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.

中文翻译：

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量子退火的多车涂装车间优化

我们提出了二元涂装车间问题 (BPSP) 的泛化，以解决汽车行业应用，即多车涂装车间 (MCPS) 问题。优化的目标是在制造过程中最大限度地减少油漆车间队列中汽车之间的颜色切换次数，这是一个已知的 NP 难问题。我们区分了涂装车间问题的不同子类，并展示了如何将基本的 MCPS 问题表述为 Ising 模型。本研究中使用的问题实例是使用德国沃尔夫斯堡工厂的真实数据生成的。我们将 D-Wave 2000Q 和 Advantage 量子处理器的性能与其他经典求解器和 D-Wave Systems 提供的混合量子经典算法进行了比较。我们观察到量子处理器非常适合解决较小的问题，以及中间尺寸的混合算法。然而，我们发现这些算法的性能在大尺寸限制下很快接近简单贪婪算法的性能。