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Lipschitz-inspired HALRECT algorithm for derivative-free global optimization

Author

Listed:
  • Linas Stripinis

    (Vilnius University)

  • Remigijus Paulavičius

    (Vilnius University)

Abstract

This article considers a box-constrained global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Motivated by the famous DIRECT (DIviding RECTangles), a new HALRECT (HALving RECTangles) algorithm is introduced. A new deterministic approach combines halving (bisection) with a new multi-point sampling scheme in contrast to trisection and midpoint sampling used in most existing DIRECT-type algorithms. A new partitioning and sampling scheme uses more comprehensive information on the objective function. Four different strategies for selecting potentially optimal hyper-rectangles are introduced to exploit the objective function’s information effectively. The original algorithm HALRECT and other introduced HALRECT variations (twelve in total) are tested and compared with the other twelve recently introduced DIRECT-type algorithms on 96 box-constrained benchmark functions from DIRECTGOLib v1.1, and 96 perturbed their versions. Extensive experimental results are advantageous compared to state-of-the-art DIRECT-type global optimization. New HALRECT approaches offer high robustness across problems of different degrees of complexity, varying from simple—uni-modal and low dimensional to complex—multi-modal and higher dimensionality.

Suggested Citation

  • Linas Stripinis & Remigijus Paulavičius, 2024. "Lipschitz-inspired HALRECT algorithm for derivative-free global optimization," Journal of Global Optimization, Springer, vol. 88(1), pages 139-169, January.
  • Handle: RePEc:spr:jglopt:v:88:y:2024:i:1:d:10.1007_s10898-023-01296-7
    DOI: 10.1007/s10898-023-01296-7
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Na, Jonggeol & Lim, Youngsub & Han, Chonghun, 2017. "A modified DIRECT algorithm for hidden constraints in an LNG process optimization," Energy, Elsevier, vol. 126(C), pages 488-500.
    4. 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.
    5. Remigijus Paulavičius & Julius Žilinskas, 2014. "Simplicial Lipschitz optimization without the Lipschitz constant," Journal of Global Optimization, Springer, vol. 59(1), pages 23-40, May.
    6. 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.
    7. 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.
    8. 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).
    9. 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.
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