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Adaptive block coordinate DIRECT algorithm

Author

Listed:
  • Qinghua Tao

    (Tsinghua University)

  • Xiaolin Huang

    (Shanghai Jiao Tong University)

  • Shuning Wang

    (Tsinghua University)

  • Li Li

    (Tsinghua University)

Abstract

DIviding RECTangles (DIRECT) is an efficient and popular method in dealing with bound constrained optimization problems. However, DIRECT suffers from dimension curse, since its computational complexity soars when dimension increases. Besides, DIRECT also converges slowly when the objective function is flat. In this paper, we propose a coordinate DIRECT algorithm, which coincides with the spirits of other coordinate update algorithms. We transform the original problem into a series of sub-problems, where only one or several coordinates are selected to optimize and the rest keeps fixed. For each sub-problem, coordinately dividing the feasible domain enjoys low computational burden. Besides, we develop adaptive schemes to keep the efficiency and flexibility to tackle different functions. Specifically, we use block coordinate update, of which the size could be adaptively selected, and we also employ sequential quadratic programming to conduct the local search to efficiently accelerate the convergence even when the objective function is flat. With these techniques, the proposed algorithm achieves promising performance on both efficiency and accuracy in numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:4:d:10.1007_s10898-017-0541-x
    DOI: 10.1007/s10898-017-0541-x
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    References listed on IDEAS

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    1. Ratko Grbić & Emmanuel Nyarko & Rudolf Scitovski, 2013. "A modification of the DIRECT method for Lipschitz global optimization for a symmetric function," Journal of Global Optimization, Springer, vol. 57(4), pages 1193-1212, December.
    2. Qunfeng Liu & Jinping Zeng, 2015. "Global optimization by multilevel partition," Journal of Global Optimization, Springer, vol. 61(1), pages 47-69, January.
    3. 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. 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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