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.

The heterogeneous fleet and demand vehicle routing problem with time-window constraints (HFDVRPTW) is a crucial optimization problem of significant importance in real-world logistics operations. In this paper, we propose a deep reinforcement learning (DRL)-based method, termed spatial Edge-Feature EnhanCed mulTIgraph fusion encoder With spectral-based embedding and hieRarchical decOder with learnable TEmpoRal positional embedding (EFECTIW-ROTER, pronounced "Effective Router"), to tackle this complex and practical optimization problem. EFECTIW-ROTER utilizes two sparse graphs to represent node connectivity, where nodes correspond to customers and the depot. This sparsity results from the time-window constraints and customers' demand relative to the list of acceptable vehicle attributes specified for service within a heterogeneous fleet, determined by the reachability of the nodes based on these two factors. Leveraging two graph Transformer models, EFECTIW-ROTER's encoding module captures the interactions between the nodes based on these factors. One model encodes customers' heterogeneous demand with spatial edge features based on travel time between the nodes, while the second employs temporal positional embeddings to capture temporal relationships based on time-window ordering. A fusion model is introduced to integrate node interactions based on these graphs. Additionally, a spectral-attention-based pooling ensures effective state representation for the DRL-based method. EFECTIW-ROTER features a hierarchical attention decoder operating in two stages: heterogeneous vehicle selection and node selection. Enhanced with positional embeddings, the decoder is empowered to make effective routing decisions based on time-window constraints' ordering. Experimental results using real-world traffic data from two major Canadian cities confirm EFECTIW-ROTER's better performance over current state-of-the-art DRL-based and heuristic methods. EFECTIW-ROTER reduces travel times while also achieving faster computational times when compared to conventional heuristics. Additional experiments demonstrate its generalizability across larger instances.

Truck speed prediction plays a key role in truck transportation management. However, it is a very challenging task since the truck traffic usually shows complex patterns. Most of the existing traffic prediction methods lack the ability to model the dynamic spatial-temporal correlations of truck traffic or ignore contributing contextual factors that impact traffic. Also, truck traffic data is typically sparse and noisy, which makes the truck speed prediction an even more challenging task. How to improve the truck speed prediction by taking advantage of other relevant truck traffic information (such as the truck flow) has not been investigated in depth. Additionally, traffic congestions and poor driving conditions caused by extreme weather conditions can make sudden changes in the general pattern of the truck speed. In this paper, we propose a novel Multi-Task Context Based Gated Recurrent Unit Graph Convolutional Network (MT-C2G) to predict the truck speed under extreme weather conditions. MT-C2G includes four major components: The spatial dependence learning component captures the spatial dependencies shaped by the topological structure of the road network. Truck traffic feature temporal dependence modeling component is built to acquire the temporal dependencies involved in the truck traffic features, and contextual feature temporal dependence modeling component employs a layer of GRU units to capture the temporal dependencies of contextual factors. The multi-task learning component then leverages the information between the truck speed and flow prediction tasks through attention mechanism for improving the performance. Moreover, a data augmentation method SMOTE is utilized to balance the data with the extreme weather conditions. Experiments on two real datasets demonstrate that the proposed MT-C2G fairly outperforms six state-of-the-art traffic prediction methods.