One hope of using non-elitism in evolutionary computation is that it aids leaving local optima. We perform a rigorous runtime analysis 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 parameters and the problem, the expected runtime of the $(\mu,\lambda)$ EA is, apart from lower order terms, at least as large as the expected runtime of its elitist counterpart, the $(\mu+\lambda)$~EA (for which we conduct the first runtime analysis to allow this comparison). Consequently, the ability of the $(\mu,\lambda)$ EA to leave local optima to inferior solutions does not lead to a runtime advantage. We complement this lower bound with an upper bound that, for broad ranges of the 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-modal problem that is tight apart from lower order terms.

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逗号选择是否有助于应对局部最优

在进化计算中使用非精英主义的一个希望是它有助于保持局部最优。我们对基本的非精英进化算法 (EA) $(\mu,\lambda)$ EA 进行了严格的运行时分析，该算法基于具有局部最优的最基本的基准函数，即跳转函数。我们证明，对于参数和问题的所有合理值，$(\mu,\lambda)$ EA 的预期运行时间，除了低阶项，至少与其精英对应物的预期运行时间一样大， $(\mu+\lambda)$~EA（我们对其进行第一次运行时分析以允许进行这种比较）。因此，$(\mu,\lambda)$ EA 将局部最优留给劣质解决方案的能力不会带来运行时优势。我们用一个上限补充这个下限，对于广泛的参数范围，除了低阶项之外，与我们的下界相同。这是非精英算法在多模态问题上的第一个运行时结果，该问题与低阶项无关。