A tri-population based co-evolutionary framework for constrained multi-objective optimization problems

Balancing between the optimization of objective functions and constraint satisfaction is essential to handle constrained multi-objective optimization problems (CMOPs). Recently, various methods have been presented to enhance the performance for the constrained multi-objective optimization evolutionary algorithms (CMOEAs). However, most of them encounter difficulties when dealing with the CMOPs with complex feasible regions. To overcome this drawback, this paper proposes a tri-population based co-evolutionary framework (TriP): i) the first and second populations are evolved through a weak co-evolutionary relation for the original and unconstrained problems respectively to handle CMOPs with relatively simple constraints; and ii) the third population is evolved solely for the constraint relaxed problem with constraint relaxation technique. The cooperation of three populations preserve the advantages of weak co-evolution and constraint relaxation. Experiments on six benchmark CMOPs with 65 instances and diverse features are performed. Compared to 9 state-of-the-art CMOEAs, the proposed framework yields highly competitive performance and the best versatility. In addition, the effectiveness of the proposed framework on handling real-world CMOPs is also verified.