THE DYNAMICS OF MUTATION-SELECTION ALGORITHMS WITH LARGE POPULATION SIZES

We build the mutation-selection algorithm by randomly perturbing a ver y simple selection scheme. Our process belongs to the class of the gen eralized simulated annealing algorithms studied by Trouve. When the po pulation size m is large, the various quantities associated with the a lgorithm are affine functions of m and the hierarchy of cycles on the set of uniform populations stabilizes. If the mutation kernel is symme tric, the limiting distribution is the uniform distribution over the s et of the global maxima of the fitness function. The optimal convergen ce exponent defined by Azencott, Catoni and Trouve is an affine strict ly increasing function of m.