A constrained multiobjective evolutionary algorithm based on adaptive constraint regulation

Many constrained multiobjective evolutionary algorithms have been proposed in recent years. However, different regions of a multiobjective optimization problem may have different difficulties in meeting constraints, which leads to an unbalanced search on different regions. Currently, there is a lack of research in this area. Considering that different regions may require different strategies to balance the feasibility and convergence of solutions, this paper proposes an adaptive constraint regulation method to adjust the constraint violation of an infeasible solution by its K-nearest neighbors. This work achieves different evaluations of the constraint violation for these infeasible solutions in different regions. The population is updated by using the constraint dominance principle according to the regulated constraint violation. Some infeasible solutions that have the smallest constraint violation among their K-nearest neighbors are treated as feasible solutions. It is helpful for us to leverage the information of these valuable infeasible solutions. Furthermore, an adaptive mechanism is presented to adjust the size K of the neighbors according to the number of generations and the number of feasible solutions in the current population. Comparative studies on forty-one benchmark test instances clearly show that the proposed algorithm can effectively balance the feasibility, convergence, and diversity of the solutions.