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Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method

Received: 15 June 2015     Accepted: 1 July 2015     Published: 16 July 2016
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Abstract

We present a newly developed Replica Exchange algorithm using q -Gaussian Swarm Quantum Particle Optimization (REX@q-GSQPO) method for solving the problem of finding the global optimum. The basis of the algorithm is to run multiple copies of independent swarms at different values of q parameter. Based on an energy criterion, chosen to satisfy the detailed balance, we are swapping the particle coordinates of neighboring swarms at regular iteration intervals. The swarm replicas with high q values are characterized by high diversity of particles allowing escaping local minima faster, while the low q replicas, characterized by low diversity of particles, are used to sample more efficiently the local basins. We compared the new algorithm with the standard Gaussian Swarm Quantum Particle Optimization (GSQPO) and q-Gaussian Swarm Quantum Particle Optimization (q-GSQPO) algorithms, and found that the new algorithm is more robust in terms of the number of fitness function calls, and more efficient in terms of ability to convergence faster to the global minimum. In additional, we also provide a method for optimally allocating the swarm replicas among different q values. Our algorithm is tested for three benchmark functions, which are known to be multimodal problems, at different dimensionalities.

Published in Engineering and Applied Sciences (Volume 1, Issue 2)
DOI 10.11648/j.eas.20160102.12
Page(s) 20-25
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Swarm Quantum Particle, q-Gaussian Distribution, Global Optimization, Replica Exchange

References
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Cite This Article
  • APA Style

    Hiqmet Kamberaj. (2016). Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method. Engineering and Applied Sciences, 1(2), 20-25. https://doi.org/10.11648/j.eas.20160102.12

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    ACS Style

    Hiqmet Kamberaj. Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method. Eng. Appl. Sci. 2016, 1(2), 20-25. doi: 10.11648/j.eas.20160102.12

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    AMA Style

    Hiqmet Kamberaj. Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method. Eng Appl Sci. 2016;1(2):20-25. doi: 10.11648/j.eas.20160102.12

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  • @article{10.11648/j.eas.20160102.12,
      author = {Hiqmet Kamberaj},
      title = {Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method},
      journal = {Engineering and Applied Sciences},
      volume = {1},
      number = {2},
      pages = {20-25},
      doi = {10.11648/j.eas.20160102.12},
      url = {https://doi.org/10.11648/j.eas.20160102.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eas.20160102.12},
      abstract = {We present a newly developed Replica Exchange algorithm using q -Gaussian Swarm Quantum Particle Optimization (REX@q-GSQPO) method for solving the problem of finding the global optimum. The basis of the algorithm is to run multiple copies of independent swarms at different values of q parameter. Based on an energy criterion, chosen to satisfy the detailed balance, we are swapping the particle coordinates of neighboring swarms at regular iteration intervals. The swarm replicas with high q values are characterized by high diversity of particles allowing escaping local minima faster, while the low q replicas, characterized by low diversity of particles, are used to sample more efficiently the local basins. We compared the new algorithm with the standard Gaussian Swarm Quantum Particle Optimization (GSQPO) and q-Gaussian Swarm Quantum Particle Optimization (q-GSQPO) algorithms, and found that the new algorithm is more robust in terms of the number of fitness function calls, and more efficient in terms of ability to convergence faster to the global minimum. In additional, we also provide a method for optimally allocating the swarm replicas among different q values. Our algorithm is tested for three benchmark functions, which are known to be multimodal problems, at different dimensionalities.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method
    AU  - Hiqmet Kamberaj
    Y1  - 2016/07/16
    PY  - 2016
    N1  - https://doi.org/10.11648/j.eas.20160102.12
    DO  - 10.11648/j.eas.20160102.12
    T2  - Engineering and Applied Sciences
    JF  - Engineering and Applied Sciences
    JO  - Engineering and Applied Sciences
    SP  - 20
    EP  - 25
    PB  - Science Publishing Group
    SN  - 2575-1468
    UR  - https://doi.org/10.11648/j.eas.20160102.12
    AB  - We present a newly developed Replica Exchange algorithm using q -Gaussian Swarm Quantum Particle Optimization (REX@q-GSQPO) method for solving the problem of finding the global optimum. The basis of the algorithm is to run multiple copies of independent swarms at different values of q parameter. Based on an energy criterion, chosen to satisfy the detailed balance, we are swapping the particle coordinates of neighboring swarms at regular iteration intervals. The swarm replicas with high q values are characterized by high diversity of particles allowing escaping local minima faster, while the low q replicas, characterized by low diversity of particles, are used to sample more efficiently the local basins. We compared the new algorithm with the standard Gaussian Swarm Quantum Particle Optimization (GSQPO) and q-Gaussian Swarm Quantum Particle Optimization (q-GSQPO) algorithms, and found that the new algorithm is more robust in terms of the number of fitness function calls, and more efficient in terms of ability to convergence faster to the global minimum. In additional, we also provide a method for optimally allocating the swarm replicas among different q values. Our algorithm is tested for three benchmark functions, which are known to be multimodal problems, at different dimensionalities.
    VL  - 1
    IS  - 2
    ER  - 

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Author Information
  • Faculty of Engineering, Department of Computer Engineering, International Balkan University, Skopje, R. of Macedonia

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