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Exploratory Power of the Harmony Search Algorithm: Analysis and Improvements for Global Numerical Optimization

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5 Author(s)
Das, S. ; Dept. of Electron. & Telecommun. Eng., Jadavpur Univ., Kolkata, India ; Mukhopadhyay, A. ; Roy, A. ; Abraham, A.
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The theoretical analysis of evolutionary algorithms is believed to be very important for understanding their internal search mechanism and thus to develop more efficient algorithms. This paper presents a simple mathematical analysis of the explorative search behavior of a recently developed metaheuristic algorithm called harmony search (HS). HS is a derivative-free real parameter optimization algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. This paper analyzes the evolution of the population-variance over successive generations in HS and thereby draws some important conclusions regarding the explorative power of HS. A simple but very useful modification to the classical HS has been proposed in light of the mathematical analysis undertaken here. A comparison with the most recently published variants of HS and four other state-of-the-art optimization algorithms over 15 unconstrained and five constrained benchmark functions reflects the efficiency of the modified HS in terms of final accuracy, convergence speed, and robustness.

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Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on  (Volume:41 ,  Issue: 1 )