  Existing learning-based methods for solving job shop scheduling problems
(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, strengthening our method's practical
value. 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. All the code and data are
publicly available online at https://github.com/zcaicaros/TBGAT.
