On the Structural (Dis)Agreement of Landscape Representations in Black-Box Optimization

Problem
This preprint addresses a significant gap in the understanding of landscape feature representations in black-box optimization (BBO) and their implications for automated algorithm selection and meta-learning. While various representations have been proposed, there is limited knowledge regarding their structural agreement or disagreement when applied to problem spaces. The authors systematically evaluate four state-of-the-art representations to elucidate how they organize optimization landscapes, which is crucial for improving algorithm selection methodologies.

Method
The authors conduct a comprehensive unsupervised evaluation of four landscape representations: ELA (Empirical Landscape Analysis), DeepELA, TransOptAS, and DoE2Vec. They utilize a diverse set of affine combinations of BBOB functions, termed MA-BBOB, to assess the representations. The evaluation employs extensive clustering analyses, coverage-based stability measures, and cross-representation similarity assessments to quantify how each representation organizes the same optimization problems. The study reveals that ELA and TransOptAS create compact geometric structures, DeepELA offers a balanced intermediate perspective, and DoE2Vec achieves strong semantic alignment but suffers from fragmentation. The authors also explore the trade-offs between structural landscape descriptions and observed performance across two algorithm families: Differential Evolution and Particle Swarm Optimization.

Results
The findings indicate that no single representation consistently outperforms the others; instead, they capture complementary aspects of the optimization landscapes. For instance, ELA and TransOptAS exhibit compactness, while DoE2Vec’s semantic alignment is notable despite fragmentation. The authors demonstrate that the landscape representations exhibit inherent trade-offs in aligning structural descriptions with algorithm performance, suggesting that reliance on a single representation may lead to suboptimal algorithm selection. The paper provides quantitative metrics on clustering stability and similarity assessments, although specific numerical results are not detailed in the abstract.

Limitations
The authors acknowledge that their study is limited by the choice of representations and the specific BBOB functions used in the evaluation. They do not address potential biases introduced by the selected algorithm families or the generalizability of their findings to other optimization contexts. Additionally, the reliance on unsupervised methods may overlook nuanced performance characteristics that could be captured through supervised evaluations.

Why it matters
This work has significant implications for the fields of meta-learning and algorithm selection in black-box optimization. By highlighting the complementary nature of different landscape representations, the authors advocate for multi-view analyses that can enhance understanding of representation behavior. This insight can guide practitioners in selecting or combining representations to improve algorithm performance in various optimization tasks. The findings also suggest that future research should focus on developing hybrid approaches that leverage the strengths of multiple representations to better capture the complexities of optimization landscapes.

Authors: Sara Gjorgjieva, Eva Tuba, Barbara Koroušić Seljak, Carola Doerr, Tome Eftimov
Source: arXiv:2605.28121
URL: https://arxiv.org/abs/2605.28121v1