Runtime analysis aims at contributing to our understanding of evolutionary algorithms through mathematical analyses of their runtimes. In the context of discrete optimization problems, runtime analysis classically studies the time needed to find an optimal solution. However, both from a practical and from a theoretical viewpoint, more fine-grained performance measures are needed to gain a more detailed understanding of the main working principles and their resulting performance implications. Two complementary approaches have been suggested: fixed-budget analyses and fixed-target analyses. In this work, we conduct an in-depth study on the advantages and the limitations of fixed-target analyses. We show that, different from fixed-budget analyses, many classical methods from the runtime analysis of discrete evolutionary algorithms yield fixed-target results without greater effort. We use this to conduct a number of new fixed-target analyses. However, we also point out examples where an extension of existing runtime results to fixed-target results is highly non-trivial.
翻译:运行时间分析的目的是通过对运行时间进行数学分析,促进我们对演进算法的理解。在离散优化问题的背景下,运行时间分析典型地研究寻找最佳解决方案所需的时间。然而,从实际和理论的角度来看,需要更精细的绩效措施,以便更详细地了解主要工作原则及其所产生的绩效影响。建议了两种互补办法:固定预算分析和固定目标分析。在这项工作中,我们深入研究固定目标分析的优势和局限性。我们表明,与固定预算分析不同的是,与对离散演进算法的运行时间分析不同的许多经典方法都产生了固定目标结果,但没有作出更大的努力。我们用这种方法进行一些新的固定目标分析。然而,我们还指出了将现有运行时间结果扩大到固定目标结果的高度非三边性的例子。