A New Genetic Algorithm Working on State Domain Order Statistics

Daniel Delahaye (1) , Stéphane Puechmorel (2)

1 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
2 ENAC - Ecole Nationale de l'Aviation Civile

This paper presents a new concept of Genetic Algorithm in which an individual is coded as a domain of the state space and is evaluated with the help of order statistics. For this first version only continuous criteria has been investigated. An hypercube domain of the state space is associated with each individual and is randomly sampled according to a distribution for which asymptotic extremes are known. Regular fitnesses are computed for all the samples in each domain and are combined to produce a prospectiveness criterion. A regular GA and this new GA are compared on classical N dimensional functions such as Sphere, Step, Ackley, Griewank for dfferent values of N. A final comparison is given on the classical Lennard-Jones Molecular Conformation problem with 30 atoms. For both versions, a regular GA has been used; the first one works on state points and the other one on state domains. For all tests, and for the same number of criterion evaluations, this new algorithm performs much better than the classical one.

Mots clés: order statistics; state domains; genetic algorithm

Domaines: Optimisation et contrôle [math.OC]

Daniel Delahaye, Stéphane Puechmorel. A New Genetic Algorithm Working on State Domain Order Statistics. Lecture Notes in Computer Science, 2000, Parallel Problem Solving from Nature - PPSN VI. 6th International Conference Paris, France, September 18–20, 2000 Proceedings, 1917, pp.777-786. ⟨10.1007/3-540-45356-3_76⟩. ⟨hal-01205254⟩