Escaping Local Optima with Non-Elitist Evolutionary Algorithms

Most discrete evolutionary algorithms (EAs) implement elitism, meaning that they make the biologically implausible assumption fittest individuals never die. While elitism favours exploitation and ensures best seen solutions are not lost, it has been widely conjectured non-elitism is necessary to explore promising fitness valleys without getting stuck in local optima. Determining when non-elitist EAs outperform elitist one of most fundamental open problems computation. A recent analysis a EA shows this algorithm does its counterparts on benchmark problem JUMP. We solve through rigorous runtime population-based class multi-modal problems. show with 3-tournament selection appropriate mutation rates, optimises expected polynomial time, while an requires exponential time overwhelmingly high probability. key insight our non-linear profile tournament mechanism which, allows small sub-population reside optimum rest population explores valley. In contrast, we comma-selection which have profile, fails optimise time. The theoretical complemented empirical investigation instances set cover problem, showing can perform better than ones. also provide examples where usage rates close error thresholds beneficial employing EAs.