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

Source: arXiv - 2605.28121v1

Overview

This paper investigates how four popular landscape‑feature representations—ELA, DeepELA, TransOptAS, and DoE2Vec—structure the space of black‑box optimization problems. By clustering thousands of synthetic benchmark functions, the authors reveal that each representation “sees” the problem landscape differently, which has direct consequences for algorithm selection and meta‑learning pipelines.

Key Contributions

• Systematic, unsupervised comparison of four state‑of‑the‑art landscape encodings on a large, diversified benchmark (MA‑BBOB, an affine combination of BBOB functions).
• Extensive clustering and stability analysis showing that ELA and TransOptAS produce tight, geometric clusters, DeepELA yields a balanced middle ground, while DoE2Vec creates semantically meaningful but highly fragmented clusters.
• Cross‑representation similarity assessment, demonstrating that the four encodings capture largely complementary information rather than redundant views of the same landscape.
• Empirical link to algorithm performance (Differential Evolution and Particle Swarm Optimization), exposing an inherent trade‑off: no single representation can fully predict how an algorithm will behave across all problems.
• Guidelines for practitioners on when to prefer a single representation versus a multi‑view combination in downstream tasks such as automated algorithm selection or hyper‑parameter tuning.

Methodology

1. Benchmark construction – The authors generated the MA‑BBOB suite, consisting of thousands of problem instances created by affine combinations of the classic BBOB functions. This yields a rich, continuous spectrum of landscape shapes.
2. Feature extraction – For every instance they computed four different representations:
   • ELA (Exploratory Landscape Analysis) – hand‑crafted statistical descriptors.
   • DeepELA – a neural‑network encoder trained on raw samples.
   • TransOptAS – a transformer‑based model that learns task‑agnostic embeddings.
   • DoE2Vec – a design‑of‑experiments‑driven embedding that emphasizes semantic similarity.
3. Unsupervised clustering – Using k‑means, hierarchical clustering, and DBSCAN, they grouped problem instances based on each representation’s vectors.
4. Stability & coverage metrics – They measured how consistent clusters were across multiple random seeds (stability) and how much of the problem space each representation covered (coverage).
5. Cross‑representation similarity – Pairwise Adjusted Rand Index (ARI) and Mutual Information scores quantified overlap between the clusterings produced by different encodings.
6. Performance alignment – For each problem instance they recorded the best‑found fitness of DE and PSO. Correlation analyses examined how well each representation’s clusters aligned with observed algorithm performance.

Results & Findings

• Distinct structural views – ELA and TransOptAS produce compact, geometrically regular clusters (high intra‑cluster similarity, low fragmentation). DeepELA’s clusters are larger and more balanced, while DoE2Vec yields many small, semantically coherent groups.
• Low agreement between representations – ARI scores between any two encodings were modest (≈0.2–0.35), confirming that they capture different facets of the landscape.
• Stability vs. coverage trade‑off – ELA and TransOptAS are highly stable but cover only a subset of the problem space; DoE2Vec covers more diverse regions but with lower stability. DeepELA sits in the middle.
• Performance correlation is representation‑dependent – DE performance aligns best with clusters from TransOptAS, whereas PSO performance correlates more with DoE2Vec’s semantic groups. No single representation explains >55 % of the variance in algorithm outcomes.
• Complementarity wins – Combining embeddings (e.g., concatenating DeepELA and DoE2Vec) improves the predictive power for algorithm selection by ~12 % compared to any single view.

Practical Implications

• Algorithm selection pipelines should consider multi‑view feature sets rather than relying on a single landscape descriptor. A simple concatenation or ensemble of representations can boost prediction accuracy for which optimizer will perform best on a new problem.
• Meta‑learning frameworks (e.g., AutoML for optimization) can leverage the complementary nature of these encodings to build richer surrogate models, potentially reducing the number of expensive benchmark runs.
• Benchmark design – The MA‑BBOB suite demonstrates a scalable way to generate diverse synthetic problems; developers can adopt similar affine combinations to stress‑test their own optimizers.
• Tooling – Existing libraries (e.g., flacco for ELA, PyTorch implementations for DeepELA/TransOptAS) can be integrated into a unified feature extraction pipeline, enabling rapid prototyping of multi‑representation meta‑learners.
• Performance diagnostics – By inspecting which representation’s clusters a new problem falls into, practitioners can get an early hint about which optimizer family (DE‑style vs. PSO‑style) is likely to be more effective.

Limitations & Future Work

• Synthetic focus – The study relies on MA‑BBOB, a synthetic benchmark; real‑world problems may exhibit additional complexities (constraints, noisy evaluations) that could affect representation behavior.
• Fixed hyper‑parameters – Feature extractors were used with their default settings; tuning these could change stability and coverage outcomes.
• Scalability – Computing DoE2Vec embeddings is computationally heavier than ELA, which may limit its use in large‑scale automated pipelines.
• Future directions suggested by the authors include: extending the analysis to constrained and noisy optimization settings, exploring dynamic (online) representations that adapt as more evaluations are collected, and investigating automated methods for selecting the optimal combination of representations for a given downstream task.

Authors

• Sara Gjorgjieva
• Eva Tuba
• Barbara Koroušić Seljak
• Carola Doerr
• Tome Eftimov

Paper Information

• arXiv ID: 2605.28121v1
• Categories: cs.NE
• Published: May 27, 2026
• PDF: Download PDF