Enhancing the competitive swarm optimizer with covariance matrix adaptation for large scale optimization

Competitive swarm optimizer (CSO) has been shown to be an effective optimization algorithm for large scale optimization. However, the learning strategy of a loser particle used in CSO is axis-parallel. Then, it may not be able to solve the high ill-conditioned test functions due to the lack of considering the correlation of different component. This paper presents an enhanced competitive swarm optimizer with covariance matrix adaptation to alleviate this problem. Since covariance matrix is independent of the coordinate system, covariance matrix adaptation evolution strategy (CMA-ES) is embedded into CSO. On the one hand, better particles generated by CMA-ES can provide an effective way to capture the efficient search direction. On the other hand, some high-quality particles are employed to estimate the covariance matrix of Gaussian model. Then, the evolution direction information is integrated into the learned Gaussian model to improve search efficiency of the proposed algorithm. Experimental and statistical analyses are performed on CEC2014 benchmark functions, engineering design problems and time series prediction problems. Results show that the proposed algorithm has a superior performance in comparison with other state-of-the-art optimization algorithms and some variants of CSO.