Boosting Column Generation with Graph Neural Networks for Joint Rider Trip Planning and Crew Shift Scheduling

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 oversubscription 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 Attention and Gated GNN-Informed Column Generation (AGGNNI-CG), that hybridizes column generation and machine learning to obtain near-optimal solutions to the JRTPCSSP with real-life 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 problem, 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, which 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 substantial improvements compared to the baseline column generation approach, which typically cannot produce high-quality feasible solutions in reasonable time on large-scale complex instances. AGGNNI-CG also produces significant improvements in service quality compared to the existing system.