Soft Computing

, Volume 21, Issue 23, pp 6983–7004 | Cite as

Hierarchical multi-swarm cooperative teaching–learning-based optimization for global optimization

  • Feng Zou
  • Debao Chen
  • Renquan Lu
  • Peng Wang
Methodologies and Application


Hierarchical cooperation mechanism, which is inspired by the features of specialization and cooperation in the social organizations, has been successfully used to increase the diversity of the population and avoid premature convergence for solving complex optimization problems. In this paper, a new two-level hierarchical multi-swarm cooperative TLBO variant called HMCTLBO is presented to solve global optimization problems. In the proposed HMCTLBO algorithm, all learners are randomly divided into several sub-swarms with equal amounts of learners at the bottom level of the hierarchy. The learners of each swarm evolve only in their corresponding swarm in parallel independently to maintain the diversity and improve the exploration capability of the population. Moreover, all the best learners from each swarm compose the new swarm at the top level of the hierarchy, and each learner of the swarm evolves according to Gaussian sampling learning. Furthermore, a randomized regrouping strategy is performed, and a subspace searching strategy based on Latin hypercube sampling is introduced to maintain the diversity of the population. To verify the performance of the proposed approaches, 48 benchmark test functions are evaluated. Conducted experiments indicate that the proposed HMCTLBO algorithm is competitive to some existing TLBO variants and other optimization algorithms.


Hierarchical multi-swarm cooperation Teaching–learning-based optimization Gaussian sampling learning Regrouping Latin hypercube sampling 



This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61572224, 61304082) and the National Science Fund for Distinguished Young Scholars (Grants No. 61425009). This work is also partially supported by the Major Project of Natural Science Research in Anhui Province (Grant No. KJ2015ZD36), the Natural Science Foundation in colleges and universities of Anhui Province (Grant No. KJ2016A639), International Science and technology cooperation project of Anhui Province (10080703003) and the seventh batch of Anhui province “115” industrial innovation team of Anhui personnel (2014-02).

Compliance with ethical standards

Conflict of interest

The authors whose names are listed in the publication certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this publication.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Physics and Electronic InformationHuaiBei Normal UniversityHuaibeiChina
  2. 2.School of AutomationGuangdong University of TechnologyGuangzhouChina

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