# Quantifying Individual and Joint Module Impact in Modular Optimization Frameworks

arXiv: https://arxiv.org/abs/2405.11964 · HTML: https://mlsanity.com/paper/2405.11964/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2024.

## Built on by (most cited first, 3 of 3)

- [Evolutionary Computation and Explainable AI: A Roadmap to Understandable Intelligent Systems](https://mlsanity.com/paper/2406.07811/) (2024)
- [Tracing the Interactions of Modular CMA-ES Configurations Across Problem Landscapes](https://mlsanity.com/paper/2507.02331/) (2025)
- [Quantifying the Impact of Modules and Their Interactions in the PSO-X Framework](https://mlsanity.com/paper/2601.04100/) (2026)

## Abstract (arXiv)

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~textitweights option and~textitmirrored modules for low dimensional problems, and the~textitbase sampler for high dimensional problems. The large individual influence of the~textitlpsr 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.