A Multistage Algorithm for Solving Multiobjective Optimization Problems With Multiconstraints

There are usually multiple constraints in constrained multiobjective optimization. Those constraints reduce the feasible area of the constrained multiobjective optimization problems (CMOPs) and make it difficult for current multiobjective optimization algorithms (CMOEAs) to obtain satisfactory feasible solutions. In order to solve this problem, this article studies the relationship between constraints, then obtains the priority between constraints according to the relationship between the pareto front (PF) of the single constraint and their common PF. Meanwhile, this article proposes a multistage CMOEA and applies this priority, which can save computing resources while helping the algorithm converge. The proposed algorithm completely abandons the feasibility in the early stage to better explore the objective space, and obtains the priority of constraints according to the relationship. Then, the algorithm evaluates a single constraint in the medium stage to further explore the objective space according to this priority, and abandons the evaluation of some less important constraints according to the relationship to save the evaluation times. At the end stage of the algorithm, the feasibility will be fully considered to improve the quality of the solutions obtained in the first two stages, and finally get the solutions with good convergence, feasibility, and diversity. The results on five CMOP suites and three real-world CMOPs show that the algorithm proposed in this article can have strong competitiveness in existing constrained multiobjective optimization.