当求解者“情绪化”时：量化与预测混合整数规划中的性能变异性
When Solvers Get Moody: Quantifying and Predicting Performance Variability in Mixed Integer Programming
AI总结：
本研究针对混合整数规划求解器的性能变异性，提出加权变异性得分（WVS）指标，构建带门控尾端提升的树状预测器，可基于早期特征预测WVS，为算法公平评估提供支撑。
摘要：
混合整数规划（MIP）求解器应用广泛，但即使在看似中性的扰动下，其性能也会出现大幅波动。这种变异性会给基准测试和计算研究的解释带来困扰。我们提出加权变异性得分（WVS），这是一种稳健的多分量指标，用于聚合归一化运行时间、最终最优性间隙、线性规划（LP）迭代次数以及分支定界节点数在重复运行中的离散程度。在MIPLIB 2017实例的一个大子集上，每个实例在四小时时限内进行100次随机运行，WVS呈现右偏分布且存在显著的上尾：许多实例基本稳定，但部分实例表现出无法仅用基本属性解释的大幅变异性。值得注意的是，该实验在两次SCIP运行中证明了开放实例“neos-5045105-creuse”的最优性。利用静态描述符和根级特征，带门控尾端提升的树状预测器在密封测试分割上实现了0.058的平均绝对误差和0.65的斯皮尔曼秩相关。特征重要性分析显示，根退化、矩阵结构、系数范围和预处理缩减是高WVS的主要驱动因素。由于变异性具有系统性且可通过低成本的早期运行特征部分预测，我们的发现为 preemptive调优提供了实用工具，并为新算法的更公平评估奠定了基础。
英文摘要：
Mixed-integer programming (MIP) solvers are widely used, yet their performance can vary substantially even under seemingly neutral perturbations. Such variability complicates benchmarking, and the interpretation of computational studies. We introduce the Weighted Variability Score (WVS), a robust multi-component metric that aggregates dispersion in normalized runtime, final optimality gap, LP iterations, and branch-and-bound nodes across repeated runs. On a large subset of MIPLIB 2017 instances, each solved in 100 randomized runs under a four-hour limit, WVS reveals a right-skewed distribution with a substantial upper tail: many instances are essentially stable, but some exhibit large variability that is not explained by basic properties alone. Notably, this experiment proved optimality for the open instance 'neos-5045105-creuse' in two SCIP runs. Using static descriptors and root-level features, a tree-based predictor with a gated tail uplift achieves a mean absolute error of 0.058 and Spearman rank correlation of 0.65 on a sealed test split. Feature-importance analysis highlights root degeneracy, matrix structure, coefficient ranges, and presolve reductions as the main drivers of high WVS. Because variability is systematic and partially predictable from inexpensive early-run features, our findings offer a practical tool for preemptive tuning and lay a foundation for fairer evaluation of new algorithms.
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。
