Competitive swarm optimization with subset selection based manifold learning for multimodal multi-objective optimization

There are two major challenges when handling the multimodal multi-objective optimization (MMO) problems. One is the loss of diversity since most of the evolutionary algorithms designed for MMO prefer the base algorithm with rapid convergence. Therefore, the extra niching or other diversity preserving mechanism is inevitable. The other is the distribution of the Pareto optimal solutions with imbalanced density. Since the Pareto optimal sets may show different characteristics in the decision space, it is tough to converge the solutions to the Pareto front uniformly. To address these issues, subset selection and manifold learning based competitive swarm optimization algorithm, namely MMO_CSO, is proposed. Competitive swarm optimizer which has well balance on both diversity and convergence is adopted. Moreover, a subset selection strategy is applied to select diversified individuals for learning the manifold structure of the Pareto set. Thereby, the subset selection based manifold learning mechanism is designed to generate the promising solutions which could approach the real Pareto solutions and fill the sparse Pareto subregion. Compared against six state-of-the-art peer algorithms, the proposed MMO_CSO has a better performance to search for the Pareto optimal solutions both in decision space and objective space on CEC2019 MMO benchmarks.