Preventing premature convergence and proving the optimality in evolutionary algorithms

Charlie Vanaret (1) , Jean-Baptiste Gotteland (1) , Nicolas Durand (1) , Jean-Marc Alliot (2)

1 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
2 IRIT-APO - Algorithmes Parallèles et Optimisation

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.

Domaines: Recherche opérationnelle [math.OC]; Intelligence artificielle [cs.AI]; Optimisation et contrôle [math.OC]

Charlie Vanaret, Jean-Baptiste Gotteland, Nicolas Durand, Jean-Marc Alliot. Preventing premature convergence and proving the optimality in evolutionary algorithms. EA 2013, 11th International Conference on Artificial Evolution, Oct 2013, Bordeaux, France. pp 84-94 ; ISBN : 9782953926736. ⟨hal-00880716⟩