Deep Dynamic Attention Model with Gate Mechanism for Solving Time-dependent Vehicle Routing Problems

Vehicle routing problems (VRPs) are a type of classical combinatorial optimization problems widely existing in logistics and transportation operations. There has been an increasing interest to use deep reinforcement learning (DRL) techniques to tackle VRPs, and previous DRL-based studies assumed time-independent travel times between customers. However, travel times in real-world road networks are time-varying, which need to be considered in practical VRPs. We thus propose a Deep Dynamic Attention Models with Gate Mechanisms (DDAM-GM) to learn heuristics for time-dependent VRPs (TDVRPs) in real-world road networks. It extracts the information of node location, node demand, and time-varying travel times between nodes to obtain enhanced node embeddings through a dimension-reducing MHA layer and a synchronous encoder. In addition, we use a gate mechanism to obtain better context embedding. On the basis of a 110-day travel time dataset with 240 time periods per day from an urban road network with 408 nodes and 1250 directed links, we conduct a series of experiments to validate the effectiveness of the proposed model on TDVRPs without and with consideration of time windows, respectively. Experimental results show that our model outperforms significantly two state-of-the-art DRL-based models.