Exploring or reducing noise? A global optimization algorithm in the presence of noise

Didier Rullière (1) , Alaeddine Faleh (1) , Frédéric Planchet (1) , Wassim Youssef (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 Winter & associés

We consider the problem of the global minimization of a function observed with noise. This problem occurs for example when the objective function is estimated through stochastic simulations. We propose an original method for iteratively partitioning the search domain when this area is a nite union of simplexes. On each subdomain of the partition, we compute an indicator measuring if the subdomain is likely or not to contain a global minimizer. Next areas to be explored are chosen in accordance with this indicator. Con dence sets for minimizers are given. Numerical applications show empirical convergence results, and illustrate the compromise to be made between the global exploration of the search domain and the focalization around potential minimizers of the problem.

Mots clés: Golbal Optimisation; Simplex; Branch-and-Bound; Kriging

Domaines: Economies et finances; Optimisation et contrôle [math.OC]

Didier Rullière, Alaeddine Faleh, Frédéric Planchet, Wassim Youssef. Exploring or reducing noise? A global optimization algorithm in the presence of noise. Structural and Multidisciplinary Optimization, 2013, 47 (6), pp.921-936. ⟨10.1007/s00158-012-0874-5⟩. ⟨hal-00759677⟩