We give a detailed analysis of the optimization time of the -Evolutionary Algorithm under two simple fitness functions (OneMax and LeadingOnes). The problem has been approached in the evolutionary algorithm literature in various ways and with different degrees of rigor. Our asymptotic approximations for the mean and the variance represent the strongest of their kind. The approach we develop is based on an asymptotic resolution of the underlying recurrences and can also be extended to characterize the corresponding limiting distributions. While most of our approximations can be derived by simple heuristic calculations based on the idea of matched asymptotics, the rigorous justifications are challenging and require a delicate error analysis.

中文翻译：

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(1+1)-进化算法的概率分析

我们详细分析了-Evolutionary Algorithm在两个简单的适应度函数（OneMax和LeadingOnes）下的优化时间。在进化算法文献中，这个问题已经以不同的方式和不同的严格程度来解决。我们对均值和方差的渐近近似代表了同类中最强的。我们开发的方法基于潜在递归的渐近分辨率，也可以扩展到表征相应的极限分布。虽然我们的大多数近似值都可以通过基于匹配渐近性思想的简单启发式计算得出，但严格的证明具有挑战性，需要精细的误差分析。