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

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.

VaLiPro: Linear Programming Validator for Cluster Computing Systems

“…The specifications of this system are given in Table 1. For experiments, we used random LP problems generated by the program FRaGenLP [29] with the following parameters: α = 200 (the length of the bounding-hypercube edge), θ = 100 (the radius of the large hypersphere), ρ = 50 (the radius of the small hypersphere), L max = 0.35 (the upper bound of near parallelism for hyperplanes), S min = 100 (the minimum acceptable closeness for hyperplanes), a max = 1000 (the upper absolute bound for the coefficients), and b max = 10 000 (the upper absolute bound for the constant terms). The experiments were conducted for the following dimensions: n = 15, n = 17, and n = 19.…”