arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1804.04737cs.DCcs.MS
收藏

大规模线性规划的可扩展共享内存并行单纯形算法

A Scalable Shared-Memory Parallel Simplex for Large-Scale Linear Programming

Demetrios Coutinho, Felipe O. Lins e Silva, Daniel Aloise, Samuel, Xavier-de-Souza

摘要:

单纯形表在工业界和学术界得到了广泛的应用和研究。随着大数据时代的到来,越来越大的问题需要在越来越大的机器中解决,这些机器的架构类型在该算法的概念中并不存在。在本文中,我们提出了一个共享内存并行实现的单纯形表算法密集的大规模线性规划(LP)的问题,用于现代多核架构。我们提出的一般计划,并解释了并行化的标准单纯形算法的每一步所采取的策略,强调解决性能瓶颈的解决方案。我们分析了加速比和并行效率相对于标准的单纯形算法,使用64个处理核心的共享存储器系统的建议的实施。实验进行了几个不同的问题,多达8192个变量和约束,在其原始和对偶配方。结果表明,当我们使用更多的变量比不等式约束的配方的性能大多是好得多。此外,他们表明,并行化策略,以避免瓶颈导致的实施规模以及与问题的大小和核心数达到一定的限制问题的大小。进一步的分析表明,这一比例限制是资源限制的结果。尽管如此,我们的实现还是能够达到19倍左右的加速。

英文摘要:

The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the conception of this algorithm. In this paper, we present a shared-memory parallel implementation of the Simplex tableau algorithm for dense large-scale Linear Programming (LP) problems for use in modern multi-core architectures. We present the general scheme and explain the strategies taken to parallelize each step of the standard simplex algorithm, emphasizing the solutions found to solve performance bottlenecks. We analyzed the speedup and the parallel efficiency for the proposed implementation relative to the standard Simplex algorithm using a shared-memory system with 64 processing cores. The experiments were performed for several different problems, with up to 8192 variables and constraints, in their primal and dual formulations. The results show that the performance is mostly much better when we use the formulation with more variables than inequality constraints. Also, they show that the parallelization strategies applied to avoid bottlenecks lead the implementation to scale well with the problem size and the core count up to a certain limit of problem size. Further analysis showed that this scaling limit was an effect of resource limitation. Even though, our implementation was able to reach speedups in the order of 19x.

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。

↑