MA-BBOB: Many-Affine Combinations of BBOB Functions for Evaluating AutoML Approaches in Noiseless Numerical Black-Box Optimization Contexts

TL;DR

This paper introduces MA-BBOB, a flexible method for generating diverse black-box optimization instances by combining BBOB functions, aiding in benchmarking AutoML approaches and analyzing landscape features for algorithm selection.

Contribution

It generalizes instance generation for black-box optimization by allowing multiple affine combinations and varied optima locations, enhancing benchmarking diversity and analysis capabilities.

Findings

MA-BBOB effectively fills the instance space.

Performance patterns are preserved across generated instances.

Landscape features may be useful for algorithm selection.

Abstract

Extending a recent suggestion to generate new instances for numerical black-box optimization benchmarking by interpolating pairs of the well-established BBOB functions from the COmparing COntinuous Optimizers (COCO) platform, we propose in this work a further generalization that allows multiple affine combinations of the original instances and arbitrarily chosen locations of the global optima. We demonstrate that the MA-BBOB generator can help fill the instance space, while overall patterns in algorithm performance are preserved. By combining the landscape features of the problems with the performance data, we pose the question of whether these features are as useful for algorithm selection as previous studies suggested. MA-BBOB is built on the publicly available IOHprofiler platform, which facilitates standardized experimentation routines, provides access to the interactive IOHanalyzer module for performance analysis and visualization, and enables comparisons with the rich and growing data collection available for the (MA-)BBOB functions.