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An empirical study of various candidate selection and partitioning techniques in the DIRECT framework

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  • Linas Stripinis

    (Vilnius University, Institute of Data Science and Digital Technologies)

  • Remigijus Paulavičius

    (Vilnius University, Institute of Data Science and Digital Technologies)

Abstract

Over the last three decades, many attempts have been made to improve the DIRECT (DIviding RECTangles) algorithm’s efficiency. Various novel ideas and extensions have been suggested. The main two steps of DIRECT-type algorithms are selecting and partitioning potentially optimal rectangles. However, the most efficient combination of these two steps is an area that has not been investigated so far. This paper presents a study covering an extensive examination of various candidate selection and partitioning techniques within the same DIRECT algorithmic framework. Twelve DIRECT-type algorithmic variations are compared on 800 randomly generated GKLS-type test problems and 96 box-constrained global optimization problems from DIRECTGOLib v1.1 with varying complexity. Based on these studies, we have identified the most efficient selection and partitioning combinations leading to new, more efficient, DIRECT-type algorithms. All these algorithms are included in the latest version of DIRECTGO v1.1.0 and are publicly available.

Suggested Citation

  • Linas Stripinis & Remigijus Paulavičius, 2024. "An empirical study of various candidate selection and partitioning techniques in the DIRECT framework," Journal of Global Optimization, Springer, vol. 88(3), pages 723-753, March.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:3:d:10.1007_s10898-022-01185-5
    DOI: 10.1007/s10898-022-01185-5
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    References listed on IDEAS

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    1. D. Serafino & G. Liuzzi & V. Piccialli & F. Riccio & G. Toraldo, 2011. "A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 175-190, October.
    2. Qunfeng Liu, 2013. "Linear scaling and the DIRECT algorithm," Journal of Global Optimization, Springer, vol. 56(3), pages 1233-1245, July.
    3. 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.
    4. 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.
    5. 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.
    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. 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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