A Multi-task Framework for Solving Multimodal Multiobjective Optimization Problems

In multimodal multiobjective optimization problems, there may have more than one Pareto optimal solution corresponding to the same objective vector. The key is to find solutions converged and well-distributed. Even though the existing evolutionary multimodal multiobjective algorithms have taken both the distance in the decision space and objective space into consideration, most of them still focus on convergence property. This may omit some regions difficult to search in the decision space during the process of converging to the Pareto front. In order to resolve this problem and maintain the diversity in the whole process, we propose a differential evolutionary algorithm in a muti-task framework (MT-MMEA). This framework uses an \(\varepsilon \)-based auxiliary task only concerning the diversity in decision space and provides well-distributed individuals to the main task by knowledge transfer method. The main task evolves using a non-dominated sorting strategy and outputs the final population as the result. MT-MMEA is comprehensively tested on two MMOP benchmarks and compared with six state-of-the-art algorithms. The results show that our algorithm has a superior performance in solving these problems.