Soft Computing

, Volume 21, Issue 22, pp 6713–6738 | Cite as

A comparative study on swarm intelligence for structure learning of Bayesian networks

  • Junzhong Ji
  • Cuicui Yang
  • Jiming Liu
  • Jinduo Liu
  • Baocai Yin
Methodologies and Application


A Bayesian network (BN) is an important probabilistic model in the field of artificial intelligence and a powerful formalism used to describe uncertainty in the real world. As science and technology develop, considerable data on complex systems have been acquired by various means, which presents a significant challenge regarding how to accurately and robustly learn a network structure for a complex system. To address this challenge, many BN structure learning methods based on swarm intelligence have been developed. In this study, we perform a systematic comparison of three typical methods based on ant colony optimization, artificial bee colony algorithm, and bacterial foraging optimization. First, we analyze and summarize their main characteristics from the perspective of stochastic searching. Second, we conduct thorough experimental comparisons to examine the roles of different mechanisms in each method by means of multiaspect metrics, i.e., the K2 score, structural differences, and execution time. Next, we perform further experiments to validate the robustness of different algorithms on some benchmark data sets with noise. Finally, we present the prospects and references for researchers who are engaged in learning BN networks.


Bayesian network structure learning Swarm intelligence Ant colony optimization Artificial bee colony algorithm Bacterial foraging optimization 



We would like to thank the anonymous referees for their many valuable suggestions and comments. We thank the authors of the corresponding algorithms for sharing the binary executable systems. This work is partly supported by the NSFC Research Program (61375059, 61332016), the National “973” Key Basic Research Program of China (2014CB744601), the Specialized Research Fund for the Doctoral Program of Higher Education (20121103110031), and the Beijing Municipal Education Research Plan key Project (Beijing Municipal Fund Class B) (KZ201410005004).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Junzhong Ji
    • 1
  • Cuicui Yang
    • 1
  • Jiming Liu
    • 2
  • Jinduo Liu
    • 1
  • Baocai Yin
    • 1
  1. 1.Beijing Municipal Key Laboratory of Multimedia and Intelligent Software Technology, College of Computer Science and TechnologyBeijing University of TechnologyBeijingChina
  2. 2.Department of Computer Science and TechnologyHong Kong Baptist UniversityKowloon TongHong Kong

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