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Global optimization by multilevel partition

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  • Qunfeng Liu
  • Jinping Zeng

Abstract

Partition-based algorithms, such as the DIRECT algorithm, are popular algorithms for solving global optimization problems. However, these algorithms often have an eventually inefficient behavior due to much more costs requirement to obtain a solution with higher accuracy. In this paper, we present an algorithm framework for bound constrained global optimization problems based on a multilevel partition strategy. This multilevel partition strategy can be regarded as a combination of the basic partition strategy and the multigrid algorithm, which is one of the best algorithms to solve partial differential equation. Our basic idea is to combine the multigrid algorithm with the partition-based algorithm to improve the eventually inefficient behavior of the partition-based algorithm. First, we provide a general framework of the partition-based algorithms which include the DIRECT algorithm as a special case. Then we present a strategy to build the subproblem at the coarse level. This strategy is easy to implement and brings no more computational costs. Under mild conditions, we show that the sequence generated by the proposed global optimization algorithm framework converges to the global optimum. Finally, we employ the original DIRECT algorithm to build a specific global optimization algorithm based on multilevel partition and compare it with the original DIRECT algorithm. Our numerical results show that obtained algorithm improves significantly the eventually inefficient behavior of the original DIRECT algorithm when the required accuracy is high. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Qunfeng Liu & Jinping Zeng, 2015. "Global optimization by multilevel partition," Journal of Global Optimization, Springer, vol. 61(1), pages 47-69, January.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:1:p:47-69
    DOI: 10.1007/s10898-014-0152-8
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    References listed on IDEAS

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    1. Giampaolo Liuzzi & Stefano Lucidi & Veronica Piccialli, 2010. "A partition-based global optimization algorithm," Journal of Global Optimization, Springer, vol. 48(1), pages 113-128, 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 & 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.
    2. 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.
    3. E. F. Campana & M. Diez & G. Liuzzi & S. Lucidi & R. Pellegrini & V. Piccialli & F. Rinaldi & A. Serani, 2018. "A multi-objective DIRECT algorithm for ship hull optimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 53-72, September.
    4. C. J. Price & M. Reale & B. L. Robertson, 2021. "Oscars-ii: an algorithm for bound constrained global optimization," Journal of Global Optimization, Springer, vol. 79(1), pages 39-57, January.
    5. 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.
    6. 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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