SED2AM: Solving Multi-Trip Time-Dependent Vehicle Routing Problem Using Deep Reinforcement Learning

Deep Reinforcement Learning (DRL)-based frameworks, featuring Transformer-style policy networks, have demonstrated their efficacy across various Vehicle Routing Problem (VRP) variants. However, the application of these methods to the Multi-Trip Time-Dependent Vehicle Routing Problem (MTTDVRP) with maximum working hours constraints—a pivotal element of urban logistics—remains largely unexplored. This article introduces a DRL-based method called the Simultaneous Encoder and Dual Decoder Attention Model (SED2AM), tailored for the MTTDVRP with maximum working hours constraints. The proposed method introduces a temporal locality inductive bias to the encoding module of the policy networks, enabling it to effectively account for the time dependency in travel distance/time. The decoding module of SED2AM includes a vehicle selection decoder that selects a vehicle from the fleet, effectively associating trips with vehicles for functional multi-trip routing. Additionally, this decoding module is equipped with a trip construction decoder leveraged for constructing trips for the vehicles. This policy model is equipped with two classes of state representations, fleet state, and routing state, providing the information needed for effective route construction in the presence of maximum working hours constraints. Experimental results using real-world datasets from two major Canadian cities not only show that SED2AM outperforms the current state-of-the-art DRL-based and metaheuristic-based baselines but also demonstrate its generalizability to solve larger scale problems.