Quantum annealing (QA) can be used to efficiently solve quadratic unconstrained binary optimization (QUBO) problems. Grid partitioning (GP), which is a classic NP-hard integer programming problem, can potentially be solved much faster using QA. However, inequality constraints in the GP optimization model are difficult to handle. In this study, a novel solution framework based on QA is proposed for GP problems. The integer slack (IS) and binary expansion methods are applied to transform GP problems into QUBO problems. Instead of introducing continuous variables in traditional slack methods, the proposed IS method can avoid complex iteration processes when using QA. The case study demonstrates that the IS method obtains accurate feasible solutions with less calculation time.

中文翻译：

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使用整数松弛变量进行网格划分的量子退火


量子退火 (QA) 可用于有效解决二次无约束二元优化 (QUBO) 问题。网格划分 (GP) 是一个经典的 NP 难整数规划问题，使用 QA 可以更快地解决。然而，GP优化模型中的不等式约束很难处理。在本研究中，针对 GP 问题提出了一种基于 QA 的新颖解决方案框架。应用整数松弛（IS）和二元展开方法将GP问题转化为QUBO问题。所提出的 IS 方法没有在传统的 slack 方法中引入连续变量，而是可以避免使用 QA 时复杂的迭代过程。案例研究表明IS方法能够以较少的计算时间获得准确的可行解。