标题： 扩展样本持久性变量缩减用于约束组合优化问题 显示英文标题

标题： Extending Sample Persistence Variable Reduction for Constrained Combinatorial Optimization Problems

摘要： 受约束的组合优化问题（CCOPs）由于解空间的指数增长而难以解决。 当使用伊辛机求解时，通常通过惩罚函数方法来强制约束，其系数必须仔细调整以平衡可行性与目标质量。 变量缩减技术，如样本持续性变量缩减（SPVAR），可以缓解伊辛机的硬件限制，但它们在CCOPs上的行为仍不够明确。 基于我们之前的提议，我们扩展并全面评估了多惩罚SPVAR（MP-SPVAR），该方法通过跨多个惩罚系数的解持续性来固定变量。 在基准问题上的实验，包括二次分配问题和二次背包问题，表明MP-SPVAR在保持或提高近似比的同时，获得了更高的可行解比例。 对小惩罚下的低能态的检查阐明了可行性何时下降以及编码选择如何影响解质量和可行性之间的权衡。 这些结果使MP-SPVAR成为CCOPs的一种实用变量缩减策略，并为系统化的惩罚调优、更广泛的问题类别以及与量子启发优化硬件及量子算法的集成奠定了基础。 显示英文摘要

摘要： Constrained combinatorial optimization problems (CCOPs) are challenging to solve due to the exponential growth of the solution space. When tackled with Ising machines, constraints are typically enforced by the penalty function method, whose coefficients must be carefully tuned to balance feasibility and objective quality. Variable-reduction techniques such as sample persistence variable reduction (SPVAR) can mitigate hardware limitations of Ising machines, yet their behavior on CCOPs remains insufficiently understood. Building on our prior proposal, we extend and comprehensively evaluate multi-penalty SPVAR (MP-SPVAR), which fixes variables using solution persistence aggregated across multiple penalty coefficients. Experiments on benchmark problems, including the quadratic assignment problem and the quadratic knapsack problem, demonstrate that MP-SPVAR attains higher feasible-solution ratios while matching or improving approximation ratios relative to the conventional SPVAR algorithm. An examination of low-energy states under small penalties clarifies when feasibility degrades and how encoding choices affect the trade-off between solution quality and feasibility. These results position MP-SPVAR as a practical variable-reduction strategy for CCOPs and lay a foundation for systematic penalty tuning, broader problem classes, and integration with quantum-inspired optimization hardware as well as quantum algorithms.