A Hybrid Parallelization Scheme for Standard Simplex Method based on CPU/GPU Collaboration

Simplex Parallelization in a Fully Hybrid Hardware Platform

“…These speedup values are quite satisfactory and they validate the worth of using desktop-level GPUs for this kind of scientific computations, although their DP performance is relatively low. They are also comparable to other relevant approaches in the literature, and quite better than the ones of [20] Additionally, in Fig.1 the behavior of our GPU-only approach over different sizes of LP problems is shown, in terms of the corresponding speedup curves). The experiments have been performed over randomly generated dense LP problems ranging in size from 640x640 to 10000x10000, of similar properties as in [19,33], and with double precision arithmetic.…”

“…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.…”

“…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.…”

“…The complementary single-node hybrid parallellization scheme presented in section V (that assumes the existence of a CUDA-enabled GPU as well) has also been implemented with the use of OpenMP 4.5 API and CUDA 7.0 Toolkit, and it has been extensively tested over a real hybrid hardware platform (much more powerful than the one in [20]). More concretely, for this set of experiments we've used an Intel Dual Quad Core 3.0GHz Xeon system (8 cores in total), as well as one GTX 760 and one GTX TitanX NVIDIA GPUs, which are of different technologies (Kepler and Maxwell respectively).…”

“…A very early version of this work (in a much less powerful platform, without adopting full CPU/GPU collaboration, and without addressing the fully hybrid platform integration) has been presented in [18,20]. The rest of the paper is organized as follows.…”