Optimising Rolling Stock Planning including Maintenance with Constraint Programming and Quantum Annealing

TL;DR

This paper compares Constraint Programming and Quantum Annealing methods for optimizing rolling stock planning with maintenance, using real data and quantum computers, finding comparable results at current technology levels.

Contribution

It introduces a QUBO model for Quantum Annealing in rolling stock planning and compares it with a detailed CP approach using real-world data.

Findings

Both approaches yield comparable results.

Quantum Annealing shows potential but is limited by current hardware.

Classical methods remain competitive at present.

Abstract

We propose and compare Constraint Programming (CP) and Quantum Annealing (QA) approaches for rolling stock assignment optimisation considering necessary maintenance tasks. In the CP approach, we model the problem with an Alldifferent constraint, extensions of the Element constraint, and logical implications, among others. For the QA approach, we develop a quadratic unconstrained binary optimisation (QUBO) model. For evaluation, we use data sets based on real data from Deutsche Bahn and run the QA approach on real quantum computers from D-Wave. Classical computers are used to evaluate the CP approach as well as tabu search for the QUBO model. At the current development stage of the physical quantum annealers, we find that both approaches tend to produce comparable results.