Machine-learning-based arc selection for constrained shortest path problems in column generation
This work addresses efficiency improvements for optimization practitioners in routing and scheduling domains, representing an incremental advance in heuristic methods.
The paper tackled the computational bottleneck of solving NP-hard constrained shortest path problems in column generation by proposing a machine learning heuristic to reduce network size, achieving up to 40% reduction in computational time for vehicle and crew scheduling and vehicle routing with time windows.
Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is divided between these two parts. In routing or scheduling applications, the problems are mostly defined on a network, and the PP is usually an NP-hard shortest path problem with resource constraints. In this work, we propose a new heuristic pricing algorithm based on machine learning. By taking advantage of the data collected during previous executions, the objective is to reduce the size of the network and accelerate the PP, keeping only the arcs that have a high chance to be part of the linear relaxation solution. The method has been applied to two specific problems: the vehicle and crew scheduling problem in public transit and the vehicle routing problem with time windows. Reductions in computational time of up to 40% can be obtained.