Adaptive Merging and Coordinated Offspring Generation in Multi-Population Evolutionary Multi-Modal Multi-Objective Optimization

Multi-modal multi-objective optimization problems (MMOPs) have attracted increased attention in recent years, where solutions share the same Pareto front in the objective space but distribute differently in the decision space. However, most existing multi-modal multi-objective evolutionary algorithms fail to or have a low convergence speed to solve high-dimensional MMOPs with sparse Pareto optimal solutions, which have found a wide range of applications in many areas, such as neural architecture search and feature selection. To find a suitable number of Pareto optimal sets quickly, we propose an adaptive merging method in multi-population, in which subpopulations satisfying a certain criterion are merged into one subpopulation in this work. In addition, a coordinated offspring generation strategy that takes into account the sparsity ratio of the current subpopulations is introduced to generate more promising off-spring solutions, where dimensions with high sparsity should have a higher chance of being mutated. Comparative experimental results comparing four state-of-the-art peer algorithms on eight widely used benchmark problems verify the effectiveness of the proposed method.