论文标题

具有可配置的交叉概率的基准测试$(μ+λ)$遗传算法

Benchmarking a $(μ+λ)$ Genetic Algorithm with Configurable Crossover Probability

论文作者

Ye, Furong, Wang, Hao, Doerr, Carola, Bäck, Thomas

论文摘要

我们研究了一个$(μ+λ)$遗传算法(气)的家族,该算法是从突变或重组两个随机选择的父母而产生后代的。通过缩放交叉概率,我们可以从完全突变的算法插入到完全交叉的GA。我们通过经验手段分析性能如何取决于人口大小和交叉概率的相互作用。 我们对25个伪树状优化问题的比较表明,基于几个简单的优化任务的基于交叉配置的优势,而对于更复杂的优化问题的图片却相当混杂。此外,我们观察到,``快速''突变方案具有幂律分布突变强度在复杂优化任务与交叉结合时在复杂优化任务上的标准位突变优于标准位突变,但在没有交叉的情况下性能更糟。 然后,我们仔细研究了众所周知的Leading Leaders基准问题上的基于交叉的$(μ+λ)$气体的出乎意料的良好性能。我们观察到,随着人口大小$μ$的增加,最佳的交叉概率会增加。同时,它随着问题维度的增加而降低,表明在运行时分析中经典应用的渐近视图中,交叉的优势不可见。因此,我们认为,固定维度的数学研究可能有助于我们观察到效果,而这些效果仅专注于渐近性能范围。

We investigate a family of $(μ+λ)$ Genetic Algorithms (GAs) which creates offspring either from mutation or by recombining two randomly chosen parents. By scaling the crossover probability, we can thus interpolate from a fully mutation-only algorithm towards a fully crossover-based GA. We analyze, by empirical means, how the performance depends on the interplay of population size and the crossover probability. Our comparison on 25 pseudo-Boolean optimization problems reveals an advantage of crossover-based configurations on several easy optimization tasks, whereas the picture for more complex optimization problems is rather mixed. Moreover, we observe that the ``fast'' mutation scheme with its are power-law distributed mutation strengths outperforms standard bit mutation on complex optimization tasks when it is combined with crossover, but performs worse in the absence of crossover. We then take a closer look at the surprisingly good performance of the crossover-based $(μ+λ)$ GAs on the well-known LeadingOnes benchmark problem. We observe that the optimal crossover probability increases with increasing population size $μ$. At the same time, it decreases with increasing problem dimension, indicating that the advantages of the crossover are not visible in the asymptotic view classically applied in runtime analysis. We therefore argue that a mathematical investigation for fixed dimensions might help us observe effects which are not visible when focusing exclusively on asymptotic performance bounds.

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