Solving the Vehicle Routing Problem with Stochastic Travel Cost Using Deep Reinforcement Learning

The Vehicle Routing Problem (VRP) is a classic combinatorial optimization problem commonly encountered in the fields of transportation and logistics. This paper focuses on a variant of the VRP, namely the Vehicle Routing Problem with Stochastic Travel Cost (VRP-STC). In VRP-STC, the introduction of stochastic travel costs increases the complexity of the problem, rendering traditional algorithms unsuitable for solving it. In this paper, the GAT-AM model combining Graph Attention Networks (GAT) and multi-head Attention Mechanism (AM) is employed. The GAT-AM model uses an encoder–decoder architecture and employs a deep reinforcement learning algorithm. The GAT in the encoder learns feature representations of nodes in different subspaces, while the decoder uses multi-head AM to construct policies through both greedy and sampling decoding methods. This increases solution diversity, thereby finding high-quality solutions. The REINFORCE with Rollout Baseline algorithm is used to train the learnable parameters within the neural network. Test results show that the advantages of GAT-AM become greater as problem complexity increases, with the optimal solution generally unattainable through traditional algorithms within an acceptable timeframe.