Memetic Computing

, Volume 10, Issue 2, pp 135–150 | Cite as

Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm with Gaussian mutation

  • Yanhong FengEmail author
  • Juan Yang
  • Congcong Wu
  • Mei Lu
  • Xiang-Jun Zhao
Regular Research Paper


Recently, inspired by the migration behavior of monarch butterflies in nature, a metaheuristic optimization algorithm, called monarch butterfly optimization (MBO), was proposed. In the present study, a novel chaotic MBO algorithm (CMBO) is proposed, in which chaos theory is introduced in order to enhance its global optimization ability. Here, 12 one-dimensional classical chaotic maps are used to tune two main migration processes of monarch butterflies. Meanwhile, applying Gaussian mutation operator to some worst individuals can effectively prevent premature convergence of the optimization process. The performance of CMBO is verified and analyzed by three groups of large-scale 0–1 knapsack problems instances. The results show that the introduction of appropriate chaotic map and Gaussian perturbation can significantly improve the solution quality together with the overall performance of the proposed CMBO algorithm. The proposed CMBO can outperform the standard MBO and other eight state-of-the-art canonical algorithms.


Monarch butterfly optimization Chaotic maps Gaussian mutation operator 0–1 Knapsack problems 



This work was supported by National Natural Science Foundation of China (Nos. 61272297, and 61402207) and Hebei GEO Universtiy Youth Foundation (No. QN201601).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yanhong Feng
    • 1
    Email author
  • Juan Yang
    • 2
  • Congcong Wu
    • 1
  • Mei Lu
    • 3
  • Xiang-Jun Zhao
    • 3
  1. 1.School of Information EngineeringHebei GEO UniversityShijiazhuangChina
  2. 2.School of Mathematical SciencesKaili UniversityKailiChina
  3. 3.School of Computer Science and TechnologyJiangsu Normal UniversityXuzhouChina

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