A Multiform Optimization Framework for Constrained Multiobjective Optimization.

Constrained multiobjective optimization problems (CMOPs) pose great difficulties to the existing multiobjective evolutionary algorithms (MOEAs), in terms of constraint handling and the tradeoffs between diversity and convergence. The constraints divide the search space into feasible and infeasible regions. A key to solving CMOPs is how to effectively utilize the information of both feasible and infeasible solutions during the optimization process. In this article, we propose a multiform optimization framework to solve a CMOP task together with an auxiliary CMOP task in a multitask setting. The proposed framework is designed to conduct a search in different sizes of feasible space that is derived from the original CMOP task. The derived feasible space is easier to search and can provide a useful inductive bias to the search process of the original CMOP task, by leveraging the transferable knowledge shared between them, thereby helping the search to toward the Pareto optimal solutions from both the infeasible and feasible regions of the search space. The proposed framework is instantiated in three kinds of MOEAs: 1) dominance-based; 2) decomposition-based; and 3) indicator-based algorithms. Experiments on four sets of benchmark test problems demonstrate the superiority of the proposed method over four representative constraint-handling techniques. In addition, the comparison against five state-of-the-art-constrained MOEAs demonstrates that the proposed approach outperforms these contender algorithms. Finally, the proposed method is successfully applied to solve a real-world antenna array synthesis problem.