Benchmarking the PSA-CMA-ES on the BBOB noiseless testbed

We evaluate the CMA-ES with population size adaptation mechanism (PSA-CMA-ES) on the BBOB noiseless testbed. On one hand, the PSA-CMA-ES with a simple restart strategy shows performance competitive with the best 2009 portfolio on most well-structured multimodal functions. On the other hand, it is not effective on weakly-structured multimodal functions. Moreover, on most uni-modal functions, the scale-up of performance measure w.r.t. the dimension tends to be worse than the default CMA-ES, implying that the population size is adapted greater than needed on the unimodal functions. To improve performance on unimodal functions and weakly-structured multimodal functions, we additionally propose a restart strategy for the PSA-CMA-ES. The proposed strategy consists of three search regimes. The resulted restart strategy shows improved performance on unimodal functions and weakly-structured multimodal functions with a little compromise in the performance on well-structured multimodal functions. The overall performance is competitive to the BIPOP-CMA-ES.