On the Utility of Probing Trajectories for Algorithm-Selection

TL;DR

This work reframes algorithm selection by using probing trajectories—short, solver-driven time-series—as the input instead of traditional instance-centric features. Short trajectories enable low-budget predictions while preserving information about algorithm behavior, and they can be reused to warm-start the chosen solver. Across the BBOB/COCO benchmark with CMA-ES, PSO, and DE, trajectory-based inputs, especially when concatenated across algorithms, outperform traditional Exploratory Landscape Analysis features at comparable budgets, with near-perfect accuracy at higher budgets. The study also reveals that similarity from an algorithm perspective does not always align with human-defined function categories, underscoring the potential of algorithm-centric representations for cross-instance learning and efficient warm-starting in optimization systems.

Abstract

Machine-learning approaches to algorithm-selection typically take data describing an instance as input. Input data can take the form of features derived from the instance description or fitness landscape, or can be a direct representation of the instance itself, i.e. an image or textual description. Regardless of the choice of input, there is an implicit assumption that instances that are similar will elicit similar performance from algorithm, and that a model is capable of learning this relationship. We argue that viewing algorithm-selection purely from an instance perspective can be misleading as it fails to account for how an algorithm `views' similarity between instances. We propose a novel `algorithm-centric' method for describing instances that can be used to train models for algorithm-selection: specifically, we use short probing trajectories calculated by applying a solver to an instance for a very short period of time. The approach is demonstrated to be promising, providing comparable or better results to computationally expensive landscape-based feature-based approaches. Furthermore, projecting the trajectories into a 2-dimensional space illustrates that functions that are similar from an algorithm-perspective do not necessarily correspond to the accepted categorisation of these functions from a human perspective.

Figures (4)

• Figure 1: Accuracy of classification on the LOIO cross-validation for best-so-far and current probing-trajectories, time series features and time series feature selection for $2$ and $7$ generations. Median ELA feature accuracy is represented by lines for $300$ and $500$ function evaluations.
• Figure 2: Accuracy of classification on the LOIO cross-validation for best-so-far and current probing-trajectories, time series features and time series feature selection for $2$ and $7$ generations. Median ELA feature accuracy is represented by lines for $300$ and $500$ function evaluations.
• Figure 3: Boxplot of accuracy of classification of the 'best' and 'current' trajectory-based classifiers on $ALL$ trajectories from $2$ to $7$ generations on LOIO cross-validations.
• Figure 4: UMAP 2d projection of the $ALL_{current}$ time series of runs on function instances for $7$ generations for each algorithm and BBOB functions ($560$ function evaluations).