Mutation and recombination operators play a key role in determining the performance of Genetic and Evolutionary Algorithms (GEAs). Prior work has analyzed the effects of these operators on genotypic variation, often using locality metrics that measure the sensitivity and stability of genotype-phenotype representations to these operators. In this paper, we focus on an important subset of representations, namely nonredundant bitstring-to-integer representations, and analyze them through the lens of Rothlauf’s widely used locality metrics. Our main research question is, does strong locality predict good GEA performance for these representations? Our main findings, both theoretical and empirical, show the answer to be negative. To this end, we define locality metrics equivalent to Rothlauf’s that are tailored to our domain: the point locality for single-bit mutation and general locality for recombination. With these definitions, we derive tight bounds and a closed-form expected value for point locality. For general locality we show that it is asymptotically equivalent across all representations and operators. We also reproduce three established GEA empirical results to understand the predictive power of point locality on GEA performance, focusing on two popular and often juxtaposed representations: standard binary and binary-reflected Gray.

中文翻译：

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遗传和进化算法中二进制表示形式的局部性分析

突变和重组算子在确定遗传和进化算法（GEA）的性能中起关键作用。以前的工作已经分析了这些算子对基因型变异的影响，通常使用局部性指标来测量基因型-表型表征对这些算子的敏感性和稳定性。在本文中，我们关注于表示的一个重要子集，即非冗余的位串到整数的表示，并通过罗斯劳夫广泛使用的局部性度量的角度对它们进行了分析。我们的主要研究问题是，强本地性会为这些表示形式预测良好的GEA绩效吗？我们的主要发现，无论是理论上还是经验上的，都表明答案是负面的。为此，我们定义了与Rothlauf等效的本地化指标，这些指标是针对我们的域量身定制的：单位突变的点局部性和重组的一般局部性。通过这些定义，我们得出点局部性的紧密边界和封闭形式的期望值。对于一般局部性，我们表明它在所有表示和算符上都渐近等效。我们还重现了三个已建立的GEA实验结果，以了解点局部性对GEA性能的预测能力，重点关注两种流行且经常并列的表示形式：标准二进制和二进制反射的Gray。