An Improved Harmony Search Algorithm with Differential Mutation Operator

• Autorzy: Chakraborty P. , Roy G.G. , Das S. , Jain D. , Abraham A.
• Języki publikacji: EN

Abstrakty

EN

Harmony Search (HS) is a recently developed stochastic algorithm which imitates the music improvisation process. In this process, the musicians improvise their instrument pitches searching for the perfect state of harmony. Practical experiences, however, suggest that the algorithm suffers from the problems of slow and/or premature convergence over multimodal and rough fitness landscapes. This paper presents an attempt to improve the search performance of HS by hybridizing it with Differential Evolution (DE) algorithm. The performance of the resulting hybrid algorithm has been compared with classical HS, the global best HS, and a very popular variant of DE over a test-suite of six well known benchmark functions and one interesting practical optimization problem. The comparison is based on the following performance indices - (i) accuracy of final result, (ii) computational speed, and (iii) frequency of hitting the optima.

Słowa kluczowe

EN

global optimization; meta-heuristics; harmony search; Differential Evolution (DE); explorative power; population variance

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2009
• Tom: Vol. 95, nr 4
• Strony: 401--426
• Opis fizyczny: Bibliogr. 35 poz., tab., wykr.

Twórcy

autor

Chakraborty P.

autor

Roy G.G.

autor

Das S.

autor

Jain D.

autor

Abraham A.

• Machine Intelligence Research Labs (MIR Labs), Scientific Network for Innovation and Research Excellence, P.O. Box 2259 Auburn, Washington 98071-2259, USA.,

Bibliografia

• [1] T. Bäck, D. Fogel, Z. Michalewicz, Handbook of Evolutionary Computation, Oxford Univ. Press, 1997.
• [2] A.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing, Springer, 2003.
• [3] D. Ashlock, Evolutionary Computation for Modeling and Optimization, Springer, 2006.
• [4] E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: From Natural to Artificial System, Oxford University Press, New York, 1999.
• [5] J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence, Morgan Kaufmann, San Francisco, CA, 2001.
• [6] A. P. Engelbrecht, Fundamentals of Computational Swarm Intelligence, John Wiley & Sons, 2006.
• [7] Z.W. Geem, J.H. Kim, and G.V. Loganathan, "A new heuristic optimization algorithm: harmony search", Simulation 76(2), 60-68, 2001.
• [8] K.S. Lee and Z.W. Geem, "A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice", Computer Methods in Applied Mechanics and Engineering, Eng, 194, 3902-3933, 2004.
• [9] Z.W. Geem (Ed.), Music-Inspired Harmony Search Algorithm: Theory and Applications, Studies in Computational Intelligence, Springer, 2009.
• [10] Z.W. Geem, J.H. Kim, and G.V. Loganathan, "Harmony search optimization: application to pipe network design", Int. J. Model. Simul, 22,(2), 125-133, 2002.
• [11] K. S. Lee and Z.W. Geem, "A new structural optimization method based on the harmony search algorithm", Computers and Structures, 82, pp. 781-798, Elsevier, 2004.
• [12] Z. W. Geem, K. S. Lee, and Y. Park, "Application of harmony search to vehicle routing", American Journal of Applied Sciences, 2(12), 1552-1557, 2005.
• [13] A. Vasebi, M. Fesanghary, and S. M. T. Bathaeea, "Combined heat and power economic dispatch by harmony search algorithm", International Journal of Electrical Power and Energy Systems, Vol. 29, No. 10, 713-719, Elsevier, 2007.
• [14] Z. W. Geem, "Optimal scheduling of multiple dam system using harmony search algorithm", Lecture Notes in Computer Science, Vol. 4507, 316-323, Springer, 2007.
• [15] M. Mahdavi, M. Fesanghary, and E. Damangir, "An improved harmony search algorithm for solving optimization problems", Applied Mathematics and Computation, Vol. 188, 1567-1579, Elsevier Science, 2007.
• [16] M. G. H. Omran and M. Mahdavi, "Global-best harmony search", Applied Mathematics and Computation, Vol.198, 643-656, Elsevier Science, 2008.
• [17] M. Fesanghary, M. Mahdavi, M. Minary-Jolandan, Y. Alizadeh, "Hybridizing sequential quadratic programming with HS algorithm for engineering optimization", Computer Methods in Applied Mechanics and Engineering, Volume 197, Issues 33- 40, 1, pp. 3080-3091, Elsevier, June 2008.
• [18] P.T. Boggs and J.W. Tolle, "Sequential quadratic programming", Acta Numerica, 4, 1-52, 1995.
• [19] H.-G. Beyer and H.-P. Schwefel, "Evolution strategies: a comprehensive introduction", Natural Computing, 1(1):3-52, 2002.
• [20] R. Storn and K. V. Price, "Differential evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces", Technical Report TR-95-012, ICSI, http://http.icsi.berkeley. edu/~storn/litera.html, 1995.
• [21] , "Differential Evolution - a simple and efficient heuristic for global optimization over continuous spaces", Journal of Global Optimization, 11(4) 341-359, 1997.
• [22] R. Storn, K. V. Price, and J. Lampinen,Differential Evolution - A Practical Approach to Global Optimization, Springer, Berlin, 2005.
• [23] D. Zaharie, "Critical values for the control parameters of differential evolution algorithms", in R. Matousek, P. Osmera (eds.), Proc. of Mendel 2002, 8-th International Conference on Soft Computing, Brno,Czech Republic, June 2002, pp. 62-67.
• [24] R. Parncutt, Harmony: A Psychoacoustical Approach, Springer Verlag, 1989.
• [25] A.E. Eiben and C.A. Schippers, "On evolutionary exploration and exploitation", Fundamenta Informaticae, 35, 1-16, IOS Press, 1998.
• [26] X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, 3(2), 82-102, July 1999.
• [27] P. J. Angeline, "Evolutionary optimization versus particle swarm optimization: Philosophy and the performance difference," Lecture Notes in Computer Science (vol. 1447), Proc. of 7th International Conference on. Evolutionary Programming - Evolutionary Programming VII, pp. 84-89, 1998
• [28] A. E. Eiben, R. Hinterding, and Z. Michalewicz, "Parameter control in evolutionary algorithms," IEEE Transactions on Evolutionary Computation, vol.3, no. 2, pp. 124-141, 1999.
• [29] T. P. Runarsson and X. Yao, "Stochastic ranking for constrained evolutionary optimization," IEEE Transactions on Evolutionary Computation, vol. 4, no. 3, pp. 284-294, Sep. 2000.
• [30] S. A. Kazarlis, S. E. Papadakis, J. B. Theochairs, and V. Petridis, "Microgenetic algorithms as generalized hill-climbing operators for GA optimization," IEEE Transactions on Evolutionary Computation, vol. 5, no. 3, pp. 204-217, Jun. 2001.
• [31] S. Koziel and Z. Michalewicz, "Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization," IEEE Transactions on Evolutionary Computation, vol. 7, no. 1, pp. 19-44, 1999.
• [32] Z. Michalewicz and G. Nazhiyath, "Genocop III: A co-evolutionary algorithm for numerical optimization problems with nonlinear constraints," in Proceedings of the 2nd IEEE Conference on Evolutionary Computation. Piscataway, NJ: IEEE Press, vol. 2, pp. 647-651, 1995.
• [33] Z. Michalewicz and M. Schoenauer, "Evolutionary algorithms for constrained parameter optimization problems," Evolutionary Computation, vol. 4, no. 1, pp. 1-32, 1996.
• [34] L. Jiao, Y. Li, M. Gong, and X. Zhang, "Quantum-inspired immune clonal algorithm for global numerical optimization", IEEE Transactions on System, Man, and Cybernetics, Part B, Vol. 38, No.5, 1234-1253, 2008.
• [35] N. Mladenovi´c, J. Petrovic, V. Kovacevic-Vujicic, and M. Cangalovic, "Solving spread-spectrum radar polyphase code design problem by tabu search and variable neighborhood search," European Journal of Operational Research, 153, 389-399, 2003.