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This research advances algorithm selection in constraint programming by leveraging Weisfeiler-Lehman graph kernels to capture structural problem features without relying on manually engineered statistics or training heavy GNNs. The study demonstrates that these cut-based representations provide a robust predictive signal for solver performance, effectively bridging the gap between traditional feature extraction and deep learning approaches.
Using Weisfeiler-Leman Features for Algorithm Selection in Constraint Optimisation
arXiv:2610.12119v1 Announce Type: cross Abstract: Algorithm Selection is essential for efficient Constraint Programming. Over the years, many algorithm selectors based on machine learning methods have been successfully applied, yet traditional feature extraction methods often rely on manually decided instance-level statistics that fail to capture the underlying problem structure. In this paper we aim to bridge this gap by introducing a novel, automated feature extraction methodology that integrates graph conversion and Weisfeiler-Lehman graph kernels to generate robust structural representations of problem instances. The 1-WL test bounds the graph-distinguishing power of standard message-passing Graph Neural Networks (GNNs), and suitable GNN architectures match this bound \citep{Xuetal2018}. WL-based features offer an alternative that does not require training a GNN. Our primary contribution is a cut-based representation (\texttt{WLc}) designed to model structural partitions and provide a more nuanced predictive signal. We evaluate our approach on instances from the 2023--2025 MiniZinc Challenges across two tasks: maximizing Borda count scores and maximizing predictive accuracy. Experimental results across Support Vector Machines, Random Forests, and Multi-Layer Perceptrons demonstrate that cut-based features outperform \texttt{fzn2feat} with SVMs, while results with RFs and MLPs are closer.
Abstract:Algorithm Selection is essential for efficient Constraint Programming. Over the years, many algorithm selectors based on machine learning methods have been successfully applied, yet traditional feature extraction methods often rely on manually decided instance-level statistics that fail to capture the underlying problem structure. In this paper we aim to bridge this gap by introducing a novel, automated feature extraction methodology that integrates graph conversion and Weisfeiler-Lehman graph kernels to generate robust structural representations of problem instances. The 1-WL test bounds the graph-distinguishing power of standard message-passing Graph Neural Networks (GNNs), and suitable GNN architectures match this bound \citep{Xuetal2018}. WL-based features offer an alternative that does not require training a GNN. Our primary contribution is a cut-based representation (\texttt{WLc}) designed to model structural partitions and provide a more nuanced predictive signal. We evaluate our approach on instances from the 2023--2025 MiniZinc Challenges across two tasks: maximizing Borda count scores and maximizing predictive accuracy. Experimental results across Support Vector Machines, Random Forests, and Multi-Layer Perceptrons demonstrate that cut-based features outperform \texttt{fzn2feat} with SVMs, while results with RFs and MLPs are closer.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.12119 [cs.LG]
(or arXiv:2610.12119v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.12119 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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