Geometric Probing for Algorithm Selection in Continuous Black-Box Optimization

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.