Constraints Separation Based Evolutionary Multitasking for Constrained Multi-Objective Optimization Problems

Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.

Multiobjective Differential Evolution for Higher-Dimensional Multimodal Multiobjective Optimization

In multimodal multiobjective optimization problems(MMOPs),there are several Pareto optimal solutions corre-sponding to the identical objective vector.This paper proposes a new differential evolution algorithm to solve MMOPs with higher-dimensional decision variables.Due to the increase in the dimensions of decision variables in real-world MMOPs,it is diffi-cult for current multimodal multiobjective optimization evolu-tionary algorithms(MMOEAs)to find multiple Pareto optimal solutions.The proposed algorithm adopts a dual-population framework and an improved environmental selection method.It utilizes a convergence archive to help the first population improve the quality of solutions.The improved environmental selection method enables the other population to search the remaining decision space and reserve more Pareto optimal solutions through the information of the first population.The combination of these two strategies helps to effectively balance and enhance conver-gence and diversity performance.In addition,to study the per-formance of the proposed algorithm,a novel set of multimodal multiobjective optimization test functions with extensible decision variables is designed.The proposed MMOEA is certified to be effective through comparison with six state-of-the-art MMOEAs on the test functions.