The article presents and evaluates a scalable FRaGenLP algorithm for generating random linear programming problems of large dimension $n$ on cluster computing systems. To ensure the consistency of the problem and the boundedness of the feasible region, the constraint system includes $2n+1$ standard inequalities, called support inequalities. New random inequalities are generated and added to the system in a manner that ensures the consistency of the constraints. Furthermore, the algorithm uses two likeness metrics to prevent the addition of a new random inequality that is similar to one already present in the constraint system. The algorithm also rejects random inequalities that cannot affect the solution of the linear programming problem bounded by the support inequalities. The parallel implementation of the FRaGenLP algorithm is performed in C++ through the parallel BSF-skeleton, which encapsulates all aspects related to the MPI-based parallelization of the program. We provide the results of large-scale computational experiments on a cluster computing system to study the scalability of the FRaGenLP algorithm.

中文翻译：

---

FRaGenLP：集群计算系统的随机线性规划问题的生成器

本文介绍并评估了一种可伸缩的FRaGenLP算法，用于在集群计算系统上生成大尺寸$ n $的随机线性规划问题。为了确保问题的一致性和可行区域的有界性，约束系统包括2n + 1 $标准不等式，称为支持不等式。生成新的随机不等式并将其添加到系统中，以确保约束的一致性。此外，该算法使用两个相似度度量来防止添加新的不等式，该不等式与约束系统中已经存在的不等式相似。该算法还拒绝了不会影响以支持不等式为边界的线性规划问题的解决方案的随机不等式。FRaGenLP算法的并行实现是通过并行BSF骨架在C ++中执行的，该骨架封装了与基于MPI的程序并行化有关的所有方面。我们提供了在集群计算系统上进行大规模计算实验的结果，以研究FRaGenLP算法的可伸缩性。