Black-box Optimization Benchmarking of NIPOP-aCMA-ES and NBIPOP-aCMA-ES on the BBOB-2012 Noiseless Testbed

Ilya Loshchilov (1) , Marc Schoenauer (1, 2) , Michèle Sebag (2)

1 TAO - Machine Learning and Optimisation
2 LRI - Laboratoire de Recherche en Informatique

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 $10^6D$ 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 benchmarking of BIPOP-CMA-ES with the weighted active covariance matrix update (BIPOP-aCMA-ES). The comparison shows that NIPOP-aCMA-ES usually outperforms 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.

Mots clés: Benchmarking; black-box optimization; evolution strategy; CMA-ES; self-adaptation; restart strategies

Domaines: Intelligence artificielle [cs.AI]

Ilya Loshchilov, Marc Schoenauer, Michèle Sebag. Black-box Optimization Benchmarking of NIPOP-aCMA-ES and NBIPOP-aCMA-ES on the BBOB-2012 Noiseless Testbed. Workshop Proceedings of the {GECCO} Genetic and Evolutionary Computation Conference, Jul 2012, Philadelphia, United States. ⟨hal-00737409⟩