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

The present paper introduces a new representation-driven approach to per-instance algorithm selection, applied to black-box optimization, for automatically choosing the most promising solver from a fixed portfolio. Prior work in continuous optimization largely relies on numerical descriptors, including Exploratory Landscape Analysis features and learned embeddings such as Deep-ELA. This work studies a complementary representation: contour-map visualizations of probed landscapes. A CNN regressor takes multiple instance-specific contour views (stacked or encoded per view and aggregated) and predicts per-solver performance, enabling selection by the predicted best value. On the standard BBOB 2009 single-objective protocol, the resulting selectors significantly outperform the single best solver (SBS) and are competitive with feature-based baselines. A subsequent bi-objective evaluation under the DeepELA setting further indicates that the same image-based principle can be competitive when using windowed contour views. Overall, the results suggest that simple vision models can exploit spatial structure in probed landscapes for algorithm selection without handcrafted ELA features.

Automated algorithm selection in black-box optimization typically relies on supervised models that map landscape features to algorithm performance labels. Such models are costly to train, benchmark-dependent, and often fail to generalize to unseen problem classes. We study an unsupervised alternative: multi-kernel clustering over heterogeneous landscape representations, in which problem instances are grouped without using performance labels in the clustering stage, and the resulting clusters are mapped post hoc to solver recommendations through a strictly separated three-stage evaluation protocol. Drawing on two decades of advances in multiple kernel learning, we adopt a multi-kernel k-means formulation that jointly learns cluster assignments and kernel weights over four heterogeneous landscape views: ELA, DeepELA, DoE2Vec, and TransOptAS. On affine BBOB-derived selector tasks for Differential Evolution (DE) and Particle Swarm Optimization (PSO) at a fixed evaluation budget, we report mean plus or minus standard deviation selector profiles over 50 independent random seeds for stochastic configurations. Multi-kernel clustering obtains the strongest mean profile on the DE portfolio and remains competitive with, and nominally ahead of, the leading baselines on the more compressed PSO portfolio, where differences among the best methods are small relative to stochastic variation. In representative median-seed runs used for visualization, the learned kernel weights retain ELA and TransOptAS while assigning zero weight to DeepELA and DoE2Vec, providing a task-specific interpretation of which representations are retained by the multi-kernel model for selector-oriented grouping.

Classical space-filling designs often fail to provide reliable statistical results for Exploratory Landscape Analysis (ELA) when only limited evaluation budgets are available, as commonly occurs in high-dimensional problems or other resource-constrained settings, resulting in noisy and unstable landscape descriptors. To address this challenge, we propose an alternative sampling strategy for ELA based on random linear embeddings. Rather than sampling uniformly in the full decision space, we allocate the budget to randomly oriented low-dimensional subspaces and investigate whether this improves the robustness of the resulting landscape descriptors. We compare full-space and embedding-based sampling strategies across several classical ELA feature sets on the noiseless Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) environment, in a 20-dimensional setting. Our results suggest that random linear embeddings constitute a promising alternative for budget-constrained ELA, although their effectiveness remains dependent on the feature class and the underlying problem.