Efficient Implementation of the Simplex Method on a CPU-GPU System

Abstract

The Simplex algorithm is a well known method to solve linear programming (LP) problems. In this paper, we propose a parallel implementation of the Simplex on a CPU-GPU systems via CUDA. Double precision implementation is used in order to improve the quality of solutions. Computational tests have been carried out on randomly generated instances for non-sparse LP problems. The tests show a maximum speedup of 12.5 on a GTX 260 board.

Simplex Parallelization in a Fully Hybrid Hardware Platform

“…In our hybrid approach, part of the corresponding operations are being performed in the GPU, using appropriate reduction techniques. Our experiments showed (as opposed to [19] and [20]) that the performance obtained by sharing these reduction steps in both the CPU and GPU, was at least equivalent (and in any case note worse) to the alternative followed there (of performing the reduction operations totally in the CPU). The relatively large size of the tested problems, the double precision operations, and the limitations of the NVIDIA architecture itself, lead to limited efficiency when the GPU participates in the reduction computations.…”

“…In [32] another implementation of the revised simplex method on GPU was proposed, which permits one to speed up solution with a maximum factor of 18 in single precision on a GeForce 9600 GT GPU card as compared with GLPK solver run on Intel Core 2 Duo 3GHz CPU. Lalami et al [19] have presented a GPU mainly based parallel implementation via CUDA of the standard simplex algorithm for dense LP problems. Experiments carried out on an Intel Xeon 3GHz and a GTX 260 GPU have shown substantial speedup of 12.5 in double precision, for randomly generated LP problems of size up to 8000x8000.…”

“…To our knowledge there is no relevant approach in the literature adopting extended CPU/GPU collaboration (i.e. not only for the reduction operations as in [19] or semi-hybrid as in [20]) for parallelizing the simplex method.…”

“…Next, with regard to the required CPU/GPU collaboration we apply a suitable extension of the GPU-oriented parallel approach presented in [19] 1 , by assigning a portion (a number of columns) of the full simplex tableau to be processed by the GPU and leaving the remaining portion to be processed by the CPU. However, with respect to the internal processing within the GPU-cores, the distribution scheme of the corresponding tableau portion is turned to a block-oriented one, which fits better to the internal architecture and the processing capabilities of an NVIDIA GPU [19].…”

“…However, with respect to the internal processing within the GPU-cores, the distribution scheme of the corresponding tableau portion is turned to a block-oriented one, which fits better to the internal architecture and the processing capabilities of an NVIDIA GPU [19].…”