发表机构
Graduate School of Information Sciences, Tohoku University; Department of Physics, Institute of Science Tokyo; Research and Education Institute for Semiconductors and Informatics, Kumamoto University; Sigma-I Co., Ltd.（东北大学情报科学研究生院; 东京科学大学物理系; 熊本大学半导体与信息学研究与教育学院; Sigma-I有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对含约束和连续变量的实际模型，开发避免连续变量离散化的有限温度公式处理混合二进制二次规划，在二次p中位数问题上评估，相比其他方法能更可靠生成可行解，条件相对误差表现良好，时间到目标实验中速度更快。
AI 中文摘要
量子退火和相关组合优化方法通常将二次无约束二进制优化（QUBO）问题作为输入，而许多实际模型包含约束和连续变量。标准QUBO转换会离散连续变量，增加二进制维度并使可行低能态更难采样。我们为一类可分离的混合二进制二次规划（MBQPs）开发了有限温度公式以避免这种离散化。在固定拉格朗日乘数时，连续部分通过解析积分去除，仅进入乘数更新，留下关于原始二进制变量的QUBO。我们在二次p中位数问题的连续松弛上评估该方法。与基于惩罚的QUBO公式相比，它能更可靠地生成可行解。在适当逆温度下，其条件相对误差与小实例的局部搜索相当，对大测试实例通常更低。在时间到目标实验中，在测试范围上限，它比商业混合整数优化求解器更快达到目标。
英文摘要
Quantum annealing and related combinatorial optimization methods typically accept quadratic unconstrained binary optimization (QUBO) problems as input, whereas many practical models include constraints and continuous variables. Standard QUBO conversions discretize continuous variables, increasing the binary dimension and often making feasible low-energy states harder to sample. We develop a Lagrange-multiplier method for a separable class of mixed-binary quadratic programs (MBQPs) without discretizing continuous variables. The method is based on a finite-temperature free-energy formulation and uses QUBO sampling for the binary sector. At fixed Lagrange multipliers, the continuous sector is integrated out analytically and enters only the multiplier update, leaving a QUBO over the original binary variables. We evaluate the method on the continuous relaxation of the quadratic $p$-median problem. Compared with a penalty-based QUBO formulation, it generates feasible solutions more reliably. At an appropriate inverse temperature, its conditional relative error is comparable to that of local search for small instances and often lower for the larger tested instances. In the time-to-target comparisons, the proposed method maintains high target-reached rates for stringent fixed-accuracy targets. For the larger instances within the tested range, it also reaches the prescribed targets faster than a commercial mixed-integer optimization solver.
Comments13 pages, 5 figures
DOI：10.1038/s41598-026-73188-1
