An Adaptive Auxiliary Phase Switching Multi-Task Collaborative Constrained Multi-Objective Optimization Algorithm

To address the critical challenges of premature convergence, insufficient diversity, and constrained boundary search difficulties in constrained multi-objective optimization problems (CMOPs), this paper proposes a novel adaptive auxiliary phase switching multi-task (AAPSMT) optimization algorithm. By evaluating the population state in real time, the algorithm achieves adaptive bidirectional switching between global exploration and local exploitation. It also employs phase-differentiated migration and processing to leverage their complementary strengths, improving population diversity and convergence efficiency. To strengthen search performance near complex constraint boundaries, a local exploitation strategy with adaptive constraint relaxation anchored to the main population’s feasibility is introduced. Additionally, an archive update mechanism guided by reference vectors is developed to enhance the quality and uniformity of the solution distribution. Experimental studies on classical benchmark problems and real-world blast furnace ironmaking processes demonstrate that AAPSMT achieves notable performance advantages and shows strong potential for practical applications.