诱导子图博弈中迈向更少贪婪的量子联盟结构生成
Towards Less Greedy Quantum Coalition Structure Generation in Induced Subgraph Games
AI总结：
针对微电网划分抽象出的 NP 完全问题，本文提出多种非贪婪的 Quantum Annealing 方法，其中 4-split iterative R-QUBO 在经典求解器上表现优于 GCS-Q，为未来量子硬件研究提供潜力。
摘要：
向100%可再生能源的过渡需要管理能源网络的新技术，例如将它们划分为称为微电网的产消者合理子集。以最优方式执行此操作是一个困难的优化问题，因为它可以被抽象为 Induced Subgraph Games 中的 Coalition Structure Generation 问题，这是一个 NP 完全问题，要求将无向、完全、加权图划分为子图，以最大化其内部权重之和。最近，Venkatesh 等人（arXiv:2212.11372）发布了一种基于 Quantum Annealing (QA) 的迭代算法，称为 GCS-Q，他们声称在运行时复杂度方面，它是目前解决该问题的最佳求解器。由于该算法使 QA 在该问题上的应用看起来很有前景，但它是一种贪婪算法，因此这项工作提出了几种不那么贪婪的基于 QA 的方法，并研究它们中是否有任何一种能在解决方案质量上优于 GCS-Q。虽然我们发现目前在 D-Wave 硬件上情况并非如此，但当使用经典的 QBSolv 软件作为求解器时，它们中的大多数确实表现更优。特别是我们称为 4-split iterative R-QUBO 的算法在此显示出潜力，它在我们的数据集中找到了所有最优解，同时在运行时方面随问题规模具有良好的扩展性。因此，假设 QA 硬件随着时间的推移将具有更强的抗噪能力，它对于该问题的量子方法的未来研究似乎很有趣。
英文摘要：
The transition to 100% renewable energy requires new techniques for managing energy networks, such as dividing them into sensible subsets of prosumers called micro-grids. Doing so in an optimal manner is a difficult optimization problem, as it can be abstracted to the Coalition Structure Generation problem in Induced Subgraph Games, a NP-complete problem which requires dividing an undirected, complete, weighted graph into subgraphs in a way that maximizes the sum of their internal weights. Recently, Venkatesh et al. (arXiv:2212.11372) published a Quantum Annealing (QA)-based iterative algorithm called GCS-Q, which they claim to be the best currently existing solver for the problem in terms of runtime complexity. As this algorithm makes the application of QA to the problem seem promising, but is a greedy one, this work proposes several less greedy QA-based approaches and investigates whether any of them can outperform GCS-Q in terms of solution quality. While we find that this is not the case yet on D-Wave hardware, most of them do when using the classical QBSolv software as a solver. Especially an algorithm we call 4-split iterative R-QUBO shows potential here, finding all optima in our dataset while scaling favorably with the problem size in terms of runtime. Thus, it appears to be interesting for future research on quantum approaches to the problem, assuming QA hardware will become more noise-resilient over time.
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