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August 1996 A new genetic algorithm
Raphaël Cerf
Ann. Appl. Probab. 6(3): 778-817 (August 1996). DOI: 10.1214/aoap/1034968228


Here is a new genetic algorithm. It is built by randomly perturbing a two operator crossover-selection scheme. Three conditions of biological relevance are imposed on the crossover. A new selection mechanism is used, which has the decisive advantage of preserving the diversity of the individuals in the population. The attractors of the unperturbed process are particular equifitness subsets of populations endowed with a rich structure. The random vanishing perturbations are twofold: local perturbations of the individuals (mutations) and loosening of the selection pressure. When the population size is greater than a critical value which depends strongly on the optimization problem, their delicate asymptotic interaction ensures the convergence (possibly in finite time) of the population to the ideal attractor whose populations contain all the maxima of the fitness function. The process explores without respite the neighborhoods of the best points found so far (instead of focusing on a particular point) and finds simultaneously all the global maxima of the fitness function; it seems to be the first cooperative search procedure of this kind.


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Raphaël Cerf. "A new genetic algorithm." Ann. Appl. Probab. 6 (3) 778 - 817, August 1996.


Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0860.60017
MathSciNet: MR1410116
Digital Object Identifier: 10.1214/aoap/1034968228

Primary: 60F10 , 60J10 , 92D15

Keywords: Freidlin-Wentzell theory , Genetic algorithms , stochastic optimization

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 3 • August 1996
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