{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T10:03:24Z","timestamp":1770285804135,"version":"3.49.0"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2017,5,6]],"date-time":"2017-05-06T00:00:00Z","timestamp":1494028800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s00521-017-2952-5","type":"journal-article","created":{"date-parts":[[2017,5,6]],"date-time":"2017-05-06T05:57:08Z","timestamp":1494050228000},"page":"3707-3720","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":123,"title":["A Levy flight-based grey wolf optimizer combined with back-propagation algorithm for neural network training"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4669-0505","authenticated-orcid":false,"given":"Shima","family":"Amirsadri","sequence":"first","affiliation":[]},{"given":"Seyed Jalaleddin","family":"Mousavirad","sequence":"additional","affiliation":[]},{"given":"Hossein","family":"Ebrahimpour-Komleh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,5,6]]},"reference":[{"issue":"3\u20134","key":"2952_CR1","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/s00521-013-1408-9","volume":"23","author":"DO Baptista","year":"2013","unstructured":"Baptista DO, Morgado-Dias F (2013) A survey of artificial neural network training tools. Neural Comput Appl 23(3\u20134):609\u2013615","journal-title":"Neural Comput Appl"},{"key":"2952_CR2","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.compbiomed.2013.10.029","volume":"44","author":"N Torbati","year":"2012","unstructured":"Torbati N, Ayatollahi A, Kermani A (2012) An efficient neural network based method for medical image segmentation. Comput Biol Med 44:76\u201387","journal-title":"Comput Biol Med"},{"key":"2952_CR3","doi-asserted-by":"crossref","unstructured":"Rad SJM, Tab FA, Mollazade K (2011) Classification of rice varieties using optimal color and texture features and BP neural networks. In: Machine vision and image processing (MVIP), 2011 7th Iranian. IEEE, (2011) 1\u20135","DOI":"10.1109\/IranianMVIP.2011.6121583"},{"issue":"8","key":"2952_CR4","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1007\/s11947-009-0222-y","volume":"4","author":"M Fathi","year":"2011","unstructured":"Fathi M, Mohebbi M, Razavi SMA (2011) Application of image analysis and artificial neural network to predict mass transfer kinetics and color changes of osmotically dehydrated kiwifruit. Food Bioprocess Technol 4(8):1357\u20131366","journal-title":"Food Bioprocess Technol"},{"issue":"8","key":"2952_CR5","doi-asserted-by":"crossref","first-page":"1670","DOI":"10.1016\/j.engappai.2012.02.009","volume":"25","author":"R Taormina","year":"2012","unstructured":"Taormina R, Chau K-W, Sethi R (2012) Artificial neural network simulation of hourly groundwater levels in a coastal aquifer system of the Venice lagoon. Eng Appl Artif Intell 25(8):1670\u20131676","journal-title":"Eng Appl Artif Intell"},{"issue":"1","key":"2952_CR6","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.engappai.2011.07.006","volume":"25","author":"S Kulluk","year":"2012","unstructured":"Kulluk S, Ozbakir L, Baykasoglu A (2012) Training neural networks with harmony search algorithms for classification problems. Eng Appl Artif Intell 25(1):11\u201319","journal-title":"Eng Appl Artif Intell"},{"issue":"2","key":"2952_CR7","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1016\/j.asoc.2012.10.023","volume":"13","author":"A Askarzadeh","year":"2013","unstructured":"Askarzadeh A, Rezazadeh A (2013) Artificial neural network training using a new efficient optimization algorithm. Appl Soft Comput 13(2):1206\u20131213","journal-title":"Appl Soft Comput"},{"key":"2952_CR8","volume-title":"Fundamentals of neural networks: architectures, algorithms, and applications","author":"L Fausett","year":"1994","unstructured":"Fausett L (1994) Fundamentals of neural networks: architectures, algorithms, and applications. Prentice-Hall, Inc, Upper Saddle River"},{"key":"2952_CR9","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.ins.2014.01.038","volume":"269","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188\u2013209","journal-title":"Inf Sci"},{"key":"2952_CR10","doi-asserted-by":"crossref","unstructured":"Rumelhart DE, Hinton GE, Williams RJ (1985) Learning internal representations by error propagation. DTIC Document","DOI":"10.21236\/ADA164453"},{"issue":"2","key":"2952_CR11","first-page":"1026","volume":"185","author":"J-R Zhang","year":"2007","unstructured":"Zhang J-R, Zhang J, Lok T-M, Lyu MR (2007) A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training. Appl Math Comput 185(2):1026\u20131037","journal-title":"Appl Math Comput"},{"key":"2952_CR12","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","volume":"69","author":"S Mirjalili","year":"2014","unstructured":"Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46\u201361","journal-title":"Adv Eng Softw"},{"key":"2952_CR13","doi-asserted-by":"crossref","unstructured":"Holland JH (1992) Genetic algorithms: computer programs that \"evolve\" in ways that resemble natural selection can solve complex problems even their creators do not fully understand. Sci Am 267:66\u201372","DOI":"10.1038\/scientificamerican0792-66"},{"issue":"4","key":"2952_CR14","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","volume":"11","author":"R Storn","year":"1997","unstructured":"Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341\u2013359","journal-title":"J Glob Optim"},{"issue":"1","key":"2952_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/106365603321828970","volume":"11","author":"N Hansen","year":"2003","unstructured":"Hansen N, Muller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol Comput 11(1):1\u201318","journal-title":"Evol Comput"},{"key":"2952_CR16","unstructured":"Rechenberg I (1994) Evolution strategy. Computational intelligence: imitating life. IEEE Press, Piscataway, pp 147\u2013159"},{"key":"2952_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-7744-1","volume-title":"Simulated annealing: theory and applications","author":"PJ Laarhoven Van","year":"1987","unstructured":"Van Laarhoven PJ, Aarts EH (1987) Simulated annealing: theory and applications, vol 37. Springer Science & Business Media, Berlin"},{"issue":"3","key":"2952_CR18","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0375-9601(87)90796-1","volume":"122","author":"H Szu","year":"1987","unstructured":"Szu H, Hartley R (1987) Fast simulated annealing. Phys Lett A 122(3):157\u2013162","journal-title":"Phys Lett A"},{"issue":"13","key":"2952_CR19","doi-asserted-by":"crossref","first-page":"2232","DOI":"10.1016\/j.ins.2009.03.004","volume":"179","author":"E Rashedi","year":"2009","unstructured":"Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232\u20132248","journal-title":"Inf Sci"},{"issue":"10","key":"2952_CR20","doi-asserted-by":"crossref","first-page":"13170","DOI":"10.1016\/j.eswa.2011.04.126","volume":"38","author":"B Alatas","year":"2011","unstructured":"Alatas B (2011) ACROA: artificial chemical reaction optimization algorithm for global optimization. Expert Syst Appl 38(10):13170\u201313180","journal-title":"Expert Syst Appl"},{"key":"2952_CR21","doi-asserted-by":"crossref","unstructured":"Mendes R, Cortez P, Rocha M, Neves J (2002) Particle swarms for feedforward neural network training. In: Proceedings of the international joint conference on Neural networks, IJCNN '02, vol 2, pp 1895-1899","DOI":"10.1109\/IJCNN.2002.1007808"},{"key":"2952_CR22","doi-asserted-by":"crossref","unstructured":"Gudise VG, Venayagamoorthy GK (2003) Comparison of particle swarm optimization and backpropagation as training algorithms for neural networks. In: Swarm Intelligence Symposium, 2003. SIS\u201903. Proceedings of the 2003 IEEE. IEEE,110\u2013117","DOI":"10.1109\/SIS.2003.1202255"},{"key":"2952_CR23","doi-asserted-by":"crossref","unstructured":"Blum C, Socha K (2005) Training feed-forward neural networks with ant colony optimization: an application to pattern classification. In: Fifth international conference on hybrid intelligent systems, HIS \u201905, p 6","DOI":"10.1109\/ICHIS.2005.104"},{"issue":"3","key":"2952_CR24","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s00521-007-0084-z","volume":"16","author":"K Socha","year":"2007","unstructured":"Socha K, Blum C (2007) An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training. Neural Comput Appl 16(3):235\u2013247","journal-title":"Neural Comput Appl"},{"issue":"1","key":"2952_CR25","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1016\/j.asoc.2009.12.025","volume":"11","author":"D Karaboga","year":"2011","unstructured":"Karaboga D, Ozturk C (2011) A novel clustering approach: artificial bee colony (ABC) algorithm. Appl Soft Comput 11(1):652\u2013657","journal-title":"Appl Soft Comput"},{"key":"2952_CR26","doi-asserted-by":"crossref","unstructured":"Ozturk C, Karaboga D (2011) Hybrid artificial bee colony algorithm for neural network training. In: Evolutionary Computation (CEC), 2011 IEEE Congress on. IEEE, 84\u201388","DOI":"10.1109\/CEC.2011.5949602"},{"issue":"1","key":"2952_CR27","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","volume":"1","author":"DH Wolpert","year":"1997","unstructured":"Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. Evolut Comput IEEE Trans 1(1):67\u201382","journal-title":"Evolut Comput IEEE Trans"},{"key":"2952_CR28","unstructured":"Montana DJ, Davis L (1989) Training feedforward neural networks using genetic algorithms. In: IJCAI"},{"key":"2952_CR29","doi-asserted-by":"crossref","unstructured":"Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science. New York, NY","DOI":"10.1109\/MHS.1995.494215"},{"issue":"7","key":"2952_CR30","doi-asserted-by":"crossref","first-page":"3491","DOI":"10.1016\/j.eswa.2013.10.053","volume":"41","author":"G Das","year":"2014","unstructured":"Das G, Pattnaik PK, Padhy SK (2014) Artificial neural network trained by particle swarm optimization for non-linear channel equalization. Expert Syst Appl 41(7):3491\u20133496","journal-title":"Expert Syst Appl"},{"key":"2952_CR31","first-page":"84","volume":"26","author":"F Bergh Van den","year":"2000","unstructured":"Van den Bergh F, Engelbrecht AP (2000) Cooperative learning in neural networks using particle swarm optimizers. S Afr Comput J 26:84\u201390","journal-title":"S Afr Comput J"},{"issue":"22","key":"2952_CR32","first-page":"11125","volume":"218","author":"S Mirjalili","year":"2012","unstructured":"Mirjalili S, Hashim SZM, Sardroudi HM (2012) Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218(22):11125\u201311137","journal-title":"Appl Math Comput"},{"issue":"2","key":"2952_CR33","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1177\/003754970107600201","volume":"76","author":"ZW Geem","year":"2001","unstructured":"Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60\u201368","journal-title":"Simulation"},{"issue":"36","key":"2952_CR34","first-page":"3902","volume":"194","author":"KS Lee","year":"2005","unstructured":"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):3902\u20133933","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2952_CR35","doi-asserted-by":"crossref","unstructured":"Mirjalili SZ, Saremi S, Mirjalili SM (2015) Designing evolutionary feedforward neural networks using social spider optimization algorithm. Neural Comput App 26(8):1919\u20131928","DOI":"10.1007\/s00521-015-1847-6"},{"key":"2952_CR36","unstructured":"Ebrahimpour-Komleh H (2013) Cuckoo Optimization Algorithm for FeedForward Neural Network Training. 21th Iranian Conference on Electrical Engineering (ICEE2013), IEEE"},{"key":"2952_CR37","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.soildyn.2015.04.004","volume":"75","author":"X Song","year":"2015","unstructured":"Song X, Tang L, Zhao S, Zhang X, Li L, Huang J, Cai W (2015) Grey wolf optimizer for parameter estimation in surface waves. Soil Dyn Earthq Eng 75:147\u2013157","journal-title":"Soil Dyn Earthq Eng"},{"issue":"5","key":"2952_CR38","doi-asserted-by":"crossref","first-page":"838","DOI":"10.15866\/iremos.v7i5.2799","volume":"7","author":"HM Song","year":"2014","unstructured":"Song HM, Sulaiman MH, Mohamed MR (2014) An application of grey wolf optimizer for solving combined economic emission dispatch problems. Int Rev Model Simul (IREMOS) 7(5):838\u2013844","journal-title":"Int Rev Model Simul (IREMOS)"},{"key":"2952_CR39","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.jocs.2015.03.011","volume":"8","author":"GM Komaki","year":"2015","unstructured":"Komaki GM, Kayvanfar V (2015) Grey wolf optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time. J Comput Sci 8:109\u2013120","journal-title":"J Comput Sci"},{"key":"2952_CR40","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.asoc.2015.03.041","volume":"32","author":"MH Sulaiman","year":"2015","unstructured":"Sulaiman MH, Zuriani M, Mohamed MR, Aliman O (2015) Using the gray wolf optimizer for solving optimal reactive power dispatch problem. Appl Soft Comput 32:286\u2013292","journal-title":"Appl Soft Comput"},{"issue":"1","key":"2952_CR41","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/s10489-014-0645-7","volume":"43","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili S (2015) How effective is the Grey wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150\u2013161","journal-title":"Appl Intell"},{"key":"2952_CR42","doi-asserted-by":"crossref","unstructured":"Alba E, Chicano JF (2004) Training neural networks with GA hybrid algorithms. In: Genetic and Evolutionary Computation GECCO 2004. Springer, 852\u2013863","DOI":"10.1007\/978-3-540-24854-5_87"},{"key":"2952_CR43","doi-asserted-by":"crossref","unstructured":"Carvalho M, Ludermir TB (2006) Hybrid training of feed-forward neural networks with particle swarm optimization. In: Neural information processing. Springer, 1061\u20131070","DOI":"10.1007\/11893257_116"},{"key":"2952_CR44","doi-asserted-by":"crossref","unstructured":"Wang L, Zeng Y, Cui C, Wang H (2007) Application of artificial neural network supported by bp and particle swarm optimization algorithm for evaluating the criticality class of spare parts. In: Third international conference on natural computation, ICNC 2007, IEEE, pp 528\u2013532","DOI":"10.1109\/ICNC.2007.246"},{"key":"2952_CR45","doi-asserted-by":"crossref","unstructured":"Chechkin AV, \u00a0Metzler R, Klafter J, Yu. Gonchar V (2008) Introduction to the theory of L\u00e9vy flights. Anomalous transport: foundations and applications, Wiley, pp 129\u2013162","DOI":"10.1002\/9783527622979.ch5"},{"key":"2952_CR46","doi-asserted-by":"crossref","unstructured":"Sarangi PP, Sahu A, Panda M (2013) A hybrid differential evolution and back-propagation algorithm for feedforward neural network training. Int J Comput Appl 84(14)","DOI":"10.5120\/14641-2943"},{"key":"2952_CR47","doi-asserted-by":"crossref","unstructured":"Chen X, Wang J, Sun D, Liang J (2008) A novel hybrid Evolutionary Algorithm based on PSO and AFSA for feedforward neural network training. In: 4th international conference on wireless communications, networking and mobile computing, WiCOM'08, IEEE, pp 1\u20135","DOI":"10.1109\/WiCom.2008.2518"},{"issue":"6","key":"2952_CR48","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1016\/j.cor.2011.09.026","volume":"40","author":"X-S Yang","year":"2013","unstructured":"Yang X-S, Deb S (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40(6):1616\u20131624","journal-title":"Comput Oper Res"},{"issue":"1","key":"2952_CR49","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.engappai.2012.01.023","volume":"26","author":"M Yaghini","year":"2013","unstructured":"Yaghini M, Khoshraftar MM, Fallahi M (2013) A hybrid algorithm for artificial neural network training. Eng Appl Artif Intell 26(1):293\u2013301","journal-title":"Eng Appl Artif Intell"},{"key":"2952_CR50","unstructured":"Blake C, Merz CJ (1998) {UCI} Repository of machine learning databases"},{"key":"2952_CR51","unstructured":"Yaghini M, Khoshraftar MM, Fallahi M (2011) HIOPGA: a new hybrid metaheuristic algorithm to train feedforward neural networks for prediction. In: Proceedings of the international conference on data mining. 18\u201321"},{"issue":"6","key":"2952_CR52","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1016\/j.jss.2012.01.025","volume":"85","author":"S Dehuri","year":"2012","unstructured":"Dehuri S, Roy R, Cho S-B, Ghosh A (2012) An improved swarm optimized functional link artificial neural network (ISO-FLANN) for classification. J Syst Softw 85(6):1333\u20131345","journal-title":"J Syst Softw"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-017-2952-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-017-2952-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-017-2952-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,23]],"date-time":"2019-09-23T12:43:51Z","timestamp":1569242631000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-017-2952-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,6]]},"references-count":52,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["2952"],"URL":"https:\/\/doi.org\/10.1007\/s00521-017-2952-5","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,6]]}}}