Carola Doerr

Sara Gjorgjieva, Eva Tuba, Barbara Koroušić Seljak et al.

Landscape feature representations play a central role in automated algorithm selection and meta-learning for black-box optimization, yet little is known about how different representations agree (or disagree) in the structures they impose on problem spaces. This paper presents a systematic unsupervised evaluation of four state-of-the-art representations (ELA, DeepELA, TransOptAS, and DoE2Vec) using a diverse set of affine combinations of BBOB functions (MA-BBOB). By applying extensive clustering analyses, coverage-based stability measures, and cross-representation similarity assessments, we show that each representation organizes the same problems in markedly different ways: ELA and TransOptAS form compact geometric structures, DeepELA provides a balanced intermediate view, and DoE2Vec achieves strong semantic alignment but with substantial fragmentation. Our results reveal that no single representation dominates; rather, they capture complementary aspects of the underlying landscapes. These findings highlight the importance of multi-view analyses for understanding representation behavior and offer guidance on selecting or combining representations in downstream meta-learning and algorithm selection tasks. In addition, across two different algorithm families (Differential Evolution and Particle Swarm Optimization), we show that landscape representations face an inherent trade-off in how well they align structural landscape descriptions with observed performance, indicating that no single representation can fully capture algorithm performance.

Denis Antipov, Carola Doerr

Online algorithm selection (OAS) aims to adapt the optimization process to changes in the fitness landscape and is expected to outperform any single algorithm from a given portfolio. Although this expectation is supported by numerous empirical studies, there are currently no theoretical results proving that OAS can yield asymptotic speedups (apart from some artificial examples for hyper-heuristics). Moreover, theory-based guidelines for when and how to switch between algorithms are largely missing. In this paper, we present the first theoretical example in which switching between two algorithms -- the $(1+λ)$ EA and the $(1+(λ,λ))$ GA -- solves the OneMax problem asymptotically faster than either algorithm used in isolation. We show that an appropriate choice of population sizes for the two algorithms allows the optimum to be reached in $O(n\log\log n)$ expected time, faster than the $Θ(n\sqrt{\frac{\log n \log\log\log n}{\log\log n}})$ runtime of the best of these two algorithms with optimally tuned parameters. We first establish this bound under an idealized switching rule that changes from the $(1+λ)$ to the $(1+(λ,λ))$ GA at the optimal time. We then propose a realistic switching strategy that achieves the same performance. Our analysis combines fixed-start and fixed-target perspectives, illustrating how different algorithms dominate at different stages of the optimization process. This approach offers a promising path toward a deeper theoretical understanding of OAS.

Catalin-Viorel Dinu, Diederick Vermetten, Carola Doerr

In black-box optimization, a central question is which algorithm to use to solve a given, previously unseen, problem. Selecting a single algorithm, however, entails inherent risks: inaccuracies in the selector may lead to poor choices, and even well-performing algorithms with high variance can yield unsatisfactory results in a single run. A natural remedy is to split the evaluation budget across multiple runs of potentially different algorithms. Such sequential algorithm portfolios benefit from variance reduction and complementarities between algorithms, often outperforming approaches that allocate the entire budget to a single solver. While effective portfolios can be constructed post-hoc, transferring this idea to the algorithm selection setting is non-trivial. We show that a naive portfolio constructed over the full training set already outperforms the strongest traditional baseline, the virtual best solver. We then propose a simple yet effective k-nearest-neighbor-based finetuning approach to construct portfolios tailored to unseen instances, yielding further improvements and highlighting the effectiveness of portfolio selection in fixed-budget black-box optimization.

Imène Ait Abderrahim, Carola Doerr, Martin Durand

The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for quasi-Monte Carlo integration methods, and many other applications. Recent work has shown that classical constructions such as Sobol', Halton, or Hammersley sequences can be outperformed by large margins when considering point sets of fixed sizes rather than their convergence behavior. These results, highly relevant to the aforementioned applications, raise the question of how much existing constructions can be improved through size-specific optimization. In this work, we study this question for the so-called Kronecker construction. Focusing on the 3-dimensional setting, we show that optimizing the two configurable parameters of its construction yields point sets outperforming the state-of-the-art value for sets of at least 500 points. Using the algorithm configuration technique irace, we then derive parameters that yield new state-of-the-art discrepancy values for whole ranges of set sizes.