# Using Affine Combinations of BBOB Problems for Performance Assessment

arXiv: https://arxiv.org/abs/2303.04573 · HTML: https://mlsanity.com/paper/2303.04573/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2023.

## Built on by (most cited first, 5 of 5)

- [MA-BBOB: Many-Affine Combinations of BBOB Functions for Evaluating AutoML Approaches in Noiseless Numerical Black-Box Optimization Contexts](https://mlsanity.com/paper/2306.10627/) (2023)
- [Landscape Features in Single-Objective Continuous Optimization: Have We Hit a Wall in Algorithm Selection Generalization?](https://mlsanity.com/paper/2501.17663/) (2025)
- [Evolutionary Computation and Explainable AI: A Roadmap to Understandable Intelligent Systems](https://mlsanity.com/paper/2406.07811/) (2024)
- [Landscape-Aware Automated Algorithm Configuration using Multi-output Mixed Regression and Classification](https://mlsanity.com/paper/2409.01446/) (2024)
- [Unsupervised Multi-kernel Learning for Automated Algorithm Selection](https://mlsanity.com/paper/2607.19031/) (2026)

## Abstract (arXiv)

Benchmarking plays a major role in the development and analysis of optimization algorithms. As such, the way in which the used benchmark problems are defined significantly affects the insights that can be gained from any given benchmark study. One way to easily extend the range of available benchmark functions is through affine combinations between pairs of functions. From the perspective of landscape analysis, these function combinations smoothly transition between the two base functions. In this work, we show how these affine function combinations can be used to analyze the behavior of optimization algorithms. In particular, we highlight that by varying the weighting between the combined problems, we can gain insights into the effects of added global structure on the performance of optimization algorithms. By analyzing performance trajectories on more function combinations, we also show that aspects such as the scaling of objective functions and placement of the optimum can greatly impact how these results are interpreted.