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On MATLAB experience in accelerating DIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization

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  • Stripinis, Linas
  • Žilinskas, Julius
  • Casado, Leocadio G.
  • Paulavičius, Remigijus

Abstract

In this paper, two different acceleration techniques for a deterministic DIRECT (DIviding RECTangles)-type global optimization algorithm, DIRECT-GLce, are considered. We adopt dynamic data structures for better memory usage in MATLAB implementation. We also study shared and distributed parallel implementations of the original DIRECT-GLce algorithm, and a distributed parallel version for the aggressive counterpart. The efficiency of DIRECT-type parallel versions is evaluated solving box- and generally constrained global optimizations problems with varying complexity, including a practical NASA speed reducer design problem. Numerical results show a good efficiency, especially for the distributed parallel version of the original DIRECT-GLce on a multi-core PC.

Suggested Citation

  • Stripinis, Linas & Žilinskas, Julius & Casado, Leocadio G. & Paulavičius, Remigijus, 2021. "On MATLAB experience in accelerating DIRECT-GLce algorithm for constrained global optimization through dynamic data structures and parallelization," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305518
    DOI: 10.1016/j.amc.2020.125596
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    References listed on IDEAS

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    1. Qunfeng Liu & Jinping Zeng & Gang Yang, 2015. "MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems," Journal of Global Optimization, Springer, vol. 62(2), pages 205-227, June.
    2. Giampaolo Liuzzi & Stefano Lucidi & Veronica Piccialli, 2010. "A partition-based global optimization algorithm," Journal of Global Optimization, Springer, vol. 48(1), pages 113-128, September.
    3. Bernard Gendron & Teodor Gabriel Crainic, 1994. "Parallel Branch-and-Branch Algorithms: Survey and Synthesis," Operations Research, INFORMS, vol. 42(6), pages 1042-1066, December.
    4. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    5. G. Di Pillo & G. Liuzzi & S. Lucidi & V. Piccialli & F. Rinaldi, 2016. "A DIRECT-type approach for derivative-free constrained global optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 361-397, November.
    6. Remigijus Paulavičius & Julius Žilinskas, 2009. "Parallel Branch and Bound Algorithm with Combination of Lipschitz Bounds over Multidimensional Simplices for Multicore Computers," Springer Optimization and Its Applications, in: Parallel Scientific Computing and Optimization, pages 93-102, Springer.
    7. Qunfeng Liu & Guang Yang & Zhongzhi Zhang & Jinping Zeng, 2017. "Improving the convergence rate of the DIRECT global optimization algorithm," Journal of Global Optimization, Springer, vol. 67(4), pages 851-872, April.
    8. G. Liuzzi & S. Lucidi & V. Piccialli, 2016. "Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization," Computational Optimization and Applications, Springer, vol. 65(2), pages 449-475, November.
    9. Jonas Mockus & Remigijus Paulavičius & Dainius Rusakevičius & Dmitrij Šešok & Julius Žilinskas, 2017. "Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 425-450, January.
    10. Qunfeng Liu & Wanyou Cheng, 2014. "A modified DIRECT algorithm with bilevel partition," Journal of Global Optimization, Springer, vol. 60(3), pages 483-499, November.
    11. Remigijus Paulavičius & Lakhdar Chiter & Julius Žilinskas, 2018. "Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants," Journal of Global Optimization, Springer, vol. 71(1), pages 5-20, May.
    12. Juan F. R. Herrera & José M. G. Salmerón & Eligius M. T. Hendrix & Rafael Asenjo & Leocadio G. Casado, 2017. "On parallel Branch and Bound frameworks for Global Optimization," Journal of Global Optimization, Springer, vol. 69(3), pages 547-560, November.
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    Cited by:

    1. Vaidas Jusevičius & Remigijus Paulavičius, 2021. "Web-Based Tool for Algebraic Modeling and Mathematical Optimization," Mathematics, MDPI, vol. 9(21), pages 1-18, October.

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