A Cooperative Multistep Mutation Strategy for Multiobjective Optimization Problems With Deceptive Constraints

Constrained multiobjective optimization problems with deceptive constraints (DCMOPs) are a kind of complex optimization problems and have received some attention. For DCMOPs, the closer a solution is to the feasible region, the larger its constraint value. Moreover, multiple local infeasible regions will have different minimal constraint values according to their distances to feasible regions. Therefore, most of the existing algorithms are easy to fall into local regions, and even cannot find any feasible solution. To address DCMOPs, this article proposes a new evolutionary multitasking algorithm with a cooperative multistep mutation strategy. In this algorithm, the DCMOP is transformed into a multitasking optimization problem, in which the main task is the original DCMOP and the created auxiliary task aims to provide effective help for solving the main task. Specially, the designed cooperative multistep mutation strategy contains two contributions to solve deceptive constraints. First, a multistep mechanism is proposed, in which the individuals will use multiple different steps to generate the multiple offspring solutions along one direction, so as to expand search range to find feasible regions. Second, a cooperative mechanism between the two tasks is proposed, in which the main purpose is to provide effective and stable search directions. To be specific, an opposite solution generation method is utilized to generate the opposite solution of auxiliary population in the search space, and the direction from the auxiliary population to the main population will be formed. Combined with these two mechanisms, the proposed cooperative multistep mutation strategy can effectively improve the population diversity along the promising and stable search directions. In the experiments, the proposed algorithm is tested on the two benchmark DCMOPs, which contain objective space constraints and decision space constraints respectively. The results show the effectiveness and superiority of the proposed algorithm over the latest compared algorithms.