Particle Swarm CMA Evolution Strategy for the optimization of multi-funnel landscapes

We extend the evolution strategy with covariance matrix adaptation (CMA-ES) by collaborative concepts from particle swarm optimization (PSO). The proposed particle swarm CMA-ES (PS-CMA-ES) algorithm is a hybrid real-parameter algorithm that combines the robust local search performance of CMA-ES with the global exploration power of PSO using multiple CMA-ES instances to explore different parts of the search space in parallel. Swarm intelligence is introduced by considering individual CMA-ES instances as lumped particles that communicate with each other. This includes non-local information in CMA-ES, which improves the search direction and the sampling distribution. We evaluate the performance of PS-CMA-ES on the IEEE CEC 2005 benchmark test suite. The new PS-CMA-ES algorithm shows superior performance on noisy problems and multi-funnel problems with non-convex underlying topology.