Transition Functions for Evolutionary Algorithms on Continuous State-space

Evolutionary algorithms working on continuous search space can be regarded as general homogeneous Markov chains. The finite space problem of describing the transition matrix turns into the more complicated problem of definining and estimating a transition function. We analyze in this respect the (1+1) evolutionary algorithm on the inclined plane and corridor models. In the first case, the probability of maximal success in n iterations is derived in closed form, under uniform mutation. For the second case, the algorithm is proved to escape the corner of the corridor for both uniform and normal mutation, exponentially fast.