Machine-learning-based arc selection for constrained shortest path problems in column generation

TL;DR

This paper introduces a machine learning heuristic to select relevant arcs in constrained shortest path problems within column generation, significantly reducing computational time in routing and scheduling applications.

Contribution

It presents a novel ML-based arc selection method that accelerates the pricing problem in column generation, applicable to vehicle and crew scheduling, and vehicle routing problems.

Findings

Up to 40% reduction in computational time.

Effective arc filtering improves efficiency in NP-hard shortest path problems.

Applicable to public transit scheduling and vehicle routing with time windows.

Abstract

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.