A constrained multi-objective optimization algorithm with adaptive dual-stage search strategy utilizing the relationship between different Pareto fronts

Multi-stage dual-population constrained evolutionary algorithms (MDCMOEAs) demonstrate competitive performance in solving constrained multi-objective optimization problems (CMOPs). In these algorithms, the main population addresses the original problem, while the auxiliary population solves the helper problem across multiple stages, including both unconstrained and constrained stages. However, MDCMOEAs face challenges in effectively searching the constrained Pareto front (CPF) that overlaps with the unconstrained Pareto front (UPF), particularly when feasible regions are small or disconnected. This difficulty arises because the auxiliary population considers constraints in some stages, making it susceptible to becoming trapped in local feasible regions. To overcome this challenge, this paper proposes an algorithm with an adaptive dual-stage search strategy (ADSSCMO). First, an improved $ϵ$-constraint method is developed for the main population to tackle the original CMOPs. Second, an adaptive dual-stage search strategy is designed for the auxiliary population. This strategy dynamically evaluates the relationship between UPF and CPF and determines whether to solve the unconstrained or constrained problem. Extensive experiments on four test suites and seven real-world problems demonstrate that the proposed algorithm is more competitive than seven state-of-the-art CMOEAs.