{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T11:31:56Z","timestamp":1781523116896,"version":"3.54.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:00:00Z","timestamp":1688947200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:00:00Z","timestamp":1688947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s11063-023-11339-5","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T11:01:50Z","timestamp":1688986910000},"page":"10569-10587","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Mixed Radial Basis Function Neural Network Training Using Genetic Algorithm"],"prefix":"10.1007","volume":"55","author":[{"given":"Taoufyq","family":"Elansari","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammed","family":"Ouanan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamid","family":"Bourray","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"issue":"5","key":"11339_CR1","first-page":"1","volume":"52","author":"AC Lorena","year":"2019","unstructured":"Lorena AC, Garcia LP, Lehmann J, Souto MC, Ho TK (2019) How complex is your classification problem? a survey on measuring classification complexity. ACM Comput Surv CSUR 52(5):1\u201334","journal-title":"ACM Comput Surv CSUR"},{"issue":"6","key":"11339_CR2","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1016\/j.measurement.2010.02.014","volume":"43","author":"J Qu","year":"2010","unstructured":"Qu J, Zuo M (2010) Support vector machine based data processing algorithm for wear degree classification of slurry pump systems. Measurement 43(6):781\u2013791","journal-title":"Measurement"},{"issue":"5","key":"11339_CR3","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s00419-006-0086-9","volume":"77","author":"T Uhl","year":"2007","unstructured":"Uhl T (2007) The inverse identification problem and its technical application. Arch Appl Mech 77(5):325\u2013337","journal-title":"Arch Appl Mech"},{"issue":"1","key":"11339_CR4","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/j.gsf.2020.02.012","volume":"12","author":"H Wang","year":"2021","unstructured":"Wang H, Zhang L, Yin K, Luo H, Li J (2021) Landslide identification using machine learning. Geosci Front 12(1):351\u2013364","journal-title":"Geosci Front"},{"issue":"7","key":"11339_CR5","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1016\/S0893-6080(02)00227-7","volume":"16","author":"Y Liao","year":"2003","unstructured":"Liao Y, Fang S-C, Nuttle HL (2003) Relaxed conditions for radial-basis function networks to be universal approximators. Neural Netw 16(7):1019\u20131028","journal-title":"Neural Netw"},{"issue":"2","key":"11339_CR6","first-page":"220","volume":"2","author":"SA Sarra","year":"2009","unstructured":"Sarra SA, Kansa EJ (2009) Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations. Adv Comput Mech 2(2):220","journal-title":"Adv Comput Mech"},{"issue":"5\u20136","key":"11339_CR7","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1016\/S0893-6080(03)00083-2","volume":"16","author":"L Jianyu","year":"2003","unstructured":"Jianyu L, Siwei L, Yingjian Q, Yaping H (2003) Numerical solution of elliptic partial differential equation using radial basis function neural networks. Neural Netw 16(5\u20136):729\u2013734","journal-title":"Neural Netw"},{"key":"11339_CR8","doi-asserted-by":"crossref","unstructured":"Karayiannis NB (1997) Gradient descent learning of radial basis neural networks. In: Proceedings of international conference on neural networks (ICNN\u201997), vol 3, pp 1815\u20131820. IEEE","DOI":"10.1109\/ICNN.1997.614174"},{"issue":"2","key":"11339_CR9","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1137\/110824784","volume":"34","author":"GE Fasshauer","year":"2012","unstructured":"Fasshauer GE, McCourt MJ (2012) Stable evaluation of gaussian radial basis function interpolants. SIAM J Sci Comput 34(2):737\u2013762","journal-title":"SIAM J Sci Comput"},{"issue":"11","key":"11339_CR10","first-page":"1623","volume":"54","author":"J Wang","year":"2002","unstructured":"Wang J, Liu G (2002) A point interpolation meshless method based on radial basis functions. Neural Comput Appl 54(11):1623\u20131648","journal-title":"Neural Comput Appl"},{"issue":"4","key":"11339_CR11","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/S0893-6080(05)80038-3","volume":"5","author":"MT Musavi","year":"1992","unstructured":"Musavi MT, Ahmed W, Chan KH, Faris KB, Hummels DM (1992) On the training of radial basis function classifiers. Neural Netw 5(4):595\u2013603","journal-title":"Neural Netw"},{"issue":"1","key":"11339_CR12","first-page":"73","volume":"93","author":"C Franke","year":"1998","unstructured":"Franke C, Schaback R (1998) Solving partial differential equations by collocation using radial basis functions. Appl Math Comput 93(1):73\u201382","journal-title":"Appl Math Comput"},{"issue":"2","key":"11339_CR13","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s00521-011-0702-7","volume":"21","author":"S Ding","year":"2012","unstructured":"Ding S, Xu L, Su C, Jin F (2012) An optimizing method of rbf neural network based on genetic algorithm. Neural Comput Appl 21(2):333\u2013336","journal-title":"Neural Comput Appl"},{"issue":"3","key":"11339_CR14","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1109\/72.761725","volume":"10","author":"NB Karayiannis","year":"1999","unstructured":"Karayiannis NB (1999) Reformulated radial basis neural networks trained by gradient descent. IEEE Trans Neural Netw 10(3):657\u2013671","journal-title":"IEEE Trans Neural Netw"},{"key":"11339_CR15","doi-asserted-by":"crossref","unstructured":"Wu Y, Wang H, Zhang B, Du KL (2012) Using radial basis function networks for function approximation and classification. Int Sch Res Not","DOI":"10.5402\/2012\/324194"},{"issue":"7","key":"11339_CR16","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1109\/TPAMI.2002.1017616","volume":"24","author":"T Kanungo","year":"2002","unstructured":"Kanungo T, Mount DM, Netanyahu NS, Piatko CD, Silverman R, Wu AY (2002) An efficient k-means clustering algorithm: analysis and implementation. IEEE Trans Pattern Anal Mach Intell 24(7):881\u2013892","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"11339_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejco.2021.100007","volume":"9","author":"T Kleinert","year":"2021","unstructured":"Kleinert T, Labb\u00e9 M, Ljubi\u0107 I, Schmidt M (2021) A survey on mixed-integer programming techniques in bilevel optimization. EURO J Comput Opt 9:100007","journal-title":"EURO J Comput Opt"},{"key":"11339_CR18","doi-asserted-by":"crossref","unstructured":"Sandgren E (1988) Nonlinear integer and discrete programming in mechanical design. In: International design engineering technical conferences and computers and information in engineering conference, vol 26584, pp 95\u2013105. American Society of Mechanical Engineers","DOI":"10.1115\/DETC1988-0012"},{"key":"11339_CR19","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/0098-1354(95)87027-X","volume":"19","author":"T Westerlund","year":"1995","unstructured":"Westerlund T, Pettersson F (1995) An extended cutting plane method for solving convex minlp problems. Comput Chem Eng 19:131\u2013136","journal-title":"Comput Chem Eng"},{"issue":"1","key":"11339_CR20","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF01386316","volume":"4","author":"J Benders","year":"1962","unstructured":"Benders J (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4(1):238\u2013252","journal-title":"Numer Math"},{"issue":"4","key":"11339_CR21","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1080\/03052159208941234","volume":"19","author":"C-Y Lin","year":"1992","unstructured":"Lin C-Y, Hajela P (1992) Genetic algorithms in optimization problems with discrete and integer design variables. Eng Optim 19(4):309\u2013327","journal-title":"Eng Optim"},{"key":"11339_CR22","unstructured":"Shi Y, Eberhart R (1998) A modified particle swarm optimizer,$$\\Vert $$ in 1998 ieee international conference on evolutionary computation proceedings. In: IEEE World congress on computational intelligence (Cat. No. 98TH8360), pp 69\u201373"},{"issue":"1","key":"11339_CR23","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1109\/4235.585892","volume":"1","author":"M Dorigo","year":"1997","unstructured":"Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53\u201366","journal-title":"IEEE Trans Evol Comput"},{"key":"11339_CR24","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/1090.001.0001","volume-title":"Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence","author":"JH Holland","year":"1992","unstructured":"Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press"},{"issue":"11","key":"11339_CR25","doi-asserted-by":"publisher","first-page":"1758","DOI":"10.3390\/sym12111758","volume":"12","author":"MA Albadr","year":"2020","unstructured":"Albadr MA, Tiun S, Ayob M, Al-Dhief F (2020) Genetic algorithm based on natural selection theory for optimization problems. Symmetry 12(11):1758","journal-title":"Symmetry"},{"key":"11339_CR26","doi-asserted-by":"crossref","unstructured":"Elhassania M, Jaouad B, Ahmed EA (2014) Solving the dynamic vehicle routing problem using genetic algorithms. In: 2014 International conference on logistics operations management, pp 62\u201369. IEEE","DOI":"10.1109\/GOL.2014.6887419"},{"key":"11339_CR27","volume-title":"UCI Machine learning repository","author":"A Asuncion","year":"2007","unstructured":"Asuncion A, Newman D (2007) UCI Machine learning repository. Irvine, CA, USA"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-023-11339-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11063-023-11339-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-023-11339-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,23]],"date-time":"2024-10-23T22:19:10Z","timestamp":1729721950000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11063-023-11339-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,10]]},"references-count":27,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["11339"],"URL":"https:\/\/doi.org\/10.1007\/s11063-023-11339-5","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"value":"1370-4621","type":"print"},{"value":"1573-773X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,10]]},"assertion":[{"value":"20 June 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}