基于精确黑箱分析的最优参数选择
Optimal Parameter Choices via Precise Black-Box Analysis
摘要：
已经观察到，进化算法的一些工作原理，特别是参数的影响，不能从运行时的渐近阶的结果来理解，而只能从更精确的结果。在这项工作中，我们补充了新兴的主题，精确的运行时分析与第一精确的复杂性理论的结果。我们的愿景是，算法分析和复杂性理论之间的相互作用成为一个富有成效的工具，也比渐近数量级更精确的分析。作为具体的结果，我们证明了OneMax基准函数类的一元无偏黑箱复杂度是$n \ln(n) - cn \pm o(n)$，其中$c$是介于$0.2539$和$0.2665$之间的常数.该运行时间可以通过使用适应度依赖突变强度的简单（1+1）型算法来实现。当翻译成固定预算的角度来看，我们的算法找到的解决方案是大约13\%接近最佳比那些最好的以前已知的算法。为了证明我们的结果，我们制定了几个新版本的变量漂移定理，这也可能是独立的利益。
英文摘要：
It has been observed that some working principles of evolutionary algorithms, in particular, the influence of the parameters, cannot be understood from results on the asymptotic order of the runtime, but only from more precise results. In this work, we complement the emerging topic of precise runtime analysis with a first precise complexity theoretic result. Our vision is that the interplay between algorithm analysis and complexity theory becomes a fruitful tool also for analyses more precise than asymptotic orders of magnitude. As particular result, we prove that the unary unbiased black-box complexity of the OneMax benchmark function class is $n \ln(n) - cn \pm o(n)$ for a constant $c$ which is between $0.2539$ and $0.2665$. This runtime can be achieved with a simple (1+1)-type algorithm using a fitness-dependent mutation strength. When translated into the fixed-budget perspective, our algorithm finds solutions which are roughly 13\% closer to the optimum than those of the best previously known algorithms. To prove our results, we formulate several new versions of the variable drift theorems, which also might be of independent interest.
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