论文标题
重新访问二进制代表中的局部性
Revisiting Locality in Binary-Integer Representations
论文作者
论文摘要
突变和重组操作员在确定遗传和进化算法的速度和质量(GEAS)方面起着关键作用。先前的工作已经分析了这些操作员对基因型变异的影响,通常使用局部性指标来衡量基因型 - 表型表示对这些算子的敏感性和稳定性。 在本文中,我们专注于一个重要的表示子集,即非冗余的bittring to-Integer表示,并通过Rothlauf广泛使用的局部性指标的镜头进行分析。我们首先定义了相当于Rothlauf的局部性指标,这些指标是根据我们的域而定制的:用于单位突变的\ textIt {point locality},重新组合\ textIt {enterial locality}。通过这些定义,我们得出了紧密的界限和点位置的封闭形式的预期值。对于一般地点,我们表明,在所有表示和运营商中,它在渐近上等效。我们还重新创建了三个已建立的GEA实验,以了解点位置对GEA性能的预测能力,重点是两个流行且经常并列的表示:标准二进制和二进制反射的灰色。 我们表明,标准二进制文件证明没有比任何灰色编码(包括二进制反射的灰色)差的地方。我们在以前的研究的背景下讨论了这一结果,该研究发现二进制反射灰色以超过标准二进制,我们认为局部性不能成为强大绩效的解释。最后,我们提供了经验证据,表明在GEA的勘探阶段,弱点区域性表示可能对性能有益,而在剥削阶段,强点位置表示更有益。
Mutation and recombination operators play a key role in determining the speed and quality 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. We first define locality metrics equivalent to Rothlauf's that are tailored to our domain: the \textit{point locality} for single-bit mutation and \textit{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 recreate three established GEA experiments 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. We show that standard binary has provably no worse locality than any Gray encoding, including binary reflected Gray. We discuss this result in the context of previous studies that found binary reflected Gray to outperform standard binary, and we argue that locality cannot be the explanation for strong performance. Finally, we provide empirical evidence that weak point locality representations can be beneficial to performance in the exploration phase of the GEA, while strong point locality representations are more beneficial in the exploitation phase.