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.

翻译：文章提出并评价了一个可扩缩的 FRAGenLP 算法,用于在集束计算系统中产生大型随机线性编程问题。为了确保问题的一致性和可行区域的界限,约束系统包括2n+1美元的标准不平等,称为支持不平等。产生新的随机不平等,并以一种确保制约一致性的方式加入到系统中。此外,算法使用两个相似度度度量法,以防止在集束计算系统中增加类似于限制系统中已经存在的新的随机不平等。算法还拒绝不会影响支持不平等所约束线性编程问题的解决的随机不平等。FRAGenLP 算法的平行实施在C++通过平行的 BSF-skeleton 进行,该算法包罗了与MPI 程序平行化有关的所有方面。我们提供了集束计算系统大规模计算实验的结果,以研究FRAGenLP 算法的可扩展性。