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An efficient bilevel differential evolution algorithm with adaptation of lower level population size and search radius

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Abstract

Bilevel optimization has been recognized as one of the most difficult and challenging tasks to deal with because a solution to the upper level problem may be feasible only if it is also an optimal solution to the lower level problem. In recent years, evolutionary bilevel optimization has attracted increasing interest. In this paper, an efficient self-adaptive bilevel differential evolution (SABiLDE) with k-nearest neighbors (kNN) based interpolation is proposed to solve bilevel optimization problems. The kNN approximation is applied to estimate the optimal lower level variables for any newly generated upper candidates to improve the computational efficiency. A similarity based self-adaptive strategy for the dynamic control of lower level population size and search radius is introduced to further enhance the efficiency of the lower level function evaluations. A test set with 10 standard test problems and the SMD suite with controllable complexities are used to evaluate the performance of the proposed approach. Compared with four recent state-of-the-art methods, the numerical results produced by the proposed method are promising and show great potential for solving generic bilevel optimization problems.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of P. R. China (Grant no. 61203309, 61773390), Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/I011056/1 and Platform Grant EP/H00453X/1, and Natural and Environment Research Council (NERC) under the grant NE-V002511, National Defense Basic Research Program of China (Grant no. JCKY2019403D006), Hunan Provincial Natural Science Foundation of China (Grant No. 2018JJ2137, 2018RS3081), Hunan Provincial Science and Technology Plan of China (Grant no. 2017XK2302) and Hunan Provincial Innovation Foundation for Postgraduate (CX20190807).

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Authors and Affiliations

  1. School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Lianghong Wu & Zhenzu Liu

  2. Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD, UK

    Hua-Liang Wei

  3. School of Systems Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China

    Rui Wang

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  1. Lianghong Wu
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  2. Zhenzu Liu
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Correspondence to Lianghong Wu or Rui Wang.

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Wu, L., Liu, Z., Wei, HL. et al. An efficient bilevel differential evolution algorithm with adaptation of lower level population size and search radius. Memetic Comp. 13, 227–247 (2021). https://doi.org/10.1007/s12293-021-00335-8

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