This study explores the influence of modules on the performance of modular optimization frameworks for continuous single-objective black-box optimization. There is an extensive variety of modules to choose from when designing algorithm variants, however, there is a rather limited understanding of how each module individually influences the algorithm performance and how the modules interact with each other when combined. We use the functional ANOVA (f-ANOVA) framework to quantify the influence of individual modules and module combinations for two algorithms, the modular Covariance Matrix Adaptation (modCMA) and the modular Differential Evolution (modDE). We analyze the performance data from 324 modCMA and 576 modDE variants on the BBOB benchmark collection, for two problem dimensions, and three computational budgets. Noteworthy findings include the identification of important modules that strongly influence the performance of modCMA, such as the~\textit{weights\ option} and~\textit{mirrored} modules for low dimensional problems, and the~\textit{base\ sampler} for high dimensional problems. The large individual influence of the~\textit{lpsr} module makes it very important for the performance of modDE, regardless of the problem dimensionality and the computational budget. When comparing modCMA and modDE, modDE undergoes a shift from individual modules being more influential, to module combinations being more influential, while modCMA follows the opposite pattern, with an increase in problem dimensionality and computational budget.

翻译：本研究探讨了模块对连续单目标黑箱优化的模块化优化框架性能的影响。在设计算法变体时，可供选择的模块种类繁多，然而关于每个模块如何单独影响算法性能以及模块组合后如何相互作用的认知仍相当有限。我们采用功能方差分析（f-ANOVA）框架，量化了两种算法——模块化协方差矩阵自适应（modCMA）与模块化差分进化（modDE）——中个体模块及模块组合的影响。针对两个问题维度和三种计算预算，我们分析了324个modCMA变体和576个modDE变体在BBOB基准测试集上的性能数据。值得关注的结果包括：识别出对modCMA性能有强烈影响的重要模块，例如面向低维问题的~\textit{权重选项}与~\textit{镜像}模块，以及面向高维问题的~\textit{基础采样器}模块。无论问题维度和计算预算如何，~\textit{lpsr}模块的巨大个体影响使其对modDE性能至关重要。比较modCMA与modDE时发现，modDE呈现从个体模块更具影响力向模块组合更具影响力的转变，而modCMA则呈现相反模式（随着问题维度和计算预算的增加）。