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Experimental Study of Excessive Local Refinement Reduction Techniques for Global Optimization DIRECT-Type Algorithms

Author

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  • Linas Stripinis

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos 4, LT-08663 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Remigijus Paulavičius

    (Institute of Data Science and Digital Technologies, Vilnius University, Akademijos 4, LT-08663 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

This article considers a box-constrained global optimization problem for Lipschitz continuous functions with an unknown Lipschitz constant. The well-known derivative-free global search algorithm DIRECT (DIvide RECTangle) is a promising approach for such problems. Several studies have shown that recent two-step (global and local) Pareto selection-based algorithms are very efficient among all DIRECT-type approaches. However, despite its encouraging performance, it was also observed that the candidate selection procedure has two possible shortcomings. First, there is no limit on how small the size of selected candidates can be. Secondly, a balancing strategy between global and local candidate selection is missing. Therefore, it may waste function evaluations by over-exploring the current local minimum and delaying finding the global one. This paper reviews and employs different strategies in a two-step Pareto selection framework (1-DTC-GL) to overcome these limitations. A detailed experimental study has revealed that existing strategies do not always improve and sometimes even worsen results. Since 1-DTC-GL is a DIRECT-type algorithm, the results of this paper provide general guidance for all DIRECT-type algorithms on how to deal with excessive local refinement more efficiently.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3760-:d:940462
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    References listed on IDEAS

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    1. Chun-Yao Lee & Guang-Lin Zhuo, 2021. "A Hybrid Whale Optimization Algorithm for Global Optimization," Mathematics, MDPI, vol. 9(13), pages 1-19, June.
    2. Mishra, Sudhanshu, 2006. "Some new test functions for global optimization and performance of repulsive particle swarm method," MPRA Paper 2718, University Library of Munich, Germany.
    3. Qunfeng Liu, 2013. "Linear scaling and the DIRECT algorithm," Journal of Global Optimization, Springer, vol. 56(3), pages 1233-1245, July.
    4. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, September.
    5. Qunfeng Liu & Wanyou Cheng, 2014. "A modified DIRECT algorithm with bilevel partition," Journal of Global Optimization, Springer, vol. 60(3), pages 483-499, November.
    6. 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.
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    Cited by:

    1. Linas Stripinis & Remigijus Paulavičius, 2023. "Novel Algorithm for Linearly Constrained Derivative Free Global Optimization of Lipschitz Functions," Mathematics, MDPI, vol. 11(13), pages 1-19, June.

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