A New Genetic Algorithm Working on State Domain Order Statistics

Abstract : 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.