  Recent studies in using deep reinforcement learning (DRL) to solve Job-shop
scheduling problems (JSSP) focus on construction heuristics. However, their
performance is still far from optimality, mainly because the underlying graph
representation scheme is unsuitable for modelling partial solutions at each
construction step. This paper proposes a novel DRL-guided improvement heuristic
for solving JSSP, where graph representation is employed to encode complete
solutions. We design a Graph Neural-Network-based representation scheme,
consisting of two modules to effectively capture the information of dynamic
topology and different types of nodes in graphs encountered during the
improvement process. To speed up solution evaluation during improvement, we
present a novel message-passing mechanism that can evaluate multiple solutions
simultaneously. We prove that the computational complexity of our method scales
linearly with problem size. Experiments on classic benchmarks show that the
improvement policy learned by our method outperforms state-of-the-art DRL-based
methods by a large margin.
