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Constraint Programming (CP) is a declarative programming paradigm that allowsfor modeling and solving combinatorial optimization problems, such as theJob-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal ornear-optimal solutions for small instances, they do not scale well to largeones, i.e., they require long computation times or yield low-quality solutions.Therefore, real-world scheduling applications often resort to fast,handcrafted, priority-based dispatching heuristics to find a good initialsolution and then refine it using optimization methods.  This paper proposes a novel end-to-end approach to solving schedulingproblems by means of CP and Reinforcement Learning (RL). In contrast toprevious RL methods, tailored for a given problem by including proceduralsimulation algorithms, complex feature engineering, or handcrafted rewardfunctions, our neural-network architecture and training algorithm merelyrequire a generic CP encoding of some scheduling problem along with a set ofsmall instances. Our approach leverages existing CP solvers to train an agentlearning a Priority Dispatching Rule (PDR) that generalizes well to largeinstances, even from separate datasets. We evaluate our method on seven JSSPdatasets from the literature, showing its ability to find higher-qualitysolutions for very large instances than obtained by static PDRs and by a CPsolver within the same time limit.

An End-to-End Reinforcement Learning Approach for Job-Shop Scheduling Problems Based on Constraint Programming