An improved covariance matrix leaning and searching preference algorithm for solving CEC 2015 benchmark problems

This paper proposes an improved version of the single objective optimization evolutionary algorithm based on Covariance Matrix Learning and Searching Preference (CMLSP), named ICMLSP. ICMLSP uses the same way with CMLSP to generate high quality solutions by sampling a multivariate Gauss distribution, which uses the best solutions found so far as its mean value. However, unlike the previous one, ICMLSP uses different covariance matrix learning philosophy, that is, the principal component analysis (PCA) method is used to estimate the covariance matrix. Furthermore, ICMLSP tends to use smaller population size than CMLSP to achieve a faster search. In order to get enough information for a reliable estimation, a new cumulation strategy is designed in ICMLSP. Solutions are selected from an archive set which stores the best λ individuals in present population and last t(t >= 1) populations to estimate the covariance matrix. A new adaptive rule, which makes use of the history successful information to generate different searching step from two different Cauchy distributions, is designed for ICMLSP to balance global exploration and local exploitation. Finally, the performance of the ICMLSP has been tested on 15 noiseless optimization problems designed for the CEC 2015 Competition on Learning-based Real-Parameter Single Objective Optimization. The results are reported at the end of this paper.