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Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function

Author

Listed:
  • Jin Hee Yoon

    (Department of Mathematics and Statistics, Sejong University, Seoul 05006, Korea)

  • Zong Woo Geem

    (College of IT Convergence, Gachon University, Seongnam 13120, Korea)

Abstract

The harmony search (HS) algorithm is an evolutionary computation technique, which was inspired by music improvisation. So far, it has been applied to various scientific and engineering optimization problems including project scheduling, structural design, energy system operation, car lane detection, ecological conservation, model parameter calibration, portfolio management, banking fraud detection, law enforcement, disease spread modeling, cancer detection, astronomical observation, music composition, fine art appreciation, and sudoku puzzle solving. While there are many application-oriented papers, only few papers exist on how HS performs for finding optimal solutions. Thus, this preliminary study proposes a new approach to show how HS converges on an optimal solution under specific conditions. Here, we introduce a distance concept and prove the convergence based on the empirical probability. Moreover, a numerical example is provided to easily explain the theorem.

Suggested Citation

  • Jin Hee Yoon & Zong Woo Geem, 2021. "Empirical Convergence Theory of Harmony Search Algorithm for Box-Constrained Discrete Optimization of Convex Function," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:545-:d:510573
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    References listed on IDEAS

    as
    1. Geoffrey Fairchild & Kyle S. Hickmann & Susan M. Mniszewski & Sara Y. Del Valle & James M. Hyman, 2014. "Optimizing human activity patterns using global sensitivity analysis," Computational and Mathematical Organization Theory, Springer, vol. 20(4), pages 394-416, December.
    2. ShouHeng Tuo, 2016. "A Modified Harmony Search Algorithm For Portfolio Optimization Problems," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(1), pages 311-326.
    3. H. J. Deeg & C. Moutou & A. Erikson & Sz. Csizmadia & B. Tingley & P. Barge & H. Bruntt & M. Havel & S. Aigrain & J. M. Almenara & R. Alonso & M. Auvergne & A. Baglin & M. Barbieri & W. Benz & A. S. B, 2010. "A transiting giant planet with a temperature between 250 K and 430 K," Nature, Nature, vol. 464(7287), pages 384-387, March.
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