CENTRE DE MATHEMATIQUES APPLIQUEES 
         C.M.A.P.  

Statistical distribution of the convergence time for longpath problems
Josselin Garnier Leila Kallel

This paper studies the behavior of (1+1)-ES on Rudolph's
k-longpaths. Expected convergence time is proven to be exponential for
k equals a power of string length l.  Statistical distribution of
convergence time and its variance are calculated in the case of
constant k.  The influence of population size (as a function of l) is
investigated. It comes that a population size with a growth rate of l
quickens the search but cannot change the order of convergence
time. Different evolution strategies are compared.

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