Constrained multi-objective optimization assisted by convergence and diversity auxiliary tasks

In the field of constrained multi-objective optimization, constructing auxiliary tasks can guide the algorithm to achieve efficient search. Different forms of auxiliary tasks have their own advantages, and a reasonable combination can effectively improve the performance of the algorithm. Inspired by this, a Constrained Multi-objective Optimization Evolutionary Algorithm based on Convergence and Diversity auxiliary Tasks (CMOEA-CDT) is proposed. This algorithm achieves efficient search through simultaneous optimization and knowledge transfer of the main task, convergence auxiliary task, and diversity auxiliary task. Specifically, the main task is to find feasible Pareto front, which improves the global exploration and local exploitation of the algorithm through knowledge transfer from the convergence and diversity auxiliary tasks. In addition, the convergence auxiliary task helps the main task population traverse infeasible obstacles by ignoring constraints to achieve global search. The diversity auxiliary task aims to provide local diversity to the regions around the main task population to exploit promising search regions. The convergence and diversity of the algorithm are significantly improved by knowledge transfer between the convergence auxiliary task, diversity auxiliary task, and main task. CMOEA-CDT is compared with five state-of-the-art constrained multi-objective evolutionary optimization algorithms on 37 benchmark problems and a disc brake engineering design problem. The experimental results indicate that the proposed CMOEA-CDT respectively obtains 19 and 20 best results on the two indicators, and achieves the best performance on disc brake engineering design problem.