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Computational complexity of the exterior point simplex algorithm

Author

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  • Sophia Voulgaropoulou

    (University of Macedonia)

  • Nikolaos Samaras

    (University of Macedonia)

  • Angelo Sifaleras

    (University of Macedonia)

Abstract

In this paper, we investigate the computational behavior of the exterior point simplex algorithm. Up until now, there has been a major difference observed between the theoretical worst case complexity and practical performance of simplex-type algorithms. Computational tests have been carried out on randomly generated sparse linear problems and on a small set of benchmark problems. Specifically, 6780 linear problems were randomly generated, in order to formulate a respectable amount of experiments. Our study consists of the measurement of the number of iterations that the exterior point simplex algorithm needs for the solution of the above mentioned problems and benchmark dataset. Our purpose is to formulate representative regression models for these measurements, which would play a significant role for the evaluation of an algorithm’s efficiency. For this examination, specific characteristics, such as the number of constraints and variables, the sparsity and bit length, and the condition of matrix A, of each linear problem, were taken into account. What drew our attention was that the formulated model for the randomly generated problems reveal a linear relation among these characteristics.

Suggested Citation

  • Sophia Voulgaropoulou & Nikolaos Samaras & Angelo Sifaleras, 2019. "Computational complexity of the exterior point simplex algorithm," Operational Research, Springer, vol. 19(2), pages 297-316, June.
    • Handle: RePEc:spr:operea:v:19:y:2019:i:2:d:10.1007_s12351-017-0291-z
    DOI: 10.1007/s12351-017-0291-z
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    References listed on IDEAS

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    1. Karl-Heinz Borgwardt, 1982. "Some Distribution-Independent Results About the Asymptotic Order of the Average Number of Pivot Steps of the Simplex Method," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 441-462, August.
    2. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
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    Cited by:

    1. Sophia Voulgaropoulou & Nikolaos Samaras & Nikolaos Ploskas, 2022. "Predicting the Execution Time of the Primal and Dual Simplex Algorithms Using Artificial Neural Networks," Mathematics, MDPI, vol. 10(7), pages 1-21, March.

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