A clustering-assisted adaptive evolutionary algorithm based on decomposition for multimodal multiobjective optimization

A multimodal multiobjective optimization problem can have multiple equivalent Pareto Sets (PSs). Since the number of PSs may vary in different problems, if the population is restricted to a fixed size, the number of solutions found for each PS will inevitably fluctuate widely, which is undesirable for decision makers. To address the issue, this paper proposes a clustering-assisted adaptive evolutionary algorithm based on decomposition (CA-MMEA/D), whose search process can be roughly divided into two stages. In the first stage, an initial exploration of decision space is carried out, and then solutions with good convergence are used for clustering to estimate the number and location of multiple PSs. In the second stage, new search strategies are developed on the basis of clustering, which can take advantage of unimodal search methods. Experimental studies show that the proposed algorithm outperforms some state-of-the-art algorithms, and CA-MMEA/D can keep the number of solutions found for each PS at a relatively stable level for different problems, thus making it easier for decision makers to choose the desired solutions. The research in this paper provides new ideas for the design of decomposition-based multimodal multiobjective algorithms.