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A modified DIRECT algorithm with bilevel partition

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Abstract

It has been pointed out by Jones D. R. that the DIRECT global optimization algorithm can quickly get close to the basin of the optimum but takes longer to achieve a high degree of accuracy. In this paper, we introduce a bilevel strategy into a modifed DIRECT algorithm to overcome this shortcoming. The proposed algorithm is proved to be convergent globally. Numerical results show that the proposed algorithm is very promising.

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Acknowledgments

We would like to thank two anonymous reviewers whose suggestions improve this paper greatly. We would also like to thank Doctor Finkel D.E. and Professor Kelley C.T. for their DIRECT codes and the Jones test set codes.

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Authors and Affiliations

  1. School of Computing, Dongguan University of Technology, Dongguan, 523808, China

    Qunfeng Liu & Wanyou Cheng

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  1. Qunfeng Liu
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  2. Wanyou Cheng
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Correspondence to Qunfeng Liu.

Additional information

This work was supported by MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Project No. 13YJC630095) and NSF of China (Nos. 11271069, 11101081).

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Liu, Q., Cheng, W. A modified DIRECT algorithm with bilevel partition. J Glob Optim 60, 483–499 (2014). https://doi.org/10.1007/s10898-013-0119-1

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  • DOI: https://doi.org/10.1007/s10898-013-0119-1

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