Using Weisfeiler-Leman Features for Algorithm Selection in Constraint Optimisation

2026-10-08

AI Summary

This study addresses the limitation of conventional feature extraction for constrained optimization problems, which relies on manual statistics and struggles to capture underlying structural information. We propose an automated feature representation method based on graph transformation and the Weisfeiler-Lehman (WL) graph kernel. Specifically, we introduce a novel cut-based WLc representation that generates fine-grained and robust structural features without training graph neural networks, thereby facilitating algorithm selection. By integrating this representation with Support Vector Machines, Random Forests, and Multilayer Perceptrons, we evaluate its effectiveness empirically. Experimental results on the MiniZinc Challenge demonstrate that WLc features combined with SVM significantly outperform the existing baseline method fzn2feat, validating the efficacy of the proposed framework.

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.

Problem

• Algorithm Selection
• Constraint Optimisation
• Feature Extraction
• Weisfeiler-Leman

Innovation

• Algorithm Selection
• Weisfeiler-Lehman Graph Kernels
• Constraint Optimisation
• Feature Extraction
• Cut-based Representation