On the Utility of Populations in Evolutionary Algorithms

Evolutionary algorithms (EAs) are population-based search heuristics often used for function optimization. Typically they employ selection, crossover, and mutation as search operators. It is known that EAs are outperformed by simple hillclimbers in some cases. Thus, it may be asked whether the use of a population and crossover is at all advantageous. In this paper it is rigorously proven that the use of a population instead of just a single individual can be an advantage of its own even without making use of crossover. This establishes by example the advantage of EAs compared to (random) hill-climbers on appropriate objective functions. Moreover, we describe one particular situation where intuitively a population should outperform a single individual and present a formal proof justifying this intuition.