A novel particle swarm optimization algorithm for non-separable and ill-conditioned problems

Particle swarm optimization (PSO) is a stochastic population-based algorithm that is designed for real-parameter optimization problems. PSO is a simple and powerful algorithm. However, the performance of PSO is degraded in the case of non-separable and ill-conditioned problems. In this article, we discuss the relation between the Hessian matrix of a function and the covariance matrix of the search distribution. The covariance matrix adaptation mechanism is required to solve non-separable and ill-conditioned problems. Therefore, in order to solve such problems, we propose a simple covariance matrix adaptation mechanism that uses the difference vector of the personal best positions. In addition, we propose a selection rule to improve the local search ability. Finally, we clarify the effectiveness of the proposed method in solving non-separable and ill-conditioned problems by using test functions.