Boosting Column Generation with Graph Neural Networks for Joint Rider
  Trip Planning and Crew Shift Scheduling
Jiawei Lu Tinghan Ye Wenbo Chen Pascal Van Hentenryck
Optimizing service schedules is pivotal to the reliable, efficient, and
inclusive on-demand mobility. This pressing challenge is further exacerbated by
the increasing needs of an aging population, the over-subscription of existing
services, and the lack of effective solution methods. This study addresses the
intricacies of service scheduling, by jointly optimizing rider trip planning
and crew scheduling for a complex dynamic mobility service. The resulting
optimization problems are extremely challenging computationally for
state-of-the-art methods. To address this fundamental gap, this paper
introduces the Joint Rider Trip Planning and Crew Shift Scheduling Problem
(JRTPCSSP) and a novel solution method, called AGGNNI-CG (Attention and Gated
GNN- Informed Column Generation), that hybridizes column generation and machine
learning to obtain near-optimal solutions to the JRTPCSSP with the real-time
constraints of the application. The key idea of the machine-learning component
is to dramatically reduce the number of paths to explore in the pricing
component, accelerating the most time-consuming component of the column
generation. The machine learning component is a graph neural network with an
attention mechanism and a gated architecture, that is particularly suited to
cater for the different input sizes coming from daily operations. AGGNNI-CG has
been applied to a challenging, real-world dataset from the Paratransit system
of Chatham County in Georgia. It produces dramatic improvements compared to the
baseline column generation approach, which typically cannot produce feasible
solutions in reasonable time on both medium-sized and large-scale complex
instances. AGGNNI-CG also produces significant improvements in service compared
to the existing system.