BI-population CMA-ES Algorithms with Surrogate Models and Line Searches

In this paper, we study the performance of NIPOP-aCMA- ES and NBIPOP-aCMA-ES, recently proposed alternative restart strategies for CMA-ES. Both algorithms were tested using restarts till a total number of function evaluations of 106D was reached, where D is the dimension of the function search space. We compared new strategies to CMA-ES with IPOP and BIPOP restart schemes, two algorithms with one of the best overall performance observed during the BBOB- 2009 and BBOB-2010. We also present the first benchmark- ing of BIPOP-CMA-ES with the weighted active covariance matrix update (BIPOP-aCMA-ES). The comparison shows that NIPOP-aCMA-ES usually out- performs IPOP-aCMA-ES and has similar performance with BIPOP-aCMA-ES, using only the regime of increasing the population size. The second strategy, NBIPOP-aCMA-ES, outperforms BIPOP-aCMA-ES in dimension 40 on weakly structured multi-modal functions thanks to the adaptive allocation of computation budgets between the regimes of restarts.