Two-stage multi-population evolutionary algorithm for constrained multi-objective optimization

The key to solving the constrained multi-objective optimization problems (CMOPs) via evolutionary algorithm is to rapidly converge the population to the constrained Pareto front (PF) while ensuring the population’s diversity. However, it is challenging to trade off the convergence, diversity, and feasibility of population, in other words, balance the objective optimization and constraint satisfaction. With this in mind, we propose a two-stage multi-population evolutionary algorithm in this paper to try to balance them via the synergy of different stages and coevolution of three populations, namely, the main population that stores feasible solutions, the auxiliary population that stores non-dominated solutions ignoring constraints, and the archive population that stores promising infeasible solutions. The first stage mainly focuses on objective optimization by pushing solutions toward the constrained PF(s) from both the feasible and infeasible sides while maintaining the population’s diversity. The second stage shifts its focus to constraint satisfaction, thus it is dedicated to fine-turning feasible and promising infeasible solutions toward the constrained PF(s) as well as evenly distributing them on the constrained PF(s). The experimental results on 4 benchmark suites containing up to 47 instances show that the proposed algorithm is competitive in solving CMOPs.