发表机构
University of Southern Denmark（南丹麦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于Weisfeiler-Leman的自动化特征提取方法，构建\texttt{WLc}割表示，在MiniZinc挑战赛实例上验证其在SVM等算法选择任务中优于传统特征，为约束优化算法选择提供新方案。
AI 中文摘要
算法选择对于高效的约束编程至关重要。多年来，许多基于机器学习方法的算法选择器已成功应用，但传统特征提取方法往往依赖人工确定的实例级统计量，无法捕捉潜在的问题结构。本文旨在弥合这一差距，引入一种新颖的自动化特征提取方法，该方法整合图转换与Weisfeiler-Lehman图核，以生成问题实例的鲁棒结构表示。1-WL测试界定了标准消息传递图神经网络（GNN）的图区分能力，且合适的GNN架构可匹配该界限[Xu等人，2018]。基于WL的特征提供了无需训练GNN的替代方案。本文的主要贡献是一种基于割的表示（\texttt{WLc}），旨在对结构划分进行建模并提供更细致的预测信号。我们在2023-2025年MiniZinc挑战赛的实例上评估了我们的方法，涉及两项任务：最大化Borda计数值和最大化预测准确率。对支持向量机（SVM）、随机森林（RF）和多层感知器（MLP）的实验结果表明，基于割的特征在SVM上的表现优于\texttt{fzn2feat}，而在RF和MLP上的结果则更为接近。
英文摘要
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.
