Constraint programming (CP) is a powerful technique for solving constraint satisfaction and optimization problems. In CP solvers, the variable ordering strategy used to select which variable to explore first in the solving process has a significant impact on solver effectiveness. To address this issue, we propose a novel variable ordering strategy based on supervised learning, which we evaluate in the context of job shop scheduling problems. Our learning-based methods predict the optimal solution of a problem instance and use the predicted solution to order variables for CP solvers. \added[]{Unlike traditional variable ordering methods, our methods can learn from the characteristics of each problem instance and customize the variable ordering strategy accordingly, leading to improved solver performance.} Our experiments demonstrate that training machine learning models is highly efficient and can achieve high accuracy. Furthermore, our learned variable ordering methods perform competitively when compared to four existing methods. Finally, we demonstrate that hybridising the machine learning-based variable ordering methods with traditional domain-based methods is beneficial.

翻译：约束规划（CP）是解决约束满足与优化问题的强大技术。在CP求解器中，求解过程中用于选择首个探索变量的变量排序策略对求解器效率具有显著影响。针对该问题，本文提出一种基于监督学习的新型变量排序策略，并在作业车间调度问题背景下进行评估。我们提出的基于学习方法可预测问题实例的最优解，并利用该预测解对CP求解器的变量进行排序。与传统变量排序方法不同，我们的方法能够从每个问题实例的特征中学习，并据此定制变量排序策略，从而提升求解器性能。实验表明，机器学习模型的训练效率极高且能达到较高精度。此外，与四种现有方法相比，我们提出的学习型变量排序方法表现出竞争力。最后，我们证明将基于机器学习的变量排序方法与传统的领域驱动方法相结合是有益的。