Multi-stage multiform optimization for constrained multi-objective optimization.

The use of evolutionary algorithms to solve constrained multi-objective optimization problems (CMOPs) with various characteristics and difficulties obtains considerable attention. Most of existing methods tend to introduce an alternate formulation to simplify the original problem and facilitate the solving, which corresponds to the methodology of multiform optimization. Inspired by multiform optimization, this paper proposes a multi-stage multiform optimization framework to solve CMOPs. To prevent the population from falling into local optima in the early stages of evolution, we construct an alternate formulation that ignores all constraints. Meanwhile, in order to utilize high-quality infeasible solutions to explore more feasible regions, we construct another alternate formulation by using a constraint relaxation technique that analyzes the relationships between constraints, evaluating important constraints, and ignoring unimportant constraints. The two formulations provide exclusive and complementary searches in the objective space with the help of knowledge transfer. As both alternate formulations are designed to find the unconstrained Pareto front in the early stages and the final goal must be finding the constrained Pareto front, a multi-stage strategy is devised. Different numbers of alternate formulations are used at different stages to allocate computational resources more effectively. In addition, we propose a hybrid operator strategy to improve the performance of the algorithm by combining the advantages of different operators. Then, 33 instances and 18 real-world CMOPs are selected to evaluate the performance of the algorithm. Experimental results demonstrate the superiority or competitiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]