GASE: graph attention sampling with edges fusion for solving vehicle routing problems

Learning-based methods have become increasingly popular for solving vehicle routing problems (VRP) due to their near-optimal performance and fast inference speed. Among them, the combination of deep reinforcement learning and graph representation allows for the abstraction of node topology structures and features in an encoder–decoder style. Such an approach makes it possible to solve routing problems end-to-end without needing complicated heuristic operators designed by domain experts. Existing research studies have been focusing on novel encoding and decoding structures via various neural network models to enhance the node embedding representation. Despite the sophisticated approaches being designed for VRP, there is a noticeable lack of consideration for the graph-theoretic properties inherent to routing problems. Moreover, the potential ramifications of inter-nodal interactions on the decision-making efficacy of the models have not been adequately explored. To bridge this gap, we propose an adaptive graph attention sampling with the edges fusion framework, where nodes’ embedding is determined through attention calculation from certain highly correlated neighborhoods and edges, utilizing a filtered adjacency matrix. In detail, the selections of particular neighbors and adjacency edges are led by a multi-head attention mechanism, contributing directly to the message passing and node embedding in graph attention sampling networks. Furthermore, an adaptive actor-critic algorithm with policy improvements is incorporated to expedite the training convergence. We then conduct comprehensive experiments against baseline methods on learning-based VRP tasks from different perspectives. Our proposed model outperforms the existing methods by 2.08–6.23% and shows stronger generalization ability, achieving the state-of-the-art performance on randomly generated instances and standard benchmark datasets.