Parallelizing the dual revised simplex method

Huangfu, Qi; Hall, Julian

doi:10.1007/s12532-017-0130-5

Cited by 127 publications

(67 citation statements)

References 16 publications

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“…Two other valuable attempts are presented in [26][27] following the primal-dual simplex method and the sparse simplex method, and they've led to satisfactory results for large scale problems. Till recently, no other valuable attempts have been made to parallelize the classical revised simplex method, thus making the one presented by Huangfu and Hall [28][29] a distinguished one. 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.…”

Section: Related Workmentioning

confidence: 99%

“…Till recently, no other valuable attempts have been made to parallelize the classical revised simplex method, thus making the one presented by Huangfu and Hall [28][29] a distinguished one. 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%

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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: Related Workmentioning

confidence: 99%

Simplex Parallelization in a Fully Hybrid Hardware Platform

Mamalis¹,

Perlitis²

2017

ijacsa

View full text Add to dashboard Cite

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“…If this linear program problem is found to be unbounded, then we know that there must exists some x satisfying the conditions of a SDAS. We used the "highs" method (Huangfu and Hall, 2018) to confirm the existence of SDASs and the "revised simplex" method (Bertsimas and Tsitsiklis, 1997) to enumerate all reactions of a SDAS. Once a SDAS was confirmed to exist, we ran the integer programming process that is described in the next section for finding the autocatalytic cores subject to further specific constraints within the SDAS.…”

Section: Detecting Seed-dependent Autocatalytic Systems (Sdass) By Linear Programmingmentioning

confidence: 99%

A mechanism of abiogenesis based on complex reaction networks organized by seed-dependent autocatalytic systems

Peng

Linderoth

Baum

2021

Preprint

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Life is the canonical example of a complex system, consisting of diverse chemical components that are organized in a specific way that allows perpetuation of the living state. In contrast, the abiotic environment, which life feeds on and originated from, is much simpler and less organized. The complexity gap between the biotic and abiotic worlds, and the lack of direct observation of abiogenesis, has made explaining the origin of life one of the hardest scientific questions. A promising strategy for addressing this problem is to identify features shared by abiotic and biotic chemical systems that permit the stepwise accretion of complexity. We used such a rationale to compare abiotic and biotic reaction networks in order to evaluate the presence of autocatalysis, the underlying basis of biological self-propagation, to see if it is structured in such a way as to permit stepwise complexification. We develop the concept of, and provide an algorithm to detect, seed-dependent autocatalytic systems (SDASs), namely subnetworks that can use food chemicals to self-propagate but cannot emerge without being first seeded by some non-food chemicals. We show that serial activation of SDASs can result in incremental complexification. Furthermore, we identify life-like features that emerge during the accretion of SDASs that open up new ecological opportunities and improve the efficiency of food utilization. SDAS theory, thus, provides a conceptual roadmap from a simple abiotic environment to primitive forms of life, without the need for linear genetic polymers at the outset (though these may be added later). This framework also suggests new experiments that have the potential to detect the spontaneous emergence of life-like features, such as self-propagation and adaptability.

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“…The effectiveness of the Idiot crash is assessed via experiments with Clp (Version 1.16.10), using a set of 30 representative LP test problems in Table 1. This is the set used by Huangfu and Hall in [9], with qap15 replacing dcp2 due to QAP problems being of particular interest and the latter not being a public test problem, and nug15 replacing nug12 for consistency with the choice of QAP problems used by Mittelmann [11]. The three problems nug15, qap12 and qap15 are linearizations of quadratic assignment problems, where nug15 and qap15 differ only via row and column permutations.…”

Section: Preliminary Experimentsmentioning

confidence: 99%

The ‘Idiot’ crash quadratic penalty algorithm for linear programming and its application to linearizations of quadratic assignment problems

Galabova

Hall

2019

Optimization Methods and Software

Self Cite

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This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying algorithm is a penalty method with naive approximate minimization in each iteration. During initial iterations an approach similar to augmented Lagrangian is used. Later the technique corresponds closely to a classical quadratic penalty method. There is also a discussion of the extent to which it can be used to obtain fast approximate solutions of LP problems, in particular when applied to linearizations of quadratic assignment problems.

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Parallelizing the dual revised simplex method

Cited by 127 publications

References 16 publications

Simplex Parallelization in a Fully Hybrid Hardware Platform

Simplex Parallelization in a Fully Hybrid Hardware Platform

A mechanism of abiogenesis based on complex reaction networks organized by seed-dependent autocatalytic systems

The ‘Idiot’ crash quadratic penalty algorithm for linear programming and its application to linearizations of quadratic assignment problems

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