained multiobjective evolutionary algorithm (CMOEA) in converging to the Pareto-optimal front with diverse feasible solutions. To address this challenge, we propose a dual-population-based evolutionary algorithm, named c-DPEA, for CMOPs. c-DPEA is a cooperative coevolutionary algorithm which maintains two collaborative and complementary populations, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population1</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population2</i> . In c-DPEA, a novel self-adaptive penalty function, termed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">saPF</i> , is designed to preserve competitive infeasible solutions in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population1</i> . On the other hand, infeasible solutions in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Population2</i> are handled using a feasibility-oriented approach. To maintain an appropriate balance between convergence and diversity in c-DPEA, a new adaptive fitness function, named <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bCAD</i> , is developed. Extensive experiments on three popular test suites comprehensively validate the design components of c-DPEA. Comparison against six state-of-the-art CMOEAs demonstrates that c-DPEA is significantly superior or comparable to the contender algorithms on most of the test problems.