带紧致性约束的背包问题：一种半定规划方法
Knapsack with compactness: a semidefinite approach
AI总结：
本文针对带紧致性约束的最小背包问题提出半定规划方法，通过将紧致性融入约束或目标，并利用单一超参数平衡紧致性与准确性，在困难实例上相比混合整数规划展现出更优的有效性和灵活性。
摘要：
带紧致性约束的最小背包问题在物品有序的情况下，通过引入一个限制确保物品不能相距过远，从而扩展了经典背包问题。该问题在统计学中有应用，特别是在时间序列中变点的检测。本文针对该问题提出一种半定规划方法，将紧致性融入约束或目标中。我们研究并比较了不同的松弛方法，论证了我们的方法能提供高质量的启发式解和紧的界。特别地，我们惩罚半定模型中的单一超参数自然地平衡了计算解的紧致性与准确性之间的权衡。数值实验表明，在最难的实例上，与现有的混合整数规划公式相比，我们的方法具有有效性和 versatility。
英文摘要：
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in statistics, particularly in the detection of change-points in time series. In this paper, we propose a semidefinite programming approach for this problem, incorporating compactness in constraints or in objective. We study and compare the different relaxations, and argue that our method provides high-quality heuristics and tight bounds. In particular, the single hyperparameter of our penalized semidefinite models naturally balances the trade-off between compactness and accuracy of the computed solutions. Numerical experiments illustrate, on the hardest instances, the effectiveness and versatility of our approach compared to the existing mixed-integer programming formulation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
