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1 Departamento de Informatica Valparaíso, Chile 2 COCONUT - Agents, Apprentissage, Contraintes LIRMM - Laboratoire d-Informatique de Robotique et de Microélectronique de Montpellier 3 ENPC - École des Ponts ParisTech 4 LIGM - Laboratoire d-Informatique Gaspard-Monge 5 IMAGINE Marne-la-Vallée 6 Mines Nantes - Mines Nantes 7 TASC - Theory, Algorithms and Systems for Constraints LINA - Laboratoire d-Informatique de Nantes Atlantique, Département informatique - EMN, Inria Rennes – Bretagne Atlantique

Abstract : In deterministic continuous constrained global optimization, upper bounding the objective function generally resorts to local minimization at several nodes-iterations of the branch and bound. We propose in this paper an alternative approach when the constraints are inequalities and the feasible space has a non-null volume. First, we extract an inner region , i.e., an entirely feasible convex polyhedron or box in which all points satisfy the constraints. Second, we select a point inside the extracted inner region and update the upper bound with its cost. We describe in this paper two original inner region extraction algorithms implemented in our interval B&B called IbexOpt. They apply to nonconvex constraints involving mathematical operators like +,x,power,sqrt,exp,log,sin. This upper bounding shows very good performance obtained on medium-sized systems proposed in the COCONUT suite.

Keywords : Upper bounding Branch and bound Intervals Global optimization





Autor: Ignacio Araya - Gilles Trombettoni - Bertrand Neveu - Gilles Chabert -

Fuente: https://hal.archives-ouvertes.fr/



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