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CCMBO: a covariance-based clustered monarch butterfly algorithm for optimization problems

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Abstract

Rotationally variance nature-inspired algorithms are not efficient for solving non-separable problems. One way for solving this limitation is utilizing the concept of covariance-based learning to transform the original space into the new space in which the interactions among variables are revealed and operators perform in an appropriate coordinate system. In this paper, Monarch butterfly optimization (MBO), a new nature-inspired and rotation-variance algorithm, is studied. By focusing on making MBO more rotationally invariant, a covariance-based clustered MBO (CCMBO) is presented. In the CCMBO, two primary operators of MBO are modified. An eigenvector-based migration operator and a linearized adjusting operator are utilized to make MBO more rotationally invariant. CCMBO employs a re-initialization operator to improve its exploration ability. Also, to allow exploiting obtained information about the search space, CCMBO utilizes self-organizing map clustering. The CCMBO is evaluated on an extensive set of optimization benchmark functions. It is compared with MBO, two of its improvements, and six other state-of-the-art evolutionary algorithms. The results illustrate that CCMBO obtains significantly better performance and would be a valuable and practical algorithm for optimization problems.

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Notes

  1. Ceil(x) rounds x to the nearest integer greater than or equal to x.

  2. The Matlab code for CEC’17 test functions can be found in the website: https://github.com/P-N-Suganthan/CEC2017-BoundContrained.

  3. The MATLAB code of MBO is available in the website: https://github.com/ggw0122/Monarch-Butterfly-Optimization.

  4. The MATLAB code of GCMBO is available in: http://www.mathworks.com/matlabcentral/fileexchange/55339-gcmbo.

  5. http://dces.essex.ac.uk/staff/qzhang.

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Authors and Affiliations

  1. Department of Computer Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran

    Samaneh Yazdani

  2. Department of Industrial Engineering, Birjand University of Technology, Birjand, Iran

    Esmaeil Hadavandi

  3. Department of Electrical and Computer Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran

    Mohammad Mirzaei

Authors
  1. Samaneh Yazdani
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  2. Esmaeil Hadavandi
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  3. Mohammad Mirzaei
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Correspondence to Samaneh Yazdani.

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Yazdani, S., Hadavandi, E. & Mirzaei, M. CCMBO: a covariance-based clustered monarch butterfly algorithm for optimization problems. Memetic Comp. 14, 377–394 (2022). https://doi.org/10.1007/s12293-022-00359-8

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