Advances in the Parallelization of the Simplex Method

Mamalis, Basilis; Pantziou, Grammati

doi:10.1007/978-3-319-24024-4_17

Cited by 14 publications

(12 citation statements)

References 26 publications

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“…The authors in [28][29] have designed and implemented a very efficient parallelization scheme of the dual revised method with use of the suboptimization technique, and they have obtained speedup values comparable to those of the best commercial simplex solvers. A relevant survey which covers adequately all the recent advances in simplex parallelization can be found in [12].…”

Section: Related Workmentioning

confidence: 99%

“…4, 2017 357 | P a g e www.ijacsa.thesai.org GPU-accelerated solutions. Although in simplex parallelization there have not been noticed as many relevant attempts as one would expect and no parallel GPU-based implementation of the simplex algorithm has yet offered significantly better performance relative to an efficient sequential simplex solver (at least not in all types of problems), quite significant progress has been achieved at least for dense LP problems [12]. There also exist various approaches in the field of parallel scientific computing that adopt extended CPU/GPU collaboration [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Simplex Parallelization in a Fully Hybrid Hardware Platform

Mamalis¹,

Perlitis²

2017

ijacsa

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Abstract-The simplex method has been successfully used in solving linear programming (LP) problems for many years. Parallel approaches have also extensively been studied due to the intensive computations required, especially for the solution of large LP problems. Furthermore, the rapid proliferation of multicore CPU architectures as well as the computational power provided by the massive parallelism of modern GPUs have turned CPU / GPU collaboration models increasingly into focus over the last years for better performance. In this paper, a highly scalable implementation framework of the standard full tableau simplex method is first presented, over a hybrid parallel platform which consists of multiple multicore nodes interconnected via a high-speed communication network. The proposed approach is based on the combined use of MPI and OpenMP, adopting a suitable column-based distribution scheme for the simplex tableau. The parallelization framework is then extended in such a way that it can exploit concurrently the full power of the provided resources on a multicore single-node environment with a CUDA-enabled GPU (i.e. using the CPU cores and the GPU concurrently), based on a suitable hybrid multithreading/GPU offloading scheme with OpenMP and CUDA. The corresponding experimental results show that the hybrid MPI+OpenMP based parallelization scheme leads to particularly high speed-up and efficiency values, considerably better than in other competitive approaches, and scaling well even for very large / huge linear problems. Furthermore, the performance of the hybrid multithreading/GPU offloading scheme is clearly superior to both the OpenMP-only and the GPU-only based implementations in almost all cases, which validates the worth of using both resources concurrently. The most important, when it is used in combination with MPI in a multi-node (fully hybrid) environment, it leads to substantial improvements in the speedup achieved for large and very large LP problems.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simplex Parallelization in a Fully Hybrid Hardware Platform

Mamalis¹,

Perlitis²

2017

ijacsa

Self Cite

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“…Thus, the development of new parallel algorithms for solving LP problems and the revision of current algorithms have become imperative. As examples, we can cite the works [4][5][6][7][8]. The development of new parallel algorithms for solving large-scale linear programming problems involves testing them on benchmark and random problems.…”

Section: Introductionmentioning

confidence: 99%

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

Sokolinsky,

Sokolinskaya

2021

Preprint

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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.

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“…Thus, the development of new parallel algorithms for solving LP problems and the revision of current algorithms have become imperative. As examples, we can cite the works [4][5][6][7][8][9]. The development of new parallel algorithms for solving large-scale linear programming problems involves testing them on various benchmarks.…”

Section: Introductionmentioning

confidence: 99%

VaLiPro: Linear Programming Validator for Cluster Computing Systems

Sokolinsky,

Sokolinskaya

2021

Preprint

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The article presents and evaluates a scalable algorithm for validating solutions to linear programming problems on cluster computing systems. The main idea of the method is to generate a regular set of points (validation set) on a small-radius hypersphere centered at the solution point submitted to validation. The objective function is computed at each point of the validation that belongs to the feasible region. If all the values are less than or equal to the value of the objective function at the point that is to be validated, then this point is the correct solution. The parallel implementation of the VaLiPro algorithm is written 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 VaLiPro algorithm.

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Advances in the Parallelization of the Simplex Method

Cited by 14 publications

References 26 publications

Simplex Parallelization in a Fully Hybrid Hardware Platform

Simplex Parallelization in a Fully Hybrid Hardware Platform

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

VaLiPro: Linear Programming Validator for Cluster Computing Systems

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