Analysis of the (1+1) EA for a Dynamically Bitwise Changing OneMax

Abstract

Although evolutionary algorithms (EAs) are often successfully used for the optimization of dynamically changing objective function, there are only very few theoretical results for EAs in this scenario. In this paper we analyze the (1+1) EA for a dynamically changing OneMax, whose target bit string changes bitwise, i. e. possibly by more than one bit in a step. We compute the movement rate of the target bit string resulting in a polynomial expected first hitting time of the (1+1) EA asymptotically exactly. This strengthens a previous result, where the dynamically changing OneMax changed only at most one bit at a time.