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A parameter free filled function for unconstrained global optimization. (English) Zbl 1192.65081
Authors’ abstract: The filled function method is considered as an efficient method to find the global minimum of multidimensional functions. A number of filled functions were proposed recently, most of which have one or two adjustable parameters. However, there is no efficient criterion to choose the parameter appropriately.
In this paper, we propose a filled function without parameters. This function includes neither exponential terms nor logarithmic terms so it is superior to the traditional ones. Theories of the filled function are investigated. An algorithm which does not compute gradients while minimizing the filled function is presented. Moreover, numerical experiments demonstrate the efficiency of the proposed filled function.

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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[1] Horstr, R.; Pardalos, P.M.; Thoai, N.V., Introduction to global optimization, (1995), Kluwer Academic Publishes Dordrecht, Netherlands
[2] Boender, C.G.E.; Rinnooy Kan, A.H.G., A Bayesian analysis of the number of cells of a multinomial distribution, Statistican, 32, 240-248, (1983)
[3] Boender, C.G.E.; Rinnooy Kan, A.H.G., Bayesian stopping rules for multistart global optimization methods, Mathe. program. A B, 37, 1, 59-80, (1987) · Zbl 0626.90079
[4] Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P., Optimization by simulate annealing, Science, 220, 671-680, (1983) · Zbl 1225.90162
[5] Holland, J.H., Genetic algorithms, Scient. am., 4, 14-50, (1992)
[6] Levy, A.V.; Montalvo, A., The tunneling algorithm for the global minimization of functions, SIAM J. sci. stat. comput., 6, 15-29, (1985) · Zbl 0601.65050
[7] Yao, Y., Dynamic tunneling algorithm for global optimization, IEEE trans. syst. man cybernet., 19, 5, 1222-1230, (1989)
[8] Ge, R.P., A filled function method for finding a global minimizer if a function of several variables, Math. program., 46, 191-204, (1990) · Zbl 0694.90083
[9] Ge, R.P.; Qin, Y.F., A class of filled functions for finding global minimizers of a function of several variables, J. optim. theory appl., 54, 2, 241-252, (1987) · Zbl 0595.65072
[10] Xu, Z.; Huang, H.X.; Pardalos, P.M., Filled functions for unconstrained global optimization, J. glob. optim., 20, 49-65, (2001) · Zbl 1049.90092
[11] Wu, Z.Y.; Lee, H.W.J.; Zhang, L.S.; Yang, X.M., A novel filled function method and quasi-filled function method for global optimization, Comput. optim. appl., 34, 249-272, (2005) · Zbl 1121.90105
[12] Zhang, L.S.; NG, C.K.; Li, D.; Tian, W.W., A new filled function method for global optimization, J. global optim., 28, 17-43, (2004) · Zbl 1061.90109
[13] Liu, X., Several filled functions with mitigators, Appl. math. comput., 133, 375-387, (2002) · Zbl 1135.90372
[14] Liu, X., A new filled function applied to global optimization, Comput. oper. res., 31, 61-80, (2004) · Zbl 1039.90099
[15] Lan, An; Liansheng, Zhang; Meilin, Chen, A parameter-free filled function for unconstrained global optimization, J. Shanghai univ. (engl. ed.), 8, 2, 117-123, (2004) · Zbl 1068.90098
[16] Leifu, Gao; Xuwang, Liu, The global optimization algorithm based on chaos optimization and filled function, Operat. res. manage. sci., 18, 2, 25-29, (2009)
[17] Yang, Y.J.; Shang, Y.L., A new filled function method for unconstrained global optimization, Appl. math. comput., 173, 501-512, (2006) · Zbl 1094.65063
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