Applied Intelligence

, Volume 48, Issue 12, pp 4646–4659 | Cite as

Gradient-based adaptive particle swarm optimizer with improved extremal optimization

  • Xiaoli ZhaoEmail author
  • Jenq-Neng Hwang
  • Zhijun Fang
  • Guozhong Wang


Most real-world applications can be formulated as optimization problems, which commonly suffer from being trapped into the local optima. In this paper, we make full use of the global search capability of particle swarm optimization (PSO) and local search ability of extremal optimization (EO), and propose a gradient-based adaptive PSO with improved EO (called GAPSO-IEO) to overcome the issue of local optima deficiency of optimization in high-dimensional search and reduce the time complexity of the algorithm. In the proposed algorithm, the improved EO (IEO) is adaptively incorporated into PSO to avoid the particles being trapped into the local optima according to the evolutional states of the swarm, which are estimated based on the gradients of the fitness functions of the particles. We also improve the mutation strategy of EO by performing polynomial mutation (PLM) on each particle, instead of on each component of the particle, therefore, the algorithm is not sensitive to the dimension of the swarm. The proposed algorithm is tested on several unimodal/multimodal benchmark functions and Berkeley Segmentation Dataset and Benchmark (BSDS300). The results of experiments have shown the superiority and efficiency of the proposed approach compared with those of the state-of-the-art algorithms, and can achieve better performance in high-dimensional tasks.


Gradient Mutation strategy Adaptive particle swarm optimizer Improving extremal optimization 



The authors would like to thank the anonymous referees for their useful comments. This work is supported by the National Nature Science Foundation of China (No.61461021) and Shanghai Science and Technology Committee (No. 15590501300).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Xiaoli Zhao
    • 1
    • 2
    Email author
  • Jenq-Neng Hwang
    • 3
  • Zhijun Fang
    • 1
  • Guozhong Wang
    • 2
  1. 1.School of Electronic and Electrical EngineeringShanghai University of Engineering ScienceShanghaiChina
  2. 2.School of Communication and Information EngineeringShanghai UniversityShanghaiChina
  3. 3.Department of Electrical EngineeringUniversity of WashingtonSeattleUSA

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