Abstract
The Radial Basis Function Neural Network (RBFNN) is a feedforward artificial neural network employing radial basis functions as activation functions in the hidden layer. The output of the RBFNN is a linear combination of the outputs from the hidden layer. This paper present a Mixed Radial Basis Function Neural Network (MRBFNN) training using Genetic Algorithm (GA). The choice of the type of Radial Basis Functions (RBFs) utilized in each hidden layer neuron has a significant impact on convergence, interpolation and performance. In this work, the authors are introducing a new approach to optimizing the choice of radial basis functions, centers, radius and weights of the output layer. We model in terms of mixed-variable optimization problems with linear constraints. To solve this model we will use an approach based on the genetic algorithm, allows us to determine the types of RBF to use in the hidden layer and the optimal weight of the output layer which gives us a good generalization. The results numerically demonstrate the performance of the theoretic results presented in this paper, as well as the benefits of the new modeling.
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All data used for the experiments are publicly available (as indicated by pointers to the literature in the paper).
References
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):1–34
Qu J, Zuo M (2010) Support vector machine based data processing algorithm for wear degree classification of slurry pump systems. Measurement 43(6):781–791
Uhl T (2007) The inverse identification problem and its technical application. Arch Appl Mech 77(5):325–337
Wang H, Zhang L, Yin K, Luo H, Li J (2021) Landslide identification using machine learning. Geosci Front 12(1):351–364
Liao Y, Fang S-C, Nuttle HL (2003) Relaxed conditions for radial-basis function networks to be universal approximators. Neural Netw 16(7):1019–1028
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
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(5–6):729–734
Karayiannis NB (1997) Gradient descent learning of radial basis neural networks. In: Proceedings of international conference on neural networks (ICNN’97), vol 3, pp 1815–1820. IEEE
Fasshauer GE, McCourt MJ (2012) Stable evaluation of gaussian radial basis function interpolants. SIAM J Sci Comput 34(2):737–762
Wang J, Liu G (2002) A point interpolation meshless method based on radial basis functions. Neural Comput Appl 54(11):1623–1648
Musavi MT, Ahmed W, Chan KH, Faris KB, Hummels DM (1992) On the training of radial basis function classifiers. Neural Netw 5(4):595–603
Franke C, Schaback R (1998) Solving partial differential equations by collocation using radial basis functions. Appl Math Comput 93(1):73–82
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):333–336
Karayiannis NB (1999) Reformulated radial basis neural networks trained by gradient descent. IEEE Trans Neural Netw 10(3):657–671
Wu Y, Wang H, Zhang B, Du KL (2012) Using radial basis function networks for function approximation and classification. Int Sch Res Not
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):881–892
Kleinert T, Labbé M, Ljubić I, Schmidt M (2021) A survey on mixed-integer programming techniques in bilevel optimization. EURO J Comput Opt 9:100007
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 95–105. American Society of Mechanical Engineers
Westerlund T, Pettersson F (1995) An extended cutting plane method for solving convex minlp problems. Comput Chem Eng 19:131–136
Benders J (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4(1):238–252
Lin C-Y, Hajela P (1992) Genetic algorithms in optimization problems with discrete and integer design variables. Eng Optim 19(4):309–327
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 69–73
Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66
Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press
Albadr MA, Tiun S, Ayob M, Al-Dhief F (2020) Genetic algorithm based on natural selection theory for optimization problems. Symmetry 12(11):1758
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 62–69. IEEE
Asuncion A, Newman D (2007) UCI Machine learning repository. Irvine, CA, USA
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Elansari, T., Ouanan, M. & Bourray, H. Mixed Radial Basis Function Neural Network Training Using Genetic Algorithm. Neural Process Lett 55, 10569–10587 (2023). https://doi.org/10.1007/s11063-023-11339-5
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DOI: https://doi.org/10.1007/s11063-023-11339-5