Using Affine Combinations of BBOB Problems for Performance Assessment

TL;DR

This paper explores the use of affine combinations of BBOB benchmark functions to analyze how different problem structures affect the performance of optimization algorithms, providing new insights into landscape effects.

Contribution

It introduces a method to extend benchmark functions via affine combinations, enabling detailed analysis of algorithm behavior across varied problem landscapes.

Findings

Affine combinations reveal how global structure influences algorithm performance

Scaling and optimum placement significantly impact performance analysis

Varying function combinations provides deeper landscape insights

Abstract

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.