Learning Topological Representations with Bidirectional Graph Attention Network for Solving Job Shop Scheduling Problem

Existing learning-based methods for solving job shop scheduling problem (JSSP) usually use off-the-shelf GNN models tailored to undirected graphs and neglect the rich and meaningful topological structures of disjunctive graphs (DGs). This paper proposes the topology-aware bidirectional graph attention network (TBGAT), a novel GNN architecture based on the attention mechanism, to embed the DG for solving JSSP in a local search framework. Specifically, TBGAT embeds the DG from a forward and a backward view, respectively, where the messages are propagated by following the different topologies of the views and aggregated via graph attention. Then, we propose a novel operator based on the message-passing mechanism to calculate the forward and backward topological sorts of the DG, which are the features for characterizing the topological structures and exploited by our model. In addition, we theoretically and experimentally show that TBGAT has linear computational complexity to the number of jobs and machines, respectively, which strengthens the practical value of our method. Besides, extensive experiments on five synthetic datasets and seven classic benchmarks show that TBGAT achieves new SOTA results by outperforming a wide range of neural methods by a large margin.