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1 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l-Aérien 2 IRIT - Institut de recherche en informatique de Toulouse

Abstract : Evolutionary Algorithms EA usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality.

Autor: Charlie Vanaret - Jean-Baptiste Gotteland - Nicolas Durand - Jean-Marc Alliot -



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