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It is generally accepted that populations are useful for the globalexploration of multi-modal optimisation problems. Indeed, several theoreticalresults are available showing such advantages over single-trajectory searchheuristics. In this paper we provide evidence that evolving populations viacrossover and mutation may also benefit the optimisation time for hillclimbingunimodal functions. In particular, we prove bounds on the expected runtime ofthe standard ($\mu$+1)~GA for OneMax that are lower than its unary black boxcomplexity and decrease in the leading constant with the population size up to$\mu=O(\sqrt{\log n})$. Our analysis suggests that the optimal mutationstrategy is to flip two bits most of the time. To achieve the results weprovide two interesting contributions to the theory of randomised searchheuristics: 1) A novel application of drift analysis which compares absorptiontimes of different Markov chains without defining an explicit potentialfunction. 2) The inversion of fundamental matrices to calculate the absorptiontimes of the Markov chains. The latter strategy was previously proposed in theliterature but to the best of our knowledge this is the first time is has beenused to show non-trivial bounds on expected runtimes.

On the Benefits of Populations on the Exploitation Speed of Standard Steady-State Genetic Algorithms