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Predicting the Execution Time of the Primal and Dual Simplex Algorithms Using Artificial Neural Networks

Author

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  • Sophia Voulgaropoulou

    (Department of Applied Informatics, School of Information Sciences, University of Macedonia, GR-54636 Thessaloniki, Greece
    These authors contributed equally to this work.)

  • Nikolaos Samaras

    (Department of Applied Informatics, School of Information Sciences, University of Macedonia, GR-54636 Thessaloniki, Greece
    These authors contributed equally to this work.)

  • Nikolaos Ploskas

    (Department of Electrical & Computer Engineering, Faculty of Engineering, University of Western Macedonia, GR-50100 Kozani, Greece
    These authors contributed equally to this work.)

Abstract

Selection of the most efficient algorithm for a given set of linear programming problems has been a significant and, at the same time, challenging process for linear programming solvers. The most widely used linear programming algorithms are the primal simplex algorithm, the dual simplex algorithm, and the interior point method. Interested in algorithm selection processes in modern mathematical solvers, we had previously worked on using artificial neural networks to formulate and propose a regression model for the prediction of the execution time of the interior point method on a set of benchmark linear programming problems. Extending our previous work, we are now examining a prediction model using artificial neural networks for the performance of CPLEX’s primal and dual simplex algorithms. Our study shows that, for the examined set of benchmark linear programming problems, a regression model that can accurately predict the execution time of these algorithms could not be formed. Therefore, we are proceeding further with our analysis, treating the problem as a classification one. Instead of attempting to predict exact values for the execution time of primal and dual simplex algorithms, our models estimate classes, expressed as time ranges, under which the execution time of each algorithm is expected to fall. Experimental results show a good performance of the classification models for both primal and dual methods, with the relevant accuracy score reaching 0.83 and 0.84 , respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1038-:d:778494
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    References listed on IDEAS

    as
    1. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    2. William J. Carolan & James E. Hill & Jeffery L. Kennington & Sandra Niemi & Stephen J. Wichmann, 1990. "An Empirical Evaluation of the KORBX® Algorithms for Military Airlift Applications," Operations Research, INFORMS, vol. 38(2), pages 240-248, April.
    3. Mustafa Baz & Brady Hunsaker & Oleg Prokopyev, 2011. "How much do we “pay” for using default parameters?," Computational Optimization and Applications, Springer, vol. 48(1), pages 91-108, January.
    4. 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.
    5. Nikolaos Ploskas & Nikolaos Samaras, 2017. "Correction to: Linear Programming Using MATLAB®," Springer Optimization and Its Applications, in: Linear Programming Using MATLAB®, pages E1-E3, Springer.
    6. Maros, Istvan & Haroon Khaliq, Mohammad, 2002. "Advances in design and implementation of optimization software," European Journal of Operational Research, Elsevier, vol. 140(2), pages 322-337, July.
    7. Jianfeng Liu & Nikolaos Ploskas & Nikolaos V. Sahinidis, 2019. "Tuning BARON using derivative-free optimization algorithms," Journal of Global Optimization, Springer, vol. 74(4), pages 611-637, August.
    8. David H. Wolpert & William G. Macready, 1995. "No Free Lunch Theorems for Search," Working Papers 95-02-010, Santa Fe Institute.
    9. Castle Jennifer L. & Doornik Jurgen A & Hendry David F., 2011. "Evaluating Automatic Model Selection," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-33, February.
    10. Osman Y. Özaltın & Brady Hunsaker & Andrew J. Schaefer, 2011. "Predicting the Solution Time of Branch-and-Bound Algorithms for Mixed-Integer Programs," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 392-403, August.
    11. Nikolaos Ploskas & Nikolaos Samaras, 2017. "Linear Programming Using MATLAB®," Springer Optimization and Its Applications, Springer, number 978-3-319-65919-0, June.
    12. Alwosheel, Ahmad & van Cranenburgh, Sander & Chorus, Caspar G., 2018. "Is your dataset big enough? Sample size requirements when using artificial neural networks for discrete choice analysis," Journal of choice modelling, Elsevier, vol. 28(C), pages 167-182.
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