Covariance Matrix Learning Based Differential Evolution And Its Application Research

Differential evolution which is an efficient and robust evolutionary algorithm is a hotspot of the evolutionary computation research in recent years. In order to improve the performance in multivariate correlation problems such as rotated problems, a covariance matrix learning based differential evolution (LYDE) is presented.In LYDE, Eigen decomposition is applied to covariance matrix of current solution set to achieve an Eigen coordinate system for crossover operator. The covariance matrix learning eliminates the coordinate system dependence from differential evolution and improves the performance in multivariate correlation problems. Moreover, we embed bimodal distribution parameter setting in our algorithm. Bimodal distribution for crossover probability is composed of two normal distributions with different mean values, and makes offspring produced by crossover operator distribute around the parents with high probability. Bimodal distribution for mutation factor is composed of two Cauchy distributions with different medians, and balances global exploration and local exploitation. LYDE has been tested on 25 benchmark functions of CEC2005 test suite. The experimental results suggest that LYDE is efficient for global optimization, especially rotated problems and is robust to noise. LYDE has a faster convergence rate and a higher precision than five recent algorithms (i.e. jDE, SaDE, JADE, EPSDE, CoDE) on 25 benchmark functions. The experiment also suggests both covariance matrix learning approach and bimodal parameter setting are critical to LYDE and the two components have a cooperative effect. The parameter sensitivity experiment shows LYDE with sample rate 0.4 and learning rate 0.65 has a robust performance on test suite.In addition, we propose an approach that mapping the continuous vector space to the discrete solution space based on the minimum Euclidean distance principle. By the above method, keeping the original structure of DE, the application field of LYDE is extended from the continuous problems to a classical discrete combinatorial optimization problem—set cover problem on ichnography, which is an abstraction of emergency facility location. The experiment result shows LYDE has an excellent performance and has a faster convergence rate and a higher precision than genetic algorithm. The application of LYDE for discrete problem is promising.