Doctor of Philosophy (PhD)


Engineering Sciences

Document Type



The escalating demands of omnichannel retailing, rapid urbanization and shifting customer behaviors have propelled last-mile vehicle routing logistics to the forefront of research. This last-mile phase, recognized as a significant contributor to costs and pollution in the supply chain, necessitates efficient route optimization to minimize expenses and environmental impact. This research delves into machine learning based techniques for solving large-scale Vehicle Routing Problem (VRP), a fundamental concern in last-mile logistics, aiming to optimize delivery vehicle routing amidst diverse customer nodes and operational constraints. Three primary research subproblems are analyzed: utilizing machine learning for constructive solutions, Variable Neighborhood Search (VNS) metaheuristic, and employing hierarchical approaches for solving large-scale VRP.

We investigate the application of transformer-based deep reinforcement learning architectures for direct solutions to VRP. The standard transformer architecture poses high computational complexity during training because of the quadratic time and memory requirements of its attention unit. We explore innovative techniques to mitigate this complexity, including the linear transformer. By adopting linear transformer and reducing computational complexity of original transformers, we trained VRP solvers for problem sizes up to 300 customers efficiently. This can help distribution companies to plan routing for vehicles in under a few seconds on standard office computers for large number of customers. Additionally, we conduct an in-depth analysis of trained transformers' performance across a spectrum of problem sizes and characteristics, shedding light on their efficacy for this class of optimization problems.

Traditional improvement heuristics are directed by hand-crafted rules which limit their efficacy. In our second problem, we introduce a framework based on deep reinforcement learning named Route Edit Graph Attention Network (REGAT) to learn improvement heuristics including VNS for routing problem. Machine learning allows the algorithm to adopt and learn from previous solutions and dynamically adjust search strategies to guide the selection for the next solution. The learned policies prove to be equally efficient as traditional manually designed heuristics in lower computational time. The model generalizes to varying problem sizes and benchmark instances with less than 2% optimality gap for problem sizes ranging from 20 to 60 customers.

In the last problem, we investigate effective methodologies for addressing the challenges posed by large-scale VRP. One prominent strategy involves decomposing the problem into smaller subproblems, allowing for the utilization of transformer architecture for solving VRP. However, partitioning VRP into subproblems for ease of handling poses a potential drawback of missing out on globally optimal solutions. To address this concern, we propose a heuristic algorithm to enhance solutions in the partitioned VRP by incorporating evaluation metrics to assess route quality, thereby aiming for a comprehensive improvement of the overall solution on a global scale in a short time frame.



Committee Chair

Knapp, Gerald M.

Available for download on Saturday, December 21, 2024