Scaling Up Covariance Matrix Adaptation Evolution Strategy Using Cooperative Coevolution

Abstract

Covariance matrix adaptation evolution strategy (CMA-ES) has demonstrated competitive performance especially on multimodal non-separable problems. However, CMA-ES is not capable of dealing with problems having several hundreds dimensions. Motivated by that cooperative coevolution (CC) has scaled up many kinds of evolutionary algorithms (EAs) to high dimensional optimization problems effectively, we propose an algorithm called CC-CMA-ES which apply CC to CMA-ES in order to scale up CMA-ES to large scale problems. CC-CMA-ES adopts a new sampling scheme which does not divide population into small subpopulations and conducts mutation and crossover operations in subpopulation to generate offspring, but extracts a subspace Gaussian distribution from the global Gaussian distribution for subspace sampling. Also in CC-CMA-ES, two new decomposition strategies are proposed in order to balance exploration and exploitation. Lastly, an adaptive scheme is adopted to self-adapt appropriate decomposition strategy during evolution process. Experimental studies on a series of benchmark functions with different characteristic have been conducted and verified the excellent performance of our newly proposed algorithm and the effectiveness of the new decomposition strategies.