Comparison of simple diversity mechanisms on plateau functions

It is widely assumed and observed in experiments that the use of diversity mechanisms in evolutionary algorithms may have a great impact on its running time. Up to now there is no rigorous analysis pointing out how different diversity mechanisms influence the runtime behavior. We consider evolutionary algorithms that differ from each other in the way they ensure diversity and point out situations where the right mechanism is crucial for the success of the algorithm. The considered evolutionary algorithms either diversify the population with respect to the search points or with respect to function values. Investigating simple plateau functions, we show that using the “right” diversity strategy makes the difference between an exponential and a polynomial runtime. Later on, we examine how the drawback of the “wrong” diversity mechanism can be compensated by increasing the population size.