A novel clustering-based evolutionary algorithm with objective space decomposition for multi/many-objective optimization

The framework of decomposing a multi -objective optimization problem (MOP) into some MOPs holds considerable promise. However, its advancement is constrained by numerous elements, including the incorrect segmentation of the subspaces and the challenges in balancing convergence and diversity. To address these issues, an objective space Decomposition and Clustering-based Evolutionary Algorithm (DCEA) is proposed in this paper. Specifically, DCEA employs K-means clustering to create an appropriate mating pool for each individual without the necessity to predetermine the number of clusters. Within each mating pool, the proposed adaptive evolutionary operator is applied to produce offspring for balancing the convergence and diversity. To enhance the accuracy of partitioning, a refined environmental selection approach utilizing supplementary weight vectors is developed. Additionally, by utilizing historical clustering data, a straightforward approach to periodically adjust reference vectors for the allocation of computational resources is proposed. In experiments, both MOPs and many-objective optimization problems (MaOPs) are used to test DCEA. A total of 27 MOPs and 30 MaOPs are involved and 16 state-of-the-art algorithms are employed to compare with DCEA. Comprehensive experiments show that DCEA is an effective algorithm for solving both MOPs and MaOPs.