A novel one-parameter filled function method with an application to pathological analysis. (English) Zbl 1543.90249
Summary: The filled function method is an efficient approach for finding a global minimizer of global optimization problems. The key of this kind of methods is the design of filled function. In this paper, we propose a new filled function with one parameter that is continuously differentiable and always contains local information of objective function. Then, a new filled function method involved the proposed filled function for unconstrained global optimization problems is developed. Furthermore, numerical experiments are conducted to demonstrate the efficiency and reliability of our algorithm. We finally apply the proposed algorithm to study the pathological factors in renal cell carcinoma metastasis.
MSC:
| 90C26 | Nonconvex programming, global optimization |
Keywords:
global optimization; nonconvex optimization; filled function method; renal cell carcinoma metastasisReferences:
| [1] | Horst, R.; Pardalos, PM; Thoai, NV, Introduction to Global Optimization, 1995, Dordrecht, Netherland: Kluwer Academic Publishers, Dordrecht, Netherland · Zbl 0836.90134 |
| [2] | Horst, R.; Tuy, H., Global Optimization: Deterministic Approaches, 1993, Heidelberg: Springer-Verlag, Heidelberg |
| [3] | Pardalos, PM; Rosen, JB, Constrained Global Optimization: Algorithms and Applications, 1987, Berlin: Springer, Berlin · Zbl 0638.90064 |
| [4] | Bai, L.; Liang, JY; Dang, CY; Cao, FY, A cluster centers initialization method for clustering categorical data, Expert. Syst. Appl., 39, 8022-8029, 2012 |
| [5] | Kirkpatrick, S.; Gelatt, CD; Vecchi, MP, Optimization by simulate annealing, Science, 220, 671-680, 1983 · Zbl 1225.90162 |
| [6] | Holland, JH, Genetic algorithms, Sci. Am., 4, 14-50, 1992 |
| [7] | Zhang, Y.; Zhang, LS; Xu, YT, New filled functions for nonsmooth global optimization, Appl. Math. Model., 33, 3114-3129, 2009 · Zbl 1205.90236 |
| [8] | Levy, AV; Montalvo, A., The tunneling algorithm for the global minimization of functions, SIAM J. Sci. Comput., 6, 15-29, 1985 · Zbl 0601.65050 |
| [9] | Cetin, BC; Barhen, J.; Burdick, JW, Terminal repellar unconstrained subenergy for farst global optimization, J. Optim. Theory Appl., 77, 97-125, 1993 · Zbl 0801.49001 |
| [10] | Ge, RP, A filled function method for finding a global minimizer of a function of several variables, Math. Program., 46, 191-204, 1990 · Zbl 0694.90083 |
| [11] | Ge, RP, The theory of filled Function method for finding global minimizers of nonlinearly constrained minimization problems, J. Comput. Math., 5, 1-10, 1987 · Zbl 0692.90087 |
| [12] | Ge, RP; Qin, YF, A class of filled functions for finding global minimizers of a function of several variables, J. Optim. Theory Appl., 54, 241-252, 1987 · Zbl 0595.65072 |
| [13] | Zhang, LS; Ng, CK; Li, D.; Tian, WW, A new filled function method for global optimization, J. Glob. Optim., 28, 17-43, 2004 · Zbl 1061.90109 |
| [14] | Xu, Z.; Huang, HX; Pardalos, PM; Xu, CX, Filled functions for unconstrained global optimization, J. Glob. Optim., 20, 49-65, 2001 · Zbl 1049.90092 |
| [15] | Liu, X., Finding global minima with a computable filled function, J. Glob. Optim., 19, 151-161, 2001 · Zbl 1033.90088 |
| [16] | Lucidi, S.; Piccialli, V., New classes of globally convexized filled functions for global optimization, J. Glob. Optim., 24, 219-236, 2002 · Zbl 1047.90051 |
| [17] | Liang, YM; Zhang, LS; Li, MM; Han, BS, A filled function method for global optimization, J. Comput. Appl. Math., 205, 16-31, 2007 · Zbl 1124.65052 |
| [18] | Liu, X., A class of continuously differentiable filled functions for global optimization, IEEE Trans. Syst. Man. Cybern. Part A Syst. Human., 38, 38-47, 2008 |
| [19] | Liu, X., A class of augmented filled functions, Comput. Optim. Appl., 33, 333-347, 2006 · Zbl 1111.90090 |
| [20] | Ng, CK; Li, D.; Zhang, LS, Global descent method for global optimization, SIAM J. Optim., 20, 3161-3184, 2010 · Zbl 1208.49038 |
| [21] | Shang, YL; Zhang, LS, Finding discrete global minima with a filled function for integer programming, Eur. J. Oper. Res., 189, 31-40, 2008 · Zbl 1152.90541 |
| [22] | Yang, YJ; Shang, YL, A new filled function method for unconstrained global optimization, Appl. Math. Comput., 173, 501-512, 2006 · Zbl 1094.65063 |
| [23] | Yuan, LY; Wan, ZP; Tang, QH, A criterion for an approximation global optimal solution based on the filled functions, J. Ind. Manag. Optim., 12, 375-387, 2016 · Zbl 1317.90287 |
| [24] | Wu, ZY; Zhang, LS; Teo, KL; Bai, FS, New modified function method for global optimization, J. Optim. Theory Appl., 125, 181-203, 2005 · Zbl 1114.90100 |
| [25] | Wang, CJ; Yang, YJ; Li, J., A new filled function method for unconstrained global optimization, J. Comput. Appl. Math., 225, 68-79, 2009 · Zbl 1162.65033 |
| [26] | Wu, ZY; Bai, FS; Lee, HWJ; Yang, YJ, A filled function method for constrained global optimization, J. Glob. Optim., 39, 495-507, 2007 · Zbl 1190.90150 |
| [27] | Wu, ZY; Lee, HWJ; Zhang, LS; Yang, XM, A novel filled function method and quasi-filled function method for global optimization, Comput. Optim. Appl., 34, 249-272, 2005 · Zbl 1121.90105 |
| [28] | El-Gindy, TM; Salim, MS; Ahmed, AI, A new filled function method applied to unconstrained global optimization, Appl. Math. Comput., 273, 1246-1256, 2016 · Zbl 1410.90165 |
| [29] | Gao, CL; Yang, YJ; Han, BS, A new class of filled functions with one parameter for global optimization, Comput. Math. Appl., 62, 2393-2403, 2011 · Zbl 1231.65109 |
| [30] | Lin, HW; Gao, YL; Wang, YP, A continuously differentiable filled function method for global optimization, Numer. Algorithms, 66, 511-523, 2014 · Zbl 1296.65089 |
| [31] | Wei, F.; Wang, YP; Lin, HW, A new filled function method with two parameters for global optimization, J. Optim. Theory Appl., 163, 510-527, 2014 · Zbl 1305.65155 |
| [32] | He, QY; Zhang, Y.; Wang, SG, A new one-parameter filled function method and its application in pathological analysis, J. Simul., 7, 17-23, 2019 |
| [33] | Shang, YL; Pu, DG; Jang, AP, Finding global minimizer with one-parameter filled function on unconstrained global optimization, Appl. Math. Comput., 191, 176-182, 2007 · Zbl 1193.90174 |
| [34] | Sui, X.; Wang, YP; Liu, JH, A new filled function method combining auxiliary function for global optimization, Pac. J. Optim., 15, 23-44, 2019 · Zbl 1454.90064 |
| [35] | Qu, D.Q., Shang, Y.L., Wu, D., Sun, G.L.: Filled function method to optimize supply chain transportation costs. J. Ind. Manag. Optim. doi: doi:10.3934/jimo.2021115. · Zbl 1513.90182 |
| [36] | Liu, HY; Wang, YP; Guan, SW; Liu, XY, A new filled function method for unconstrained global optimization, Int. J. Comput. Math., 93, 2283-2296, 2017 · Zbl 1398.65125 |
| [37] | Ahmed, AI, A new parameter free filled function for solving unconstrained global optimization problems, Int. J. Comput. Math., 98, 106-119, 2021 · Zbl 1479.90163 |
| [38] | Pandiya, R.; Widodo, W.; Endrayanto, I., Non parameter-filled function for global optimization, Appl. Math. Comput., 391, 2021 · Zbl 1474.90357 |
| [39] | Wu, X.; Wang, YP; Fan, NL, A new filled function method based on adaptive search direction and valley widening for global optimization, Appl. Intell., 51, 6234-6254, 2021 |
| [40] | Liu, HY; Wang, YP; Gao, XZ; Zhang, M., A parameter free filled function method for global optimization, Pac. J. Opim., 14, 567-580, 2018 · Zbl 1461.65173 |
| [41] | Siegel, RL; Miller, KD; Jemal, A., Cancer statistics, CA Cancer J. Clin., 65, 5-29, 2015 |
| [42] | Robson, CJ; Churchill, BM; Anderson, W., The results of radical nephrectomy for renal cell carcinoma, J. Urol., 101, 297-301, 1969 |
| [43] | Ni, Z., Health statistics, 138-142, 2001, People’s Medical Publishing House |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
