A constrained multi-objective evolutionary algorithm based on decomposition with improved constrained dominance principle

Abstract

There are various constraints in many real engineering problems, and the constrained handling methods play a key role in the constrained multi-objective evolutionary algorithms (CMOEAs). Many constraint-handling strategies will struggle to reach optimum results when dealing with constrained multi-objective optimization problems (CMOPs) with large and complex infeasible areas. It brings stiffer challenges to CMOEAs in maintaining the convergence, diversity, and feasibility of the population. To remedy these issues, this paper proposes an improved constrained dominance principle (ICDP) embedded in MOEA/D, named MOEA/D-ICDP. In MOEA/D-ICDP, the original weight vector that a solution matches may not be the best suitable weight vector that this solution corresponds to, then there is a deviation between them. According to the above situation, ICDP is designed in this way. Firstly, a dynamic tolerability value about the deviation is introduced. Then ICDP adjusts the dominance relationship of solutions in light of the relationship between the deviation and tolerability so that it can preserve some valuable infeasible solutions in the early evolutionary stage and help the population to cross the large and complex regions. Three test suites and two real-world engineering optimization problems are used to evaluate the performance of the proposed MOEA/D-ICDP and the other five representative CMOEAs. The experimental results demonstrate that MOEA/D-ICDP has more excellent performance and competitiveness than the other five CMOEAs.