分布式并行结构感知预处理用于箭头形线性规划
Distributed Parallel Structure-Aware Presolving for Arrowhead Linear Programs
AI总结：
本文提出一种专为箭头形线性规划设计的结构感知并行预处理框架，显著提升了预处理效率。
摘要：
我们提出了一种专为箭头形线性规划（AHLPs）设计的结构感知并行预处理框架，适用于高性能计算（HPC）环境，集成到并行内点求解器PIPS-IPM++中。大规模线性规划问题通常包含冗余和数值病态，需要有效的预处理，但现有预处理技术大多是串行或结构无关的，在并行求解流程中可能变得耗时。在PIPS-IPM++中，AHLPs以分布式内存存储，我们的预处理在此基础上在计算节点上应用高效的并行分布式预处理，同时保持通信开销低并保留底层箭头形结构。我们通过一组多样化的AHLPs展示了我们方法的可扩展性和有效性，并将其与最先进的预处理实现进行比较，包括PaPILO和Gurobi中的预处理实现。即使在单机上，我们的预处理在移位几何均值运行时间方面也显著优于PaPILO，提高了18倍，优于Gurobi的预处理，提高了6倍，在减少问题数量方面与PaPILO相似。使用分布式计算环境，我们以13倍的速度优于Gurobi的预处理。
英文摘要：
We present a structure-aware parallel presolve framework for arrowhead linear programs (AHLPs) in high-performance computing (HPC) environments, integrated into the parallel interior point solver PIPS-IPM++. Large-scale LPs arising from automated model generation frequently contain redundancies and numerical pathologies that necessitate effective presolve, yet existing presolve techniques are primarily serial or structure-agnostic. Our presolve works on the distributed data of PIPS-IPM++, communicates only information on the linking parts of the problem, and preserves the arrowhead structure. Already on a single compute node with 64 processes, it outperforms PaPILO by a factor of 19 and Gurobi's presolve by a factor of 6 (shifted geometric mean), while removing a few percentage points fewer nonzeros. On large instances with small linking parts, multiple compute nodes make it 20 to 115 times faster than Gurobi's presolve. Presolve raises the number of instances solved by PIPS-IPM++ from 37 to 48. External presolve works with the modeler's annotation carried over, but it is slower, especially on large models, and breaks the distributed workflow. With automatic re-annotation, PIPS-IPM++ solves at most 21 instances.
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