Abstract
In this paper, a novel optimization approach is proposed using Gaussian distribution function to improve harmony search (HS) algorithm, namely “Gaussian global-best harmony search” (GGHS) algorithm. The harmony memory (HM) is adjusted using Gaussian random generation in GGHS. The GGHS algorithm consists of two adjustment steps; in the first stage, the harmony memory is adjusted by a dynamic bandwidth and the Gaussian distribution with a mean of 0 and a standard deviation of 1. In the second stage, the best memory is adjusted using a random Gaussian number with a mean of 0 and a dynamic standard deviation. The dynamic bandwidth and standard deviation are adaptively determined based on iteration number, the maximum and minimum of each design variable in the HM. Accuracy and efficiency of the GGHS algorithm have been evaluated using several benchmark mathematical examples. The numerical results illustrate that the GGHS algorithm is more accurate and efficient than other existing modified versions of harmony search algorithm. The capability of the dynamic bandwidth enhances the performance of this modified HS algorithm. The GGHS produces the better optimum results in comparison with other improved versions of harmony search algorithm.
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References
Al-Betar MA, Doush IA, Khader AT, Awadalla MA (2012) Novel selection schemes for harmony search. Appl Math Comput 218(10):6095–6117
Chakraborty P, Roy GG, Das S, Jain D (2009) An improved harmony search algorithm with differential mutation operator. Fundam Inform 95:1–26
Dai X, Yuan X, Wu L (2015) A novel harmony search algorithm with gaussian mutation for multi-objective optimization. Soft Comput. doi:10.1007/s00500-015-1868-1
Derrac J, Garcia S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18
El-Abd M (2013) An improved global-best harmony search algorithm. Appl Math Comput 222:94–106
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulations 76(2):60–68
Geem ZW, Kim J, Loganathan G (2002) Harmony search optimization: application to pipe network design. Int J Model Simul 22:125–133
Geem ZW, Tseng C, Park Y (2005) Harmony search for generalized orienteering problem: best touring in China. Springer Lecture Notes in Computer Science 3412:741–750
Gomes MH, Saraiva JT (2009) A market based active/reactive dispatch including transformer taps and reactor and capacitor banks using simulated annealing. electric power syst res 79:959–972
Guo L, Wang GG, Gandomi AH, Alavi AH, Duan HA (2014) New improved krill herd algorithm for global numerical optimization. Neurocomputing 138:392–402
Guo Z, Wang S, Yue X, Yang H (2015) Global harmony search with generalized opposition-based learning. Soft Comput. doi:10.1007/s00500-015-1912-1
Kattan A, Abdullah R (2013) A dynamic self-adaptive harmony search algorithm for continuous optimization problems. Appl Math Comput 219:8542–8567
Khalili M, Kharrat R, Salahshoor K, Haghighat Sefat M (2014) Global dynamic harmony search algorithm: GDHS. Appl Math Comput 228:195–219
Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798
Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36–38):3902–3933
Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188:1567–1579
Omran MGH, Mahdavi M (2008) Global-best harmony search. Appl Math Comput 198(2):643–656
Ouyang HB, Gao LQ, Li S, Kong XY (2015) Improved novel global harmony search with a new relaxation method for reliability optimization problems. Inf Sci 305:14–55
Pan Q, Suganthan P, Tasgetiren MF, Liang JJ (2010) A self-adaptive global best harmony search algorithm for continuous optimization problems. Appl Math Comput 216(3):830–848
Sinsuphan N, Leeton U, Kulworawanichpong T (2013) Optimal power flow solution using improved harmony search method. Appl Soft Comput 13:2364–2374
Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical Report 2005005, ITT Kanpur, India
Wang CM, Huang YF (2010) Self-adaptive harmony search algorithm for optimization. Expert Syst Appl 37:2826–2837
Wu B, Qian C, Ni W, Fan S (2012) Hybrid harmony search and artificial bee colony algorithm for global optimization problems. Comput Math Appl 64:2621–2634
Yassen ET, Ayob M, Ahmad Nazri MZ, Sabar NR (2015) Meta-harmony search algorithm for the vehicle routing problem with time windows. Inf Sci 325:140–158
Zheng L, Diao R, Shen Q (2015) Self-adjusting harmony search-based feature selection. Soft Comput 19:1567–1579
Zou D, Gao L, Li S, Wu J (2011) Solving 0–1 knapsack problem by a novel global harmony search algorithm. Appl Soft Comput 11:1556–1564
Zou DX, Gao LQ, Wu JH, Li S, Li Y (2010a) A novel global harmony search algorithm for reliability problems. Comput Ind Eng 58(2):307–316
Zou DX, Gao LQ, Wu JH, Li S (2010b) Novel global harmony search algorithm for unconstrained problems. Neurocomputing 73:3308–3318
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Keshtegar, B., Oukati Sadeq, M. Gaussian global-best harmony search algorithm for optimization problems. Soft Comput 21, 7337–7349 (2017). https://doi.org/10.1007/s00500-016-2274-z
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DOI: https://doi.org/10.1007/s00500-016-2274-z