Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria

Julien Villemonteix (1, 2) , Emmanuel Vazquez (1) , Maryan Sidorkiewicz (2) , Eric Walter (3)

1 E3S - Supélec Sciences des Systèmes
2 Département des systèmes énergétiques
3 L2S - Laboratoire des signaux et systèmes

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations usefully contributes to the localization of good candidates for the role of global minimizer, a stochastic model of the function can be built to conduct a sequential choice of evaluation points. Based on Gaussian processes and Kriging, the authors have recently introduced the informational approach to global optimization (IAGO) which provides a one-step optimal choice of evaluation points in terms of reduction of uncertainty on the location of the minimizers. To do so, the probability density of the minimizers is approximated using conditional simulations of the Gaussian process model behind Kriging. In this paper, an empirical comparison between the underlying sampling criterion called conditional minimizer entropy (CME) and the standard expected improvement sampling criterion (EI) is presented. Classical test functions are used as well as sample paths of the Gaussian model and an industrial application. They show the interest of the CME sampling criterion in terms of evaluation savings.

Keywords: Global optimization; computer simulations; kriging; Gaussian process; noisy evaluations.; noisy evaluations

Domains: Optimization and Control [math.OC]

Julien Villemonteix, Emmanuel Vazquez, Maryan Sidorkiewicz, Eric Walter. Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria. Journal of Global Optimization, 2009, 43 (2-3), pp. 373-389. ⟨10.1007/s10898-008-9313-y⟩. ⟨hal-00354656v2⟩