Abstract
Gray wolf optimizer (GWO) that is one of the meta-heuristic optimization algorithms is principally based on the hunting method and social hierarchy of the gray wolves in the nature. This paper presents the Multi-strategy Random weighted Gray Wolf Optimizer (MsRwGWO) including some effective and novel mechanisms added to the original GWO algorithm to improve the search performance. These are a transition mechanism for updating the parameter \(\overrightarrow{a}\), a weighted updating mechanism, a mutation operator, a boundary checking mechanism, a greedy selection mechanism, and an updating mechanism of leader three wolves (alpha, beta, and delta wolves). We utilized some benchmark functions known as CEC 2014 test suite to evaluate the performance of MsRwGWO algorithm in this study. Firstly, during the solution of optimization problems, the MsRwGWO algorithm's behaviors such as convergence, search history, trajectory, and average distance were analyzed. Secondly, the comparison statistical results of MsRwGWO and GWO algorithms were presented for CEC 2014 benchmarks with 10, 30, and 50 dimensions. In addition, some of the popular meta-heuristic algorithms taken from the literature were compared with the proposed MsRwGWO algorithm for 30D CEC 2014 test problems. Finally, MsRwGWO algorithm was adapted to the training process of a Multi-Layer Perceptron (MLP) used in wind speed estimation and comparative results with GWO-based MLP were obtained. The statistical results of the benchmark problems and training performance of MLP model for short-term wind speed forecasting show that the proposed MsRwGWO algorithm has better performance than GWO algorithm. Source code of MsRwGWO is publicly available at https://github.com/uguryuzgec/MsRwGWO.
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Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, 1995. Proceedings, pp 1942–1948
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence (Cat. No.98TH8360), pp 69–73
Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput J 8:687–697. https://doi.org/10.1016/j.asoc.2007.05.007
Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: Artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42:21–57. https://doi.org/10.1007/s10462-012-9328-0
Nanda SJ, Panda G (2014) A survey on nature inspired metaheuristic algorithms for partitional clustering. Swarm Evol Comput 16:1–18. https://doi.org/10.1016/j.swevo.2013.11.003
Tayarani MHN, Yao X, Xu H (2015) Meta-heuristic algorithms in car engine design: a literature survey. IEEE Trans Evol Comput 19:609–629. https://doi.org/10.1109/TEVC.2014.2355174
Beheshti Z, Shamsuddin SMH (2013) A review of population-based meta-heuristic algorithm. Int J Adv Soft Comput Appl 5(1):1–35
Holland JH (1975) Adaptation in natural and artificial systems. Ann Arbor MI Univ Michigan Press Ann Arbor, p 183. https://doi.org/10.1137/1018105
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. https://doi.org/10.1023/A:1008202821328
Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer Science & Business Media
Yüzgeç U, Becerikli Y, Türker M (2006) Nonlinear predictive control of a drying process using genetic algorithms. ISA Trans 45:589–602. https://doi.org/10.1016/S0019-0578(07)60234-1
Eusuff M, Lansey K, Pasha F (2006) Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization. Eng Optim 38:129–154. https://doi.org/10.1080/03052150500384759
Bhattacharjee KK, Sarmah SP (2014) Shuffled frog leaping algorithm and its application to 0/1 knapsack problem. Appl Soft Comput J 19:252–263. https://doi.org/10.1016/j.asoc.2014.02.010
Yang XS (2009) Harmony search as a metaheuristic algorithm. Stud Comput Intell 191:1–14
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. SIMULATION 76:60–68. https://doi.org/10.1177/003754970107600201
Gendreau M, Iori M, Laporte G, Martello S (2006) A Tabu search algorithm for a routing and container loading problem. Transp Sci 40:342–350. https://doi.org/10.1287/trsc.1050.0145
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(80):671–680. https://doi.org/10.1126/science.220.4598.671
Vinet L, Zhedanov A (2011) A ‘missing’ family of classical orthogonal polynomials. J Phys A Math Theor 44:085201. https://doi.org/10.1088/1751-8113/44/8/085201
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1:28–39. https://doi.org/10.1109/MCI.2006.329691
Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B Cybern 26:29–41. https://doi.org/10.1109/3477.484436
Li X, Shao Z, Qian J (2002) An optimizing method based on autonomous animats: fish-swarm algorithm. Syst Eng Theory Pract 22:32–38
Timmis J, Hone A, Stibor T, Clark E (2008) Theoretical advances in artificial immune systems. Theor Comput Sci 403:11–32. https://doi.org/10.1016/j.tcs.2008.02.011
Timmis J, Andrews P, Hart E (2010) On artificial immune systems and swarm intelligence. Swarm Intell 4:247–273. https://doi.org/10.1007/s11721-010-0045-5
Das S, Biswas A, Dasgupta S, Abraham A (2009) Bacterial foraging optimization algorithm: theoretical foundations, analysis, and applications. Found Comput Intell 3(3):23–55. https://doi.org/10.1007/978-3-642-01085-9_2
Li MS, Ji TY, Tang WJ et al (2010) Bacterial foraging algorithm with varying population. BioSystems 100:185–197. https://doi.org/10.1016/j.biosystems.2010.03.003
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (Ny) 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004
Sabri NM, Puteh M, Mahmood MR (2013) A review of gravitational search algorithm. Int J Adv Soft Comput Appl 5(3):1–39
Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713. https://doi.org/10.1109/TEVC.2008.919004
Lim WL, Wibowo A, Desa MI, Haron H (2016) A biogeography-based optimization algorithm hybridized with tabu search for the quadratic assignment problem. Comput Intell Neurosci. https://doi.org/10.1155/2016/5803893
Sang HY, Duan PY, Li JQ (2018) An effective invasive weed optimization algorithm for scheduling semiconductor final testing problem. Swarm Evol Comput 38:42–53. https://doi.org/10.1016/j.swevo.2017.05.007
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022
Yang XS, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput Appl 24:169–174
Yang X-S (2009) Cuckoo Search via Lévy flights. In: 2009 world congress on nature and biologically inspired computing (NaBIC), pp 210–214
Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028
Bairathi D, Gopalani D (2020) A novel swarm intelligence based optimization method: Harris hawk optimization. In: Advances in intelligent systems and computing, pp 832–842
Coello Coello CA, Becerra RL (2004) Efficient evolutionary optimization through the use of a cultural algorithm. Eng Optim 36:219–236. https://doi.org/10.1080/03052150410001647966
Soza C, Becerra RL, Riff MC, Coello Coello CA (2011) Solving timetabling problems using a cultural algorithm. Appl Soft Comput 11:337–344. https://doi.org/10.1016/j.asoc.2009.11.024
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98. https://doi.org/10.1016/j.advengsoft.2015.01.010
Kılıç H, Yüzgeç U (2019) Improved antlion optimization algorithm via tournament selection and its application to parallel machine scheduling. Comput Ind Eng 132:166–186. https://doi.org/10.1016/j.cie.2019.04.029
Iscan H, Gunduz M (2014) Parameter analysis on fruit fly optimization algorithm. J Comput Commun 2:137–141. https://doi.org/10.1109/SITIS.2015.55
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Nadimi-Shahraki MH, Taghian S, Mirjalili S (2021) An improved grey wolf optimizer for solving engineering problems. Expert Syst Appl 166:113917. https://doi.org/10.1016/j.eswa.2020.113917
Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1016/j.advengsoft.2017.01.004
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: 2007 IEEE congress on evolutionary computation, CEC 2007, pp 4661–4667
Hosseini S, Al Khaled A (2014) A survey on the imperialist competitive algorithm metaheuristic: implementation in engineering domain and directions for future research. Appl Soft Comput J 24:1078–1094
Yang XS (2007) Firefly algorithm. Nature-inspired metaheuristic algorithms, pp 79–90
Yang XS (2010) Firefly algorithm, Lévy flights and global optimization. In: Research and development in intelligent systems XXVI: incorporating applications and innovations in intelligent systems XVII, pp 1–10
Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006
Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073. https://doi.org/10.1007/s00521-015-1920-1
Mafarja M, Aljarah I, Heidari AA et al (2018) Binary dragonfly optimization for feature selection using time-varying transfer functions. Knowl Based Syst 161:185–204. https://doi.org/10.1016/j.knosys.2018.08.003
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
Barman M, Dev Choudhury NB (2020) A similarity based hybrid GWO-SVM method of power system load forecasting for regional special event days in anomalous load situations in Assam, India. Sustain Cities Soc. https://doi.org/10.1016/j.scs.2020.102311
Dogan L, Yüzgeç U (2018) Robot path planning using gray wolf optimizer. In: International conference on advanced technologies, computer engineering and science (ICATCES’18), pp 69–74
Karakas M, Yüzgeç U (2019) Opposition based gray wolf algorithm for feature selection in classification problems. In: 3rd International symposium on multidisciplinary studies and innovative technologies, ISMSIT 2019—proceedings. Institute of Electrical and Electronics Engineers Inc
Madadi A, Motlagh MM (2014) Optimal control of DC motor using grey wolf optimizer algorithm. Tech J Eng Appl 4:373–379
Medjahed SA, Ait Saadi T, Benyettou A, Ouali M (2016) Gray wolf optimizer for hyperspectral band selection. Appl Soft Comput J 40:178–186. https://doi.org/10.1016/j.asoc.2015.09.045
Li L, Sun L, Guo J et al (2017) Modified discrete grey wolf optimizer algorithm for multilevel image thresholding. Comput Intell Neurosci. https://doi.org/10.1155/2017/3295769
Ge L, Xian Y, Yan J et al (2020) A hybrid model for short-term PV output forecasting based on PCA-GWO-GRNN. J Mod Power Syst Clean Energy 8:1268–1275. https://doi.org/10.35833/MPCE.2020.000004
Liu H, Wu H, Li Y (2018) Smart wind speed forecasting using EWT decomposition, GWO evolutionary optimization, RELM learning and IEWT reconstruction. Energy Convers Manag 161:266–283. https://doi.org/10.1016/j.enconman.2018.02.006
Niu T, Wang J, Zhang K, Du P (2018) Multi-step-ahead wind speed forecasting based on optimal feature selection and a modified bat algorithm with the cognition strategy. Renew Energy 118:213–229. https://doi.org/10.1016/j.renene.2017.10.075
Xiao L, Wang J, Dong Y, Wu J (2015) Combined forecasting models for wind energy forecasting: a case study in China. Renew Sustain Energy Rev 44:271–288. https://doi.org/10.1016/j.rser.2014.12.012
Zhang W, Qu Z, Zhang K et al (2017) A combined model based on CEEMDAN and modified flower pollination algorithm for wind speed forecasting. Energy Convers Manag 136:439–451. https://doi.org/10.1016/j.enconman.2017.01.022
Wang J, Du P, Niu T, Yang W (2017) A novel hybrid system based on a new proposed algorithm—multi-objective whale optimization algorithm for wind speed forecasting. Appl Energy 208:344–360. https://doi.org/10.1016/j.apenergy.2017.10.031
Osório GJ, Matias JCO, Catalão JPS (2015) Short-term wind power forecasting using adaptive neuro-fuzzy inference system combined with evolutionary particle swarm optimization, wavelet transform and mutual information. Renew Energy 75:301–307. https://doi.org/10.1016/j.renene.2014.09.058
Fei SW, He Y (2015) Wind speed prediction using the hybrid model of wavelet decomposition and artificial bee colony algorithm-based relevance vector machine. Int J Electr Power Energy Syst 73:625–631. https://doi.org/10.1016/j.ijepes.2015.04.019
Rahmani R, Yusof R, Seyedmahmoudian M, Mekhilef S (2013) Hybrid technique of ant colony and particle swarm optimization for short term wind energy forecasting. J Wind Eng Ind Aerodyn 123:163–170. https://doi.org/10.1016/j.jweia.2013.10.004
Altan A, Karasu S, Zio E (2021) A new hybrid model for wind speed forecasting combining long short-term memory neural network, decomposition methods and grey wolf optimizer. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2020.106996
Fu W, Wang K, Tan J, Zhang K (2020) A composite framework coupling multiple feature selection, compound prediction models and novel hybrid swarm optimizer-based synchronization optimization strategy for multi-step ahead short-term wind speed forecasting. Energy Convers Manag. https://doi.org/10.1016/j.enconman.2019.112461
Wang J, Wang S, Yang W (2019) A novel non-linear combination system for short-term wind speed forecast. Renew Energy 143:1172–1192. https://doi.org/10.1016/j.renene.2019.04.154
Wu C, Wang J, Chen X et al (2020) A novel hybrid system based on multi-objective optimization for wind speed forecasting. Renew Energy 146:149–165. https://doi.org/10.1016/j.renene.2019.04.157
Singh D, Dhillon JS (2019) Ameliorated grey wolf optimization for economic load dispatch problem. Energy 169:398–419. https://doi.org/10.1016/j.energy.2018.11.034
Pradhan M, Roy PK, Pal T (2016) Grey wolf optimization applied to economic load dispatch problems. Int J Electr Power Energy Syst 83:325–334. https://doi.org/10.1016/j.ijepes.2016.04.034
Jayabarathi T, Raghunathan T, Adarsh BR, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630–641. https://doi.org/10.1016/j.energy.2016.05.105
Pradhan M, Roy PK, Pal T (2018) Oppositional based grey wolf optimization algorithm for economic dispatch problem of power system. Ain Shams Eng J 9:2015–2025. https://doi.org/10.1016/j.asej.2016.08.023
Gupta S, Deep K, Mirjalili S, Kim JH (2020) A modified sine cosine algorithm with novel transition parameter and mutation operator for global optimization. Expert Syst Appl 154:113395. https://doi.org/10.1016/j.eswa.2020.113395
Liang JJ, Qu BY, Suganthan PN (2014) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization
Long W, Liang X, Cai S et al (2017) A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems. Neural Comput Appl 28:421–438. https://doi.org/10.1007/s00521-016-2357-x
Long W, Jiao J, Liang X, Tang M (2018) An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization. Eng Appl Artif Intell 68:63–80. https://doi.org/10.1016/j.engappai.2017.10.024
Tascikaraoglu A, Uzunoglu M (2014) A review of combined approaches for prediction of short-term wind speed and power. Renew Sustain Energy Rev 34:243–254. https://doi.org/10.1016/j.rser.2014.03.033
Ma Z, Chen H, Wang J et al (2020) Application of hybrid model based on double decomposition, error correction and deep learning in short-term wind speed prediction. Energy Convers Manag. https://doi.org/10.1016/j.enconman.2019.112345
Lei M, Shiyan L, Chuanwen J et al (2009) A review on the forecasting of wind speed and generated power. Renew Sustain Energy Rev 13:915–920. https://doi.org/10.1016/j.rser.2008.02.002
Chang W-Y (2014) A literature review of wind forecasting methods. J Power Energy Eng 02:161–168. https://doi.org/10.4236/jpee.2014.24023
Liu H, Li Y, Duan Z, Chen C (2020) A review on multi-objective optimization framework in wind energy forecasting techniques and applications. Energy Convers Manag. https://doi.org/10.1016/j.enconman.2020.113324
Dokur E (2020) Swarm decomposition technique based hybrid model for very short-term solar PV power generation forecast. Elektron ir Elektrotechnika 26:79–83. https://doi.org/10.5755/j01.eie.26.3.25898
Dokur E, Kurban M, Ceyhan S (2016) Hybrid model for short term wind speed forecasting using empirical mode decomposition and artificial neural network. In: ELECO 2015—9th international conference electrical engineering, pp; 420–423. https://doi.org/10.1109/ELECO.2015.7394591
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İnaç, T., Dokur, E. & Yüzgeç, U. A multi-strategy random weighted gray wolf optimizer-based multi-layer perceptron model for short-term wind speed forecasting. Neural Comput & Applic 34, 14627–14657 (2022). https://doi.org/10.1007/s00521-022-07303-4
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DOI: https://doi.org/10.1007/s00521-022-07303-4