Enhancing Constrained Multi-Objective Optimization via Knowledge Transfer and Co-Evolution

Abstract In constrained multi-objective optimization problems (CMOPs), two critical challenges persist for existing algorithms: effectively traversing infeasible regions based on problem-specific characteristics and utilizing auxiliary populations for efficient knowledge transfer to enhance solution set feasibility, convergence, and diversity. This paper proposes a novel approach, called Enhancing Knowledge Transfer Evolutionary Multi-Objective Optimization (EKTEMO), which exploits the set relationship between the constrained Pareto front (CPF) and the unconstrained Pareto front (UPF) to enhance knowledge transfer. EKTEMO adopts a two-population co-evolutionary strategy. During the learning phase, specialized evolutionary operators guide the independent evolution of both the CPF and UPF populations. Feasibility and non-dominance criteria are used to determine the relationship type between the two populations. In the evolutionary phase, each population is assigned a distinct evolutionary operator based on the type of problem. The main population continues to focus on obtaining CPF, while the auxiliary populations adapt and support this goal through different strategies or complementary functions. In addition, an appropriate knowledge transfer mechanism is selected based on the effectiveness of knowledge from parents and offspring. This ensures that the main population can efficiently utilize information from the auxiliary population to generate feasible, convergent, and diverse solutions. Comprehensive experiments across 46 benchmark test functions and 10 real-world problems, comparing EKTEMO with nine state-of-the-art algorithms, demonstrate its superior performance in terms of inverted generational distance and hypervolume, as confirmed by Wilcoxon rank-sum test results. These findings underscore the effectiveness and robustness of EKTEMO in solving CMOPs.