Multi-car paint shop optimization with quantum annealing

TL;DR

This paper formulates the multi-car paint shop optimization problem as an Ising model and compares quantum annealing with classical methods, showing quantum advantages for small to medium instances but similar performance to greedy algorithms at large scale.

Contribution

It introduces a quantum annealing formulation for the multi-car paint shop problem and evaluates its performance against classical algorithms using real-world data.

Findings

Quantum processors excel at small problem sizes.

Hybrid quantum-classical algorithms perform well at intermediate sizes.

Performance converges to greedy algorithms for large problem instances.

Abstract

We present a generalization of the binary paint shop problem (BPSP) to tackle an automotive industry application, the multi-car paint shop (MCPS) problem. The objective of the optimization is to minimize the number of color switches between cars in a paint shop queue during manufacturing, a known NP-hard problem. We distinguish between different sub-classes of paint shop problems, and show how to formulate the basic MCPS problem as an Ising model. The problem instances used in this study are generated using real-world data from a factory in Wolfsburg, Germany. We compare the performance of the D-Wave 2000Q and Advantage quantum processors to other classical solvers and a hybrid quantum-classical algorithm offered by D-Wave Systems. We observe that the quantum processors are well-suited for smaller problems, and the hybrid algorithm for intermediate sizes. However, we find that the performance of these algorithms quickly approaches that of a simple greedy algorithm in the large size limit.