A Multitask-Assisted Evolutionary Algorithm for Constrained Multimodal Multiobjective Optimization

Constrained multimodal multiobjective optimization problems (CMMOPs) are challenging in the field of optimization, requiring to consider the balance between the constraints and objectives, the balance between exploration and exploitation in the decision space and the objective space, and the balance of diversity between the decision space and the objective space. In this work, we propose a multitask-assisted evolutionary algorithm (CMMO-MTA) to achieve these balances. In CMMO-MTA, a tri-task multitasking framework is proposed, which contains one main task and two assisting tasks. The main task aims to solve the original CMMOP, and two assisting tasks are designed to transfer desired knowledge to the main task to achieve the first two balances. Furthermore, a space balance-based selection mechanism is proposed to ensure a balanced representation of solutions in both the decision space and the objective space, thereby striking the third balance. Experimental studies are conducted on 31 test problems and a real-world application to compare the proposed algorithm with seven state-of-the-art algorithms. The results demonstrate the superiority of CMMO-MTA in solving CMMOPs.