Benchmark results for a simple hybrid algorithm on the CEC 2013 benchmark set for real-parameter optimization

In this article, we benchmark a new hybrid algorithm for continuous optimization on the 28 functions for the CEC 2013 special session and competition on real-parameter optimization. Our algorithm makes a loose coupling of (i) IPOP-CMA-ES, an advanced evolution strategy with covariance matrix adaptation integrated with an occasional restart strategy and increasing population size, and (ii) an iterated local search (ILS) algorithm that repeatedly applies a different local search from CMA-ES to perturbations of previous high-quality solutions. The central idea of the hybrid algorithm is to let IPOP-CMA-ES and ILS compete in an initial competition phase and then the winner of the two algorithms is deployed for the remainder of the computation time. A cooperative element between the two algorithms is implemented through a solution exchange from IPOP-CMA-ES to ILS. Hence, one may classify this algorithm as a loosely coupled cooperative-competitive algorithm for continuous optimization. We compare the computational results of this hybrid algorithm to the default version and a tuned version of IPOP-CMA-ES to illustrate the improvement that is obtained through this hybrid algorithm. This comparison is interesting since IPOP-CMA-ES is a state-of-the-art algorithm which somehow has become a standard benchmark to compare against for any new algorithmic proposals for continuous optimization. Our computational results show that the proposed hybrid algorithm performs significantly better than the default and tuned IPOP-CMA-ES variants on the problems of dimension 30 and 50. Thus, these results also indicate that the hybrid algorithm reaches very high performance on the CEC 2013 benchmark set.