Balancing performance between the decision space and the objective space in multimodal multiobjective optimization

Many multimodal multiobjective optimization algorithms aim to find as many Pareto optimal solutions as possible while the performance in the objective space is despised. More seriously, some algorithms even overemphasize the diversity of solution set in the decision space at the cost of convergence. How to improve convergence and diversity simultaneously is an important issue when solving multimodal multiobjective optimization problems. In this paper, we propose an evolutionary multiobjective optimization algorithm with a decomposition strategy in the decision space (EMO-DD). A decision subregion allocation and diversity archive preservation methods are proposed to promote the diversity of solutions in the decision space. Meanwhile, a bi-objective optimization problem is formulated for screening for solutions with great convergence and diversity. Combining a modified mating selection method, well-performed solutions both on the convergence and diversity are preserved and inherited. The performance of EMO-DD is compared with five state-of-the-art algorithms on fifteen test problems. The experimental results show that EMO-DD can solve multimodal multiobjective optimization problems, and can improve the performance of the solution set in both the decision and objective spaces.