A graph neural networks-based deep Q-learning approach for job shop scheduling problems in traffic management

A key problem in traffic management is to schedule the movements of vehicles to reduce unnecessary costs; this issue has arisen in applications such as train schedule management, air-traffic control, and urban traffic management. This problem can be modeled as a job shop scheduling problem (JSSP), which is an important combinatorial optimization problem that is widely applied in real-world scenarios. However, designing good approximation algorithms for JSSPs often requires significant specialized knowledge and trial-and-error. In this paper, we present an end-to-end framework for solving JSSPs by using graph neural networks (GNNs) and deep Q-Learning. This single-policy model is suitable for solving instances that have similar sizes and is trained only by observing reward signals and following feasible rules. The trained model behaves like a constructive heuristic algorithm that incrementally constructs a solution, and each action is determined by the output of a GNN, which captures the current state of the partial solution. We test the proposed approach on JSSP instances with multiple sizes and demonstrate its competitive performance in all cases (after training). Our proposed framework also has the potential to be applied to other JSS subproblems.