球函数上大种群规模下$(μ/μ_I, λ)$-ES的变异强度自适应
Mutation Strength Adaptation of the $(μ/μ_I, λ)$-ES for Large Population Sizes on the Sphere Function
AI总结：
该研究针对大种群规模下球函数上的$(μ/μ_I, λ)$-ES，分析CSA与$σ$SA两种变异强度自适应方法的特性，对比不同参数、采样方式下的进展率与稳定性差异。
摘要：
本文研究了采用各向同性变异的多重组$(μ/μ_I, λ)$-ES（进化策略）的变异强度自适应特性。为此，通过假设种群规模$μ$相对于搜索空间维度$N$较大，从实验和理论层面研究了累积步长自适应（CSA）和变异自适应（$σ$SA）的标准实现。自适应特性以球函数上的尺度不变变异强度相对于其实现正进展的最大可达值的关系来表征。结果展示了不同$σ$自适应变体在$μ$和$N$变化时的行为：标准CSA变体在球函数上表现出显著不同的自适应特性和进展率，随$μ$或$N$的变化而变慢或变快，这一点通过研究累积参数和阻尼参数的常用选择得到验证。与CSA相比，标准$σ$SA变体（采用默认学习参数设置）可实现更快的自适应和更高的进展率，但研究表明自适应会对进展率水平产生负面影响。此外，本文还阐述了采用对数正态和正态变异采样的$σ$SA在自适应性和稳定性方面的差异。
英文摘要：
The mutation strength adaptation properties of a multi-recombinative $(μ/μ_I, λ)$-ES are studied for isotropic mutations. To this end, standard implementations of cumulative step-size adaptation (CSA) and mutative self-adaptation ($σ$SA) are investigated experimentally and theoretically by assuming large population sizes ($μ$) in relation to the search space dimensionality ($N$). The adaptation is characterized in terms of the scale-invariant mutation strength on the sphere in relation to its maximum achievable value for positive progress. %The results show how the different $σ$-adaptation variants behave as $μ$ and $N$ are varied. Standard CSA-variants show notably different adaptation properties and progress rates on the sphere, becoming slower or faster as $μ$ or $N$ are varied. This is shown by investigating common choices for the cumulation and damping parameters. Standard $σ$SA-variants (with default learning parameter settings) can achieve faster adaptation and larger progress rates compared to the CSA. However, it is shown how self-adaptation affects the progress rate levels negatively. Furthermore, differences regarding the adaptation and stability of $σ$SA with log-normal and normal mutation sampling are elaborated.
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