A fast and reliable hybrid algorithm for numerical nonlinear global optimization

Abstract : Highly nonlinear and ill-conditioned numerical optimization problems take their toll on the convergence of existing resolution methods. Stochastic methods such as Evolutionary Algorithms carry out an efficient exploration of the searchspace at low cost, but get often trapped in local minima and do not prove the optimality of the solution. Deterministic methods such as Interval Branch and Bound algorithms guarantee bounds on the solution, yet struggle to converge within a reasonable time on high-dimensional problems. The contribution of this paper is a hybrid algorithm in which a Differential Evolution algorithm and an Interval Branch and Contract algorithm cooperate. Bounds and solutions are exchanged through shared memory to accelerate the proof of optimality. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate the efficiency of this algorithm on two currently unsolved problems: first by presenting new certified optimal results for the Michalewicz function for up to 75 dimensions and then by proving that the putative minimum of Lennard-Jones clusters of 5 atoms is optimal.
Type de document :
Autre publication
Preprint. 2013
Liste complète des métadonnées

Littérature citée [26 références]  Voir  Masquer  Télécharger

Contributeur : Laurence Porte <>
Soumis le : jeudi 24 avril 2014 - 14:37:57
Dernière modification le : mercredi 12 septembre 2018 - 17:46:02
Document(s) archivé(s) le : jeudi 24 juillet 2014 - 10:38:23


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-00938911, version 1


Charlie Vanaret, Jean-Baptiste Gotteland, Nicolas Durand, Jean-Marc Alliot. A fast and reliable hybrid algorithm for numerical nonlinear global optimization. Preprint. 2013. 〈hal-00938911〉



Consultations de la notice


Téléchargements de fichiers