A repulsive-distance-based maximum diversity selection algorithm for multimodal multiobjective optimization

Multimodal multiobjective optimization problems (MMOPs) area challenging class of problems. Several advanced evolutionary algorithms have been developed to solve MMOPs, but these algorithms still have some limitations, such as having many parameters, slow convergence speed, and unsatisfactory performance. To solve these problems, we propose a repulsive-distance-based maximum diversity selection algorithm (RMDS) which aims, during environmental selection, to select individuals with the best comprehensive diversity through the repulsive distance. The repulsive distance is the comprehensive Euclidean distance between an individual and selected individuals with the consideration of distribution of individuals in both the decision and objective spaces. RMDS has the following advantages: first, the repulsive distance allows rational selection of well-distributed solutions in the non-parameterized case. Second, the repulsive distance acts both in the decision and objective spaces, so it provides a good balance between the distribution of the solution set in these two spaces. Third, RDMS has a straightforward principle. Experimental results show that RMDS has superior performance incomparison with other well-known multimodal multiobjective evolutionary algorithms on 31 test functions.