GPU accelerated pivoting rules for the simplex algorithm

Simplex type algorithms perform successive pivoting operations (or iterations) in order to reach the optimal solution. The choice of the pivot element at each iteration is one of the most critical step in simplex type algorithms. The flexibility of the entering and leaving variable selection allows to develop various pivoting rules. In this paper, we have proposed some of the most well-known pivoting rules for the revised simplex algorithm on a CPU-GPU computing environment. All pivoting rules have been implemented in MATLAB and CUDA. Computational results on randomly generated optimal dense linear programs and on a set of benchmark problems (Netlib-optimal, Kennington, Netlib-infeasible, Mészáros) are also presented. These results showed that the proposed GPU implementations of the pivoting rules outperform the corresponding CPU implementations.