Improved CMA-ES with Memory based Directed Individual Generation for Real Parameter Optimization

Covariance Matrix Adaptation and Evolution Strategy (CMA-ES) is an efficient method of optimization that iteratively generates new individuals around an ever-adaptive recombination point. Although it ensures speed and high rate of exploitation, CMA-ES suffers a major drawback as the scheme of generating new members scattered around an influential mean may often lead to members drawn to local minima. The result is that while precision of better solutions increases, the ability to reform is lost. In this paper we incorporate a directional feature to the generation wise perturbation of individuals in standard version of CMA-ES that utilizes potentially useful information from previous generation to retain the influence of old recombination point. Coupled with a modified population size we attempt to form an algorithm that amalgamates the effectiveness of CMA-ES along with the ability to explore. The performance is tested on IEEE CEC (Congress on Evolutionary Computation) 2013 Special Session on Real-Parameter Optimization in 10, 30 and 50 dimensions. The results obtained clearly indicates that the proposed algorithm addressed as CMA-ES with Memory based Directed Individual Generation (CMA-ES-DIG) is able to perform excessively well on majority of the test cases in a statistically meaningful way.