A Comparative Study of CMA-ES on Large Scale Global Optimisation

In this paper, we investigate the performance of CMA-ES on large scale non-separable optimisation problems. CMA-ES is a robust local optimiser that has shown great performance on small-scale nonseparable optimisation problems. Self-adaptation of a covariance matrix makes it rotational invariant which is a desirable property, especially for solving non-separable problems. The focus of this paper is to compare the performance of CMA-ES with Cooperative Co-evolutionary Algorithms (CCEAs) for large scale global optimisation (on problems with up to 1000 real-valued variables). Since the original CMA-ES is incapable of handling problems with more than several hundreds dimensions, sep-CMA-ES was developed using only the diagonal elements of the covariance matrix. In this paper sep-CMA-ES is compared with several existing CC:EAs. Experimental results revealed that the performance of sep-CMA-ES drops significantly when the dimensionality of the problem increases. However, our results suggest that the rotational invariant property of CMA-ES can be utilised in conjunction with a CCEA to further enhance its capability to handle large scale optimisation problems.