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One hope when using non-elitism in evolutionary computation is that theability to abandon the current-best solution aids leaving local optima. Toimprove our understanding of this mechanism, we perform a rigorous runtimeanalysis of a basic non-elitist evolutionary algorithm (EA), the$(\mu,\lambda)$ EA, on the most basic benchmark function with a local optimum,the jump function. We prove that for all reasonable values of the parametersand the problem, the expected runtime of the $(\mu,\lambda)$~EA is, apart fromlower order terms, at least as large as the expected runtime of its elitistcounterpart, the $(\mu+\lambda)$~EA (for which we conduct the first runtimeanalysis on jump functions to allow this comparison). Consequently, the abilityof the $(\mu,\lambda)$~EA to leave local optima to inferior solutions does notlead to a runtime advantage.  We complement this lower bound with an upper bound that, for broad ranges ofthe parameters, is identical to our lower bound apart from lower order terms.This is the first runtime result for a non-elitist algorithm on a multi-modalproblem that is tight apart from lower order terms.

Does Comma Selection Help To Cope With Local Optima