A Dynamic Tri-Stage Framework with Neural Network-Assisted Search for Constrained Multi-objective Optimization

Constrained multi-objective optimization problems involve the optimization of multiple objective functions and the satisfaction of different constraints, which poses a challenge for algorithms to achieve a good balance between convergence and diversity. However, indiscriminately enhancing diversity can hinder convergence, while solely focusing on convergence may impair the exploration of the objective space, especially when the current stage is not well-defined. To address this issue, we propose a three-stage multi-task framework for constrained multi-objective optimization with dynamically switchable stages. This framework introduces two auxiliary tasks: one that operates during the exploration and transition stages to accelerate convergence towards the boundary of the infeasible regions and assist the population in crossing it, and another that operates in the final convergence stage to guide the population towards the constrained Pareto front. Moreover, a stage detection method is proposed, which evaluates the current stage to determine the appropriate evolutionary direction for the population, thus enabling dynamic stage transitions. In addition, a neural network-assisted search operator is designed for the auxiliary task during the transition stage, which learns the optimal offspring generation process. This operator enhances the ability of the auxiliary population to cross the infeasible regions. Finally, the performance of the proposed algorithm is superior and competitive on three test suites and six real-world engineering problems compared to seven state-of-the-art algorithms.