Constraint programming (CP) is an effective technique for solving constraint satisfaction and optimization problems. CP solvers typically use a variable ordering strategy to select which variable to explore first in the solving process, which has a large impact on the efficacy of the solvers. In this paper, we propose a novel variable ordering strategy based on supervised learning to solve job shop scheduling problems. We develop a classification model and a regression model to predict the optimal solution of a problem instance, and use the predicted solution to order variables for CP solvers. We show that training machine learning models is very efficient and can achieve a high accuracy. Our extensive experiments demonstrate that the learned variable ordering methods perform competitively compared to four existing methods. Finally, we show that hybridising the machine learning-based variable ordering methods with traditional domain-based methods is beneficial.

本文提出了一种基于监督学习的变量排序策略，针对工厂车间问题进行求解，通过分类与回归模型预测问题实例的最优解，从而优化约束规划求解器的变量搜索顺序，并表明该方法表现优异，且与传统的基于领域的方法结合的混合策略效果更佳。

通过监督学习增强约束编程以进行作业车间调度