FRaGenLP: A Generator of Random Linear Programming Problems for Cluster Computing Systems

TL;DR

This paper introduces FRaGenLP, a scalable algorithm for generating large random linear programming problems on cluster systems, ensuring problem consistency and bounded feasible regions through novel constraint management.

Contribution

The paper presents a new scalable parallel algorithm for generating large random LP problems with guaranteed consistency and boundedness, suitable for cluster computing environments.

Findings

Algorithm scales well on cluster systems

Generated problems maintain consistency and boundedness

Parallel implementation achieves high efficiency

Abstract

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.