Evolutionary algorithms - how to cope with plateaus of constant fitness and when to reject strings of the same fitness

The most simple evolutionary algorithm (EA), the so-called (1 + 1) EA, accepts an offspring if its fitness is at least as large (in the case of maximization) as the fitness of its parent. The variant (1 + 1)* EA only accepts an offspring if its fitness is strictly larger than the fitness of its parent. Here, two functions related to the class of long-path functions are presented such that the (1 + 1) EA maximizes one in polynomial time and needs exponential time for the other while the (1 + 1)* EA has the opposite behavior. These results demonstrate that small changes of an EA may change its behavior significantly. Since the (1 + 1) EA and the (1 + 1)* EA differ only on plateaus of constant fitness, the results also show how EAs behave on such plateaus. The (1 + 1) EA can pass a path of constant fitness and polynomial length in polynomial time. Finally, for these functions, it is shown that local performance measures like the quality gain and the progress rate do not describe the global behavior of EAs.