Bimodal Performance Profile of Evolutionary Search and the Effects of Crossover

Tunable performance profiles for evolutionary search on instances of the adaptive distributed database management problem have previously been plotted and published by the authors. This demonstrates a bimodal feature of convergence time with respect to population size and mutation rate. Preliminary results on other problems (one-max, De Jong functions, etc.) led to the tentative conclusion that the features of the complex profile discovered could indeed be generic, and four key hypotheses were presented. These covered the effects of problem complexity and evaluation limit on optimal and non-optimal mutation rates. This paper expands significantly on these results looking in more detail at the one-max and royal staircase problems, and demonstrates the effect of various rates of crossover on the performance profile of evolutionary search. Crucially, these results continue to demonstrate the bimodal feature and show that reduced levels of crossover extend the influence of the bimodal region to higher population sizes. A study of the coefficient of variation of convergence time shows importantly that this can be at a minimum at an optimal mutation rate which can also deliver consistent results in a minimum number of evaluations.