# Geometric Probing for Algorithm Selection in Continuous Black-Box Optimization

arXiv: https://arxiv.org/abs/2604.09095 · HTML: https://mlsanity.com/paper/2604.09095/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Automated Algorithm Selection: Survey and Perspectives](https://mlsanity.com/paper/1811.11597/) (2018)
- [Automated Algorithm Selection on Continuous Black-Box Problems By Combining Exploratory Landscape Analysis and Machine Learning](https://mlsanity.com/paper/1711.08921/) (2017)
- [Exploratory Landscape Analysis is Strongly Sensitive to the Sampling Strategy](https://mlsanity.com/paper/2006.11135/) (2020)
- [Toward Automated Algorithm Design: A Survey and Practical Guide to Meta-Black-Box-Optimization](https://mlsanity.com/paper/2411.00625/) (2024)
- [Automated Algorithm Selection: from Feature-Based to Feature-Free Approaches](https://mlsanity.com/paper/2203.13392/) (2022)
- [DoE2Vec: Deep-learning Based Features for Exploratory Landscape Analysis](https://mlsanity.com/paper/2304.01219/) (2023)
- [Evolving the Structure of Evolution Strategies](https://mlsanity.com/paper/1610.05231/) (2016)
- [Modular Differential Evolution](https://mlsanity.com/paper/2304.09524/) (2023)
- [MA-BBOB: A Problem Generator for Black-Box Optimization Using Affine Combinations and Shifts](https://mlsanity.com/paper/2312.11083/) (2023)
- [Deep-ELA: Deep Exploratory Landscape Analysis with Self-Supervised Pretrained Transformers for Single- and Multi-Objective Continuous Optimization Problems](https://mlsanity.com/paper/2401.01192/) (2024)
- [COCO: Performance Assessment](https://mlsanity.com/paper/1605.03560/) (2016)
- [Landscape Features in Single-Objective Continuous Optimization: Have We Hit a Wall in Algorithm Selection Generalization?](https://mlsanity.com/paper/2501.17663/) (2025)
- [Using the Empirical Attainment Function for Analyzing Single-objective Black-box Optimization Algorithms](https://mlsanity.com/paper/2404.02031/) (2024)
- [Impact of Training Instance Selection on Automated Algorithm Selection Models for Numerical Black-box Optimization](https://mlsanity.com/paper/2404.07539/) (2024)
- [Generalization Ability of Feature-based Performance Prediction Models: A Statistical Analysis across Benchmarks](https://mlsanity.com/paper/2405.12259/) (2024)
- [MECHBench: A Set of Black-Box Optimization Benchmarks originated from Structural Mechanics](https://mlsanity.com/paper/2511.10821/) (2025)
- [A Survey of Features Used for Representing Black-box Single-objective Continuous Optimization](https://mlsanity.com/paper/2406.06629/) (2024)
- [The Pitfalls of Benchmarking in Algorithm Selection: What We Are Getting Wrong](https://mlsanity.com/paper/2505.07750/) (2025)
- [Randomness as Reference: Benchmark Metric for Optimization in Engineering](https://mlsanity.com/paper/2511.17226/) (2025)

## Abstract (arXiv)

Automated algorithm selection for continuous black-box optimization depends on what information is acquired from a problem under a limited probing budget and how that information is represented. We introduce a geometric probing framework that samples multi-scale two-dimensional restrictions across location, orientation, and scale, and encodes their normalized objective-value maps with validity-aware convolutional processing and permutation-invariant aggregation. We compare our method with classical ELA and Deep-ELA under matched budgets, within-problem and problem-level transfer, fusion, representation, and budget analyses. We further disentangle probe acquisition from probe processing by controlled ablation. The results show that the proposed visual representation exposes solver-performance information complementary to ELA-family features and retains a relative advantage for relative expected runtime under problem-level transfer, while greater coverage, feature richness, or predictive accessibility alone does not guarantee better selection.