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A modified DIRECT algorithm with bilevel partition

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  • Qunfeng Liu
  • Wanyou Cheng

Abstract

It has been pointed out by Jones D. R. that the DIRECT global optimization algorithm can quickly get close to the basin of the optimum but takes longer to achieve a high degree of accuracy. In this paper, we introduce a bilevel strategy into a modifed DIRECT algorithm to overcome this shortcoming. The proposed algorithm is proved to be convergent globally. Numerical results show that the proposed algorithm is very promising. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Qunfeng Liu & Wanyou Cheng, 2014. "A modified DIRECT algorithm with bilevel partition," Journal of Global Optimization, Springer, vol. 60(3), pages 483-499, November.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:3:p:483-499
    DOI: 10.1007/s10898-013-0119-1
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    References listed on IDEAS

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    1. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    2. Qunfeng Liu, 2013. "Linear scaling and the DIRECT algorithm," Journal of Global Optimization, Springer, vol. 56(3), pages 1233-1245, July.
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    Citations

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    Cited by:

    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. 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.
    3. 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.
    4. 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).
    5. 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.
    6. Abdullah Al-Dujaili & S. Suresh & N. Sundararajan, 2016. "MSO: a framework for bound-constrained black-box global optimization algorithms," Journal of Global Optimization, Springer, vol. 66(4), pages 811-845, December.
    7. M. Fernanda P. Costa & Ana Maria A. C. Rocha & Edite M. G. P. Fernandes, 2018. "Filter-based DIRECT method for constrained global optimization," Journal of Global Optimization, Springer, vol. 71(3), pages 517-536, July.
    8. 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.
    9. Linas Stripinis & Remigijus Paulavičius, 2022. "Experimental Study of Excessive Local Refinement Reduction Techniques for Global Optimization DIRECT-Type Algorithms," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    10. Jesús Martínez-Frutos & David Herrero-Pérez, 2016. "Kriging-based infill sampling criterion for constraint handling in multi-objective optimization," Journal of Global Optimization, Springer, vol. 64(1), pages 97-115, January.
    11. Haitao Liu & Shengli Xu & Ying Ma & Xiaofang Wang, 2015. "Global optimization of expensive black box functions using potential Lipschitz constants and response surfaces," Journal of Global Optimization, Springer, vol. 63(2), pages 229-251, October.
    12. Qinghua Tao & Xiaolin Huang & Shuning Wang & Li Li, 2017. "Adaptive block coordinate DIRECT algorithm," Journal of Global Optimization, Springer, vol. 69(4), pages 797-822, December.

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