Soft Computing

, Volume 23, Issue 24, pp 13339–13349 | Cite as

Distributed minimum spanning tree differential evolution for multimodal optimization problems

  • Zi-Jia Wang
  • Zhi-Hui ZhanEmail author
  • Jun Zhang
Methodologies and Application


Multimodal optimization problem (MMOP) requires to find optima as many as possible for a single problem. Recently, many niching techniques have been proposed to tackle MMOPs. However, most of the niching techniques are either sensitive to the niching parameters or causing a waste of fitness evaluations. In this paper, we proposed a novel niching technique based on minimum spanning tree (MST) and applied it into differential evolution (DE), termed as MSTDE, to solve MMOPs. In every generation, an MST is built based on the distance information among the individuals. After that, we cut the M largest weighted edges of the MST to form some subtrees, so-called subpopulations. The DE operators are executed within the subpopulations. Besides, a dynamic pruning ratio (DPR) strategy is proposed to determine M with an attempt to reduce its sensitivity, so as to enhance the niching performance. Meanwhile, the DPR strategy can achieve a good balance between diversity and convergence. Besides, taking the advantage of fast availability in time from virtual machines (VMs), a distributed model is applied in MSTDE, where different subpopulations run concurrently on distributed VMs. Experiments have been conducted on the CEC2013 multimodal benchmark functions to test the performance of MSTDE, and the experimental results show that MSTDE can outperform many existed multimodal optimization algorithms.


Differential evolution Minimum spanning tree Multimodal optimization problems Distributed model 



This work was partially supported by the Outstanding Youth Science Foundation with No. 61822602, the National Natural Science Foundations of China (NSFC) with Nos. 61772207 and 61332002, the Natural Science Foundations of Guangdong Province for Distinguished Young Scholars with No. 2014A030306038, the Project for Pearl River New Star in Science and Technology with No. 201506010047, the GDUPS (2016), and the Fundamental Research Funds for the Central Universities.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Data and Computer ScienceSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  2. 2.School of Computer Science and EngineeringSouth China University of TechnologyGuangzhouPeople’s Republic of China
  3. 3.Guangdong Provincial Key Lab of Computational Intelligence and Cyberspace InformationGuangzhouPeople’s Republic of China

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