Investigating the Local-Meta-Model CMA-ES for Large Population Sizes

Zyed Bouzarkouna (1, 2) , Anne Auger (2) , Didier Yu Ding (1)

1 IFPEN - IFP Energies nouvelles
2 TAO - Machine Learning and Optimisation

For many real-life engineering optimization problems, the cost of one objective function evaluation can take several minutes or hours. In this context, a popular approach to reduce the number of function evaluations consists in building a (meta-)model of the function to be optimized using the points explored during the optimization process and replacing some (true) function evaluations by the function values given by the meta-model. In this paper, the local-meta-model CMA-ES (lmm-CMA) proposed by Kern et al. in 2006 coupling local quadratic meta-models with the Covariance Matrix Adaptation Evolution Strategy is investigated. The scaling of the algorithm with respect to the population size is analyzed and limitations of the approach for population sizes larger than the default one are shown. A new variant for deciding when the meta-model is accepted is proposed. The choice of the recombination type is also investigated to conclude that the weighted recombination is the most appropriate. Finally, this paper illustrates the influence of the different initial parameters on the convergence of the algorithm, for multimodal functions.

Mots clés: Covariance Matrix Adaptation; Evolution Strategy (CMA-ES); Optimization; Meta-models

Domaines: Analyse numérique [cs.NA]

Zyed Bouzarkouna, Anne Auger, Didier Yu Ding. Investigating the Local-Meta-Model CMA-ES for Large Population Sizes. 3rd European event on Bio-inspired algorithms for continuous\ parameter optimisation (EvoNUM'10), Apr 2010, Istanbul, Turkey. pp.402-411. ⟨hal-00450238⟩