Subspace Clustering Mutation Operator for Developing Convergent Differential Evolution Algorithm

Many researches have identified that differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter algorithms for global optimization problems. However, a stagnation problem still exists in DE variants. In order to overcome the disadvantage, two improvement ideas have gradually appeared recently. One is to combine multiple mutation operators for balancing the exploration and exploitation ability. The other is to develop convergent DE variants in theory for decreasing the occurrence probability of the stagnation. Given that, this paper proposes a subspace clustering mutation operator, called SC_qrtop. Five DE variants, which hold global convergence in probability, are then developed by combining the proposed operator and five mutation operators of DE, respectively. The SC_qrtop randomly selects an elite individual as a perturbation’s center and employs the difference between two randomly generated boundary individuals as a perturbation’s step. Theoretical analyses and numerical simulations demonstrate that SC_qrtop prefers to search in the orthogonal subspace centering on the elite individual. Experimental results on CEC2005 benchmark functions indicate that all five convergent DE variants with SC_qrtop mutation outperform the corresponding DE algorithms.