Combining Cross Entropy and MADS methods for inequality constrained optimization

Charles Audet (1) , Jean Bigeon (2, 3, 4, 5) , Romain Couderc (6, 7)

1 GERAD - Groupe d’études et de recherche en analyse des décisions
2 LS2N - Laboratoire des Sciences du Numérique de Nantes
3 LS2N - équipe OGRE - Optimisation Globale et Résolution Ensembliste
4 CNRS - Centre National de la Recherche Scientifique
5 ECN - École Centrale de Nantes
6 EPM - École Polytechnique de Montréal
7 G-SCOP_SIREP - Système d’Information, conception RobustE des Produits

This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm with the Cross-Entropy (CE) method for non smooth constrained optimization. The CE method is used as a Search step by the MADS algorithm. The result of this combination retains the convergence properties of MADS and allows an efficient exploration in order to move away from local minima. The CE method samples trial points according to a multivariate normal distribution whose mean and standard deviation are calculated from the best points found so far. Numerical experiments show an important improvement of this method to reach the feasible region and to escape local minima.

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Charles Audet, Jean Bigeon, Romain Couderc. Combining Cross Entropy and MADS methods for inequality constrained optimization. 2020. ⟨hal-03085213⟩