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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 hill-climbers 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.