On the optimization of unimodal functions with the (1 + 1) Evolutionary Algorithm

Abstract

We investigate the expected running time of the (1 + 1) EA, a very simple Evolutionary Algorithm, on the class of unimodal fitness functions with Boolean inputs. We analyze the behavior on a generalized version of long paths [6, 10] and prove an exponential lower bound on the expected running time. Thereby we show that unimodal functions can be very difficult to be optimized for the (1+1) EA. Furthermore, we prove that a little modification in the selection method can lead to huge changes in the expected running time.