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Multi GPU Implementation of the Simplex Algorithm

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Abstract

The Simplex algorithm is a well known method to solve linear programming (LP) problems. In this paper, we propose an implementation via CUDA of the Simplex method on a multi GPU architecture. Computational tests have been carried out on randomly generated instances for non-sparse LP problems. The tests show a maximum speedup of 24.5 with two Tesla C2050 boards. I. INTRODUCTION Initially developed for real time and high-definition 3D graphic applications, Graphics Processing Units (GPUs) have gained recently attention for High Performance Computing applications. Indeed, the peak computational capabilities of modern GPUs exceeds the one of top-of-the-line central processing units (CPUs). GPUs are highly parallel, multithreaded, manycore units. In November 2006, NVIDIA introduced, Compute Unified Device Architecture (CUDA), a technology that enables users to solve many complex problems on their GPU cards (see for example [1]-[4]). Some related works have been presented on the parallel implementation of algorithms on GPU for linear programming (LP) problems. O'Leary and Jung have proposed in [5] a combined CPU-GPU implementation of the Interior Point Method for LP; computational results carried out on NETLIB LP problems [6] for at most 516 variables and 758 constraints, show that some speedup can be obtained by using GPU for sufficiently large dense problems. Spampinato and Elster have proposed in [7] a parallel implementation of the revised Simplex method for LP on GPU with NVIDIA CUBLAS [8] and NVIDIA LAPACK [9] libraries. Tests were carried out on randomly generated LP problems of at most 2000 variables and 2000 constraints. The implementation showed a maximum speedup of 2.5 on a NVIDIA GTX 280 GPU as compared with sequential implementation on CPU with Intel Core2 Quad 2.83 GHz. Bieling, Peschlow and Martini have proposed in [10] an other implementation of the revised Simplex method on GPU. This implementation permits one to speed up solution with a maximum factor of 18 in single precision on a NVIDIA GeForce 9600 GT GPU card as compared with GLPK solver run on Intel Core 2 Duo 3GHz CPU. In [11], we have presented a parallel implementation via CUDA
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hal-01149739 , version 1 (15-05-2015)

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Mohamed Esseghir Lalami, Didier El Baz, Vincent Boyer. Multi GPU Implementation of the Simplex Algorithm. 2011 IEEE International Conference on High Performance Computing and Communications, Sep 2011, Banff, Canada. pp. 179-186, ⟨10.1109/HPCC.2011.32⟩. ⟨hal-01149739⟩
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