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Improving the convergence rate of the DIRECT global optimization algorithm

Author

Listed:
  • Qunfeng Liu

    (Dongguan University of Technology)

  • Guang Yang

    (Dongguan University of Technology)

  • Zhongzhi Zhang

    (Dongguan University of Technology)

  • Jinping Zeng

    (Dongguan University of Technology)

Abstract

DIRECT is derivative-free global-search algorithm has been found to perform robustly across a wide variety of low-dimensional test problems. The reason DIRECT’s robustness is its lack of algorithmic parameters that need be “tuned” to make the algorithm perform well. In particular, there is no parameter that determines the relative emphasis on global versus local search. Unfortunately, the same algorithmic features that enable DIRECT to perform so robustly have a negative side effect. In particular, DIRECT is usually quick to get close to the global minimum, but very slow to refine the solution to high accuracy. This is what we call DIRECT’s “eventually inefficient behavior.” In this paper, we outline two root causes for this undesirable behavior and propose modifications to eliminate it. The paper builds upon our previously published “MrDIRECT” algorithm, which we can now show only addressed the first root cause of the “eventually inefficient behavior.” The key contribution of the current paper is a further enhancement that allows MrDIRECT to address the second root cause as well. To demonstrate the effectiveness of the enhanced MrDIRECT, we have identified a set of test functions that highlight different situations in which DIRECT has convergence issues. Extensive numerical work with this test suite demonstrates that the enhanced version of MrDIRECT does indeed improve the convergence rate of DIRECT.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:4:d:10.1007_s10898-016-0447-z
    DOI: 10.1007/s10898-016-0447-z
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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. 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.
    4. Qunfeng Liu, 2013. "Linear scaling and the DIRECT algorithm," Journal of Global Optimization, Springer, vol. 56(3), pages 1233-1245, July.
    5. Qunfeng Liu & Jinping Zeng, 2015. "Global optimization by multilevel partition," Journal of Global Optimization, Springer, vol. 61(1), pages 47-69, January.
    6. Qunfeng Liu & Wanyou Cheng, 2014. "A modified DIRECT algorithm with bilevel partition," Journal of Global Optimization, Springer, vol. 60(3), pages 483-499, November.
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    Cited by:

    1. 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).
    2. Donald R. Jones & Joaquim R. R. A. Martins, 2021. "The DIRECT algorithm: 25 years Later," Journal of Global Optimization, Springer, vol. 79(3), pages 521-566, March.

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