A Multi-Population Evolutionary Algorithm for Solving Large-Scale Multi-Modal Multi-Objective Optimization Problems

Multi-modal multi-objective optimization problems (MMOPs) widely exist in real-world applications, which have multiple equivalent Pareto optimal solutions that are similar in the objective space but totally different in the decision space. While some evolutionary algorithms (EAs) have been developed to find the equivalent Pareto optimal solutions in recent years, they are ineffective to handle large-scale MMOPs having a large number of variables. This paper thus proposes an EA for solving large-scale MMOPs with sparse Pareto optimal solutions, i.e., most variables in the optimal solutions are zero. The proposed algorithm explores different regions of the decision space via multiple subpopulations, and guides the search behavior of the subpopulations via adaptively updated guiding vectors. The guiding vector for each subpopulation not only provides efficient convergence in the huge search space, but also differentiates its search direction from others to handle the multi-modality. While most existing evolutionary algorithms solve MMOPs with 2 to 7 decision variables, the proposed algorithm is showed to be effective for benchmark MMOPs with up to 500 decision variables. Moreover, the proposed algorithm also produces a better result than state-of-the-art methods for neural architecture search.