×

An improved harmony search based on teaching-learning strategy for unconstrained optimization problems. (English) Zbl 1299.90420

Summary: Harmony search (HS) algorithm is an emerging population-based metaheuristic algorithm, which is inspired by the music improvisation process. The HS method has been developed rapidly and applied widely during the past decade. In this paper, an improved global harmony search algorithm, named harmony search based on teaching-learning (HSTL), is presented for high dimension complex optimization problems. In HSTL algorithm, four strategies (harmony memory consideration, teaching-learning strategy, local pitch adjusting, and random mutation) are employed to maintain the proper balance between convergence and population diversity, and dynamic strategy is adopted to change the parameters. The proposed HSTL algorithm is investigated and compared with three other state-of-the-art HS optimization algorithms. Furthermore, to demonstrate the robustness and convergence, the success rate and convergence analysis is also studied. The experimental results of 31 complex benchmark functions demonstrate that the HSTL method has strong convergence and robustness and has better balance capacity of space exploration and local exploitation on high dimension complex optimization problems.

MSC:

90C59 Approximation methods and heuristics in mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Z. W. Geem, J. H. Kim, and G. V. Loganathan, “A new heuristic optimization algorithm: harmony search,” Simulation, vol. 76, no. 2, pp. 60-68, 2001.
[2] 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, vol. 194, no. 36-38, pp. 3902-3933, 2005. · Zbl 1096.74042 · doi:10.1016/j.cma.2004.09.007
[3] Z. W. Geem, J. H. Kim, and G. V. Loganathan, “Harmony search optimization: application to pipe network design,” International Journal of Modelling and Simulation, vol. 22, no. 2, pp. 125-133, 2002.
[4] K. S. Lee and Z. W. Geem, “A new structural optimization method based on the harmony search algorithm,” Computers and Structures, vol. 82, no. 9-10, pp. 781-798, 2004. · doi:10.1016/j.compstruc.2004.01.002
[5] J. Kang and W. Zhang, “Combination of fuzzy C-means and harmony search algorithms for clustering of text document,” Journal of Computational Information Systems, vol. 16, no. 7, pp. 5980-5986, 2011.
[6] A. Vasebi, M. Fesanghary, and S. M. T. Bathaee, “Combined heat and power economic dispatch by harmony search algorithm,” International Journal of Electrical Power and Energy Systems, vol. 29, no. 10, pp. 713-719, 2007. · doi:10.1016/j.ijepes.2007.06.006
[7] Z. W. Geem, “Optimal scheduling of multiple dam system using harmony search algorithm,” in Lecture Notes in Computer Science, vol. 4507, pp. 316-323, 2007.
[8] M. Mahdavi, M. Fesanghary, and E. Damangir, “An improved harmony search algorithm for solving optimization problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1567-1579, 2007. · Zbl 1119.65053 · doi:10.1016/j.amc.2006.11.033
[9] S. Tuo and L. Yong, “An improved harmony search algorithm with chaos,” Journal of Computational Information Systems, vol. 8, no. 10, pp. 4269-4276, 2012.
[10] M. G. H. Omran and M. Mahdavi, “Global-best harmony search,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 643-656, 2008. · Zbl 1146.90091 · doi:10.1016/j.amc.2007.09.004
[11] Q. K. Pan, P. N. Suganthan, J. J. Liang, and M. F. Tasgetiren, “A local-best harmony search algorithm with dynamic subpopulations,” Engineering Optimization, vol. 42, no. 2, pp. 101-117, 2010. · Zbl 1189.65129 · doi:10.1080/03052150903104366
[12] P. Chakraborty, G. G. Roy, S. Das, D. Jain, and A. Abraham, “An improved harmony search algorithm with differential mutation operator,” Fundamenta Informaticae, vol. 95, no. 4, pp. 401-426, 2009. · Zbl 1209.68169 · doi:10.3233/FI-2009-157
[13] D. X. Zou, L. Q. Gao, J. Wu, S. Li, and Y. Li, “A novel global harmony search algorithm for reliability problems,” Computers and Industrial Engineering, vol. 58, no. 2, pp. 307-316, 2010. · doi:10.1016/j.cie.2009.11.003
[14] D. Zou, L. Gao, J. Wu, and S. Li, “Novel global harmony search algorithm for unconstrained problems,” Neurocomputing, vol. 73, no. 16-18, pp. 3308-3318, 2010. · Zbl 05849286 · doi:10.1016/j.neucom.2010.07.010
[15] X. Z. Gao, X. Wang, and S. J. Ovaska, “Uni-modal and multi-modal optimization using modified Harmony Search methods,” International Journal of Innovative Computing, Information and Control, vol. 5, no. 10, pp. 2985-2996, 2009.
[16] Q. K. Pan, P. N. Suganthan, M. F. Tasgetiren, and J. J. Liang, “A self-adaptive global best harmony search algorithm for continuous optimization problems,” Applied Mathematics and Computation, vol. 216, no. 3, pp. 830-848, 2010. · Zbl 1189.65129 · doi:10.1016/j.amc.2010.01.088
[17] P. Yadav, R. Kumar, S. K. Panda, and C. S. Chang, “An intelligent tuned harmony search algorithm for optimization,” Information Sciences, vol. 196, pp. 47-72, 2012. · Zbl 06089178 · doi:10.1016/j.ins.2011.12.035
[18] R. V. Rao, V. J. Savsani, and D. P. Vakharia, “Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems,” CAD Computer Aided Design, vol. 43, no. 3, pp. 303-315, 2011. · Zbl 05861808 · doi:10.1016/j.cad.2010.12.015
[19] R. V. Rao, V. J. Savsani, and D. P. Vakharia, “Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems,” Information Sciences, vol. 183, pp. 1-15, 2012. · Zbl 06043008 · doi:10.1016/j.ins.2011.08.006
[20] R. V. Rao and V. Patel, “An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems,” International Journal of Industrial Engineering Computations, vol. 3, pp. 535-560, 2012. · doi:10.5267/j.ijiec.2012.03.007
[21] V. Rao and V. J. Savsani, Mechanical Design Optimization Using Advanced Optimization Techniques, Springer-Verlag, London, UK, 2012.
[22] R. V. Rao and V. Patel, “Multi-objective optimization of heat exchangers using a modified teaching-learning based optimization algorithm,” Applied Mathematical Modelling, vol. 37, no. 3, pp. 1147-1162, 2013. · Zbl 1351.90147 · doi:10.1016/j.apm.2012.03.043
[23] V. R. Rao and V. Patel, “Multi-objective optimization of two stage thermoelectric cooler using a modified teaching-learning-based optimization algorithm,” Engineering Applications of Artificial Intelligence, vol. 26, no. 1, pp. 430-445, 2013. · doi:10.1016/j.engappai.2012.02.016
[24] R. V. Rao, V. J. Savsani, and J. Balic, “Teaching-learning-based optimization algorithm for unconstrained and constrained real parameter optimization problems,” Engineering Optimization, vol. 44, no. 12, pp. 1447-1462, 2012. · doi:10.1080/0305215X.2011.652103
[25] S. Das, A. Mukhopadhyay, A. Roy, A. Abraham, and B. K. Panigrahi, “Exploratory power of the harmony search algorithm: analysis and improvements for global numerical optimization,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 41, no. 1, pp. 89-106, 2011. · doi:10.1109/TSMCB.2010.2046035
[26] H. Sarvari and K. Zamanifar, “Improvement of harmony search algorithm by using statistical analysis,” Artificial Intelligence Review, vol. 37, no. 3, pp. 181-215, 2012. · doi:10.1007/s10462-011-9226-x
[27] M. Fukushima, Test Functions for Unconstrained Global Optimization, http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO_files/Page364.htm.
[28] K. Tang, X. Yao, P. N. Suganthan et al., Benchmark Functions for the CEC’2008 Special Session and Competition on Large Scale Global Optimization, http://www.ntu.edu.sg/home/EPNSugan/, 2008.
[29] K. Tang, X. Li, P. N. Suganthan, Z. Yang, and T. Weise, “Benchmark functions for the CEC’2010 special session and competition on large scale global optimization,” Tech. Rep., Nature Inspired Computation and Applications Laboratory, USTC, China & Nanyang Technological University, Nanyang Avenue, Singapore, 2009.
[30] F. Herrera, M. Lozano, and D. Molina, “Test suite for the special issue of soft computing on scalability of evolutionary algorithms and other meta-heuristics for large scale continuous optimization problems,” http://sci2s.ugr.es/eamhco/CFP.php.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.