  The vehicle routing problem with two-dimensional loading constraints
(2L-CVRP) and the last-in-first-out (LIFO) rule presents significant practical
and algorithmic challenges. While numerous heuristic approaches have been
proposed to address its complexity, stemming from two NP-hard problems: the
vehicle routing problem (VRP) and the two-dimensional bin packing problem
(2D-BPP), less attention has been paid to developing exact algorithms. Bridging
this gap, this article presents an exact algorithm that integrates advanced
machine learning techniques, specifically a novel combination of attention and
recurrence mechanisms. This integration accelerates the state-of-the-art exact
algorithm by a median of 29.79% across various problem instances. Moreover, the
proposed algorithm successfully resolves an open instance in the standard
test-bed, demonstrating significant improvements brought about by the
incorporation of machine learning models. Code is available at
https://github.com/xyfffff/NCG-for-2L-CVRP.
