A multi-stage algorithm for solving multi-objective optimization problems with multi-constraints

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.There are usually multiple constraints in constrained multi-objective optimization. Those constraints reduce the feasible area of the constrained multi-objective optimization problems (CMOPs) and make it difficult for current multi-objective optimization algorithms (CMOEAs) to obtain satisfactory feasible solutions. In order to solve this problem, this paper 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 paper proposes a multi-stage 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 paper can have strong competitiveness in existing constrained multi-objective optimization