Using Affine Combinations of BBOB Problems for Performance Assessment

arXiv (Cornell University)

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.

Authors 3

1. Diederick Vermetten Aachen Leiden Institute for Advanced Computer Science Leiden

   Leiden University

   Affiliation as printed

   Leiden Institute for Advanced Computer Science Leiden , The Netherlands

2. Furong Ye Aachen Leiden Institute for Advanced Computer Science Leiden

   Leiden University

   Affiliation as printed

   Leiden Institute for Advanced Computer Science Leiden , The Netherlands

3. Carola Doerr

   Centre National de la Recherche Scientifique · Sorbonne Université · LIP6

   Affiliation as printed

   Sorbonne Université , CNRS , LIP6 Paris , France