Stochastic convergence

Abstract

Since the state transitions of an evolutionary algorithm (EA) are of stochastic nature, the deterministic concept of the "convergence to the optimum" is not appropriate. In order to clarify the exact semantic of a phrase like "the EA converges to the global optimum" one has to, at first, establish the connection between EAs and stochastic processes before distinguishing between the various modes of stochastic convergence of stochastic processes. Subsequently, this powerful framework is applied to derive convergence results for EAs.