About the Computation Time of Adaptive Evolutionary Algorithms

Abstract

The computation time of general adaptive evolutionary algorithms based on finite search space is investigated in this paper. An adaptive evolutionary algorithm can be formalized as an inhomogeneous Markov chain. By using Markov property, some exact analytic expressions of the mean first hitting time corresponding to the adaptive evolutionary algorithm are obtained. The upper and lower bounds are also estimated by introducing drift analysis and Dynkin's formula. Furthermore, the convergence of a constructive adaptive (1 + 1) ***EA is studied and its time complexity for a well-known toy problem is given.