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A projection neural-dynamic model for solving fuzzy convex nonlinear programming problems | ||
Iranian Journal of Fuzzy Systems | ||
دوره 21، شماره 3، مرداد و شهریور 2024، صفحه 37-63 اصل مقاله (1.6 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2024.46972.8276 | ||
نویسندگان | ||
Mohammadreza Jahangiri1؛ Alireza Nazemi* 2 | ||
1Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 3619995161-316, Tel-Fax No:+98-23-32300235, Shahrood, Iran. | ||
2Shahrood University of Technology | ||
چکیده | ||
In the proposed manuscript, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is gained using a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOP by RNN's, we establish a new scheme to solve the problem. By reducing the original program to an interval problem and then weighting problem, the Karush--Kuhn--Tucker (KKT) conditions are presented. Moreover, we apply the KKT conditions into a RNN as a efficient tool to solve the problem. Besides, the convergence properties and the stability analysis of the system model are provided. In the final step, several simulation examples are verified to support the obtained results. Reported results are compared with some other previous neural networks. | ||
کلیدواژهها | ||
Neural networks؛ Fuzzy nonlinear programming problem؛ Fuzzy parameters؛ Stability؛ Convergence | ||
مراجع | ||
[1] S. K. Agrawal, B. C. Fabien, Optimization of dynamic systems, Kluwer Academic Publishers, Netherlands, 1999. https://doi.org/10.1007/978-94-015-9149-2 [2] Z. Arjmandzadeh, M. Safi, A. Nazemi, A new neural network model for solving random interval linear programming problems, Neural Networks, 89 (2017), 11-18. https://doi.org/10.1016/j.neunet.2016.12.007 [3] M. Avriel, Nonlinear programming: Analysis and methods, Prentice-Hall, EnglewoodCliffs, NJ, 1976.
[4] M. S. Bazaraa, C. Shetty, H. D. Sherali, Nonlinear programming, theory and algorithms, John Wiley and Sons, NewYork, 1979. https://doi.org/10.1002/0471787779 [5] D. P. Bertsekas, J. N. Tsitsiklis, Parallel and distributed computation: Numerical methods, Prentice Hall. New Jersey: Englewood Cliffs, 1989. [6] S. Boyd, L. Vandenberghe, Convex optimization, Cambridge University Press, Cambridge, 2004. https://doi. org/10.1109/TAC.2006.884922 [7] J. J. Buckley, Possibilistic linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems, 26 (1998), 135-138. https://doi.org/10.1016/0165-0114(88)90013-9 [8] L. Campos, J. L. Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets and Systems, 32 (1989), 1-11. https://doi.org/10.1016/0165-0114(89)90084-5 [9] X. Cao, A. Francis, X. Pu, Z. Zhang, V. Katsikis, P. Stanimirovic, I. Brajevic, S. Li, A novel recurrent neural network based online portfolio analysis for high frequency trading, Expert Systems with Applications, 233 (2023), 120934. https://doi.org/10.1016/j.eswa.2023.120934 [10] X. Cao, C. Peng, Y. Zheng, S. Li, T. T. Ha, V. Shutyaev, V. Katsikis, P. Stanimirovic, Neural networks for portfolio analysis in high-frequency trading, IEEE Transactions on Neural Networks and Learning Systems, 2023. https://doi.org/10.1109/TNNLS.2023.3311169 [11] Y. H. Chen, S. C. Fang, Neurocomputing with time delay analysis for solving convex quadratic programming problems, IEEE Transactions on Neural Networks, 11 (2000), 230-240. https://doi.org/10.1109/72.822526 [12] J. S. Chen, C. H. Ko, S. Pan, A neural network based on the generalized Fischer-Burmeister function for nonlinear complementarity problems, Information Sciences, 180(5) (2010), 697-711. https://doi.org/10.1016/j.ins. 2009.11.014 [13] S. Effati, A. Ghomashi, A. Nazemi, Application of projection neural network in solving convex programming problems, Applied Mathematics and Computation, 188 (2007), 1103-1114. https://doi.org/10.1016/j.amc. 2006.10.088 [14] S. Effati, A. Mansoori, M. Eshaghnezhad, An efficient projection neural network for solving bilinear programming problems, Neurocomputing, 168 (2015), 1188-1197. https://doi.org/10.1016/j.neucom.2015.05.003 [15] M. Ehrgott, M. Wiecek, Multiobjective programming, In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multicriteria Decision Analysis: State of the Art Surveys., Springer Science + Business Media, New York, (2005), 667-722. https://doi.org/10.1007/b100605 [16] M. Eshaghnezhad, S. Effati, A. Mansoori, A neurodynamic model to solve nonlinear pseudo-monotone projection equationand its applications, IEEE Transactions on Cybernetics, 47(10) (2017), 3050-3062. https://doi.org/ 10.1109/TCYB.2016.2611529 [17] M. A. Fatma, A differential equation approach to fuzzy non-linear programming problems, Fuzzy Sets and Systems, 93 (1998), 57-61. https://doi.org/10.1016/S0165-0114(96)00217-5 [18] A. Feizi, A. Nazemi. A. Feizi, A. Nazemi, M. Rabiei, Solving the stochastic support vector regression with probabilistic constraints by a high-performance neural network model, Engineering with Computers, 38 (2021), 1-16. https://doi.org/10.1007/s00366-020-01214-5 [19] R. Fletcher, Practical methods of optimization, Wiley, NewYork, 1981. https://doi.org/10.1002/ 9781118723203 [20] M. Friedman, M. Ma, A. Kandel, Numerical solution of fuzzy differential and integral equations, Fuzzy Sets and Systems, 106 (1999), 35-48. https://doi.org/10.1016/S0165-0114(98)00355-8 [21] T. L. Friesz, D. H. Bernstein, N. J. Mehta, R. L. Tobin, S. Ganjlizadeh, Day-to-day dynamic network disequilibria and idealized traveler information systems, Operation Research, 42 (1994), 1120-1136. https://doi.org/10. 1287/opre.42.6.1120 [22] X. Gao, A novel neural network for nonlinear convex programming, IEEE Transactions on Neural Networks, 15 (2004), 613-621. https://doi.org/10.1109/TNN.2004.824425 [23] R. Ghanbari, K. Ghorbani-Moghadam, N. Mahdavi-Amiri, A variables neighborhood search algorithm for solving fuzzy quadratic programming problems using modified Kerre’s method, Soft Computing, 23 (2019), 12305-12315. https://doi.org/10.1007/s00500-019-03771-4 [24] R. Ghanbari, K. Ghorbani-Moghadam, N. Mahdavi-Amiri, A time variant multi-objective particle swarm optimization algorithm for solving fuzzy number linear programming problems using modified Kerre’s method, OPSEARCH, 58 (2021), 403-424. https://doi.org/10.1007/s12597-020-00482-5 [25] X. He, T. Huang, J. Yu, C. Li, C. Li, An inertial projection neural network for solving variational inequalities, IEEE Transactions on Cybernetics, 47 (2016), 809-814. https://doi.org/10.1109/TCYB.2016.2523541 [26] J. J. Hopfield, D. W. Tank, Neural computation of decisions in optimization problems, Biological Cybernetics, 52 (1985), 141-152. https://doi.org/10.1007/BF00339943 [27] C. Y. Hsu, B. R. Kao, V. L. Hob, K. R. Lai, Agent-based fuzzy constraint-directed negotiation mechanism for distributed job shop scheduling, Engineering Applications of Artificial Intelligence, 53 (2016), 140-154. https: //doi.org/10.1016/j.engappai.2016.04.005 [28] X. Hu, J. Wang, Solving pseudo-monotone variational inequalities and pseudo-convex optimization problems using the projection neural network, IEEE Transactions on Neural Networks, 17 (2006), 1487-1499. https://doi.org/ 10.1109/TNN.2006.879774 [29] D. Karbasi, A. Nazemi, M. Rabiei, A parametric recurrent neural network scheme for solving a class of fuzzy regression models with some real-world applications, Soft Computing, 24 (2020), 11159-11187. https://doi. org/10.1007/s00500-020-05008-1 [30] D. Karbasi, A. Nazemi, M. Rabiei, An optimization technique for solving a class of ridge fuzzy regression problems, Neural Processing Letters, 53 (2021), 3307-3338. https://doi.org/10.1007/s11063-021-10538-2 [31] D. Kinderlehrer, G. Stampacchia, An introduction to variational inequalities and their applications, Society for Industrial and Applied Mathematics, 2000. https://doi.org/10.1137/1.9780898719451 [32] S. Li, J. He, Y. Li, M. U. Rafique, Distributed recurrent neural networks for cooperative control of manipulators: A game-theoretic perspective, IEEE Transactions on Neural Networks and Learning Systems, 28(2) (2016), 415-426. https://doi.org/10.1109/TNNLS.2016.2516565 [33] S. Li, L. Jin, M. A. Mirza, Kinematic control of redundant robot arms using neural networks, John Wiley and Sons, 2019. http://dx.doi.org/10.1002/9781119557005 [34] S. Li, Y. Li, Z. Wang, A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application, Neural Networks, 39 (2013), 27-39. https://doi.org/10.1016/j.neunet. 2012.12.009 [35] Z. Li, H. Xiao, C. Yang, Y. Zhao, Model predictive control of nonholonomic chained systems using general projection neural networks optimization, IEEE Transactions on Systems, Man, and Cybernetics, 45 (2015), 1313-1321. https://doi.org/10.1109/TSMC.2015.2398833 [36] G. Li, Z. Yan, J. Wang, A one-layer recurrent neural network for constrained nonconvex optimization, Neural Networks, 61 (2015), 10-21. https://doi.org/10.1016/j.neunet.2014.09.009 [37] L. Z. Liao, H. Qi, L. Qi, Solving nonlinear complementarity problems with neural networks: A reformulation method approach, Journal of Computational and Applied Mathematics, 131(1-2) (2001), 343-359. https://doi. org/10.1016/S0377-0427(00)00262-4 [38] Q. Liu, J. Wang, L1-minimization algorithms for sparse signal reconstruction based on a projection neural network, IEEE Transactions on Neural Networks and Learning Systems, 27(3) (2016), 698-707. https://doi.org/10. 1109/TNNLS.2015.2481006 [39] J. Lu, S. C. Fang, Solving nonlinear optimization problems with fuzzy relation equation constraints, Fuzzy Sets and Systems, 119 (2001), 1-20. https://doi.org/10.1016/S0165-0114(98)00471-0 [40] T. Lu, S. T. Liu, Fuzzy nonlinear programming approach to the evaluation of manufacturing processes, Engineering Applications of Artificial Intelligence, 72 (2018), 183-189. https://doi.org/10.1016/j.engappai.2018.04.003 [41] K. Majeed, Z. Masood, R. Samar, M. A. Z. Raja, A genetic algorithm optimized Morlet wavelet artificial neural network to study the dynamics of nonlinear Troesch’s system, Applied Soft Computing, 56 (2017), 420-435. https://doi.org/10.1016/j.asoc.2017.03.028 [42] A. Mansoori, S. Effati, An efficient neurodynamic model to solve nonlinear programming problems with fuzzy parameters, Neurocomput, 334 (2019), 125-133. https://doi.org/10.1016/j.neucom.2019.01.012 [43] A. Mansoori, S. Effati, M. Eshaghnezhad, An efficient recurrent neural network model for solving fuzzy non-linear programming problems, Applied Intelligence, 46 (2017), 308-327. https://doi.org/10.1007/ s10489-016-0837-4 [44] A. Mansoori, S. Effati, M. Eshaghnezhad, A neural network to solve quadratic programming problems with fuzzy parameters, Fuzzy Optimization and Decision Making, 17(1) (2018), 75-101. https://doi.org/10.1007/ s10700-016-9261-9 [45] A. Mansoori, M. Erfanian, A dynamic model to solve the absolute value equations, Journal of Computational and Applied Mathematics, 333 (2018), 28-35. https://doi.org/10.1016/j.cam.2017.09.032 [46] A. Mansoori, M. Eshaghnezhad, S. Effati, An efficient neural network model for solving the absolute value equations, IEEE Transactions on Circuits and Systems II: Express Briefs, 65(3) (2018), 391-395. https: //doi.org/10.1109/TCSII.2017.2750065 [47] X. Miao, J. S. Chen, C. H. Ko, A smoothed NR neural network for solving nonlinear convex programs with secondorder cone constraints, Information Sciences, 268(1) (2014), 255-270. https://doi.org/10.1016/j.ins.2013. 10.017 [48] K. M. Miettinen, Non-linear multi objective optimization, Kluwer Academic Publishers, 1999. https://doi.org/ 10.1007/978-1-4615-5563-6 [49] R. K. Miller, A. N. Michel, Ordinary differential equations, Academic Press, NewYork, 1982. http://dx.doi. org/10.1109/MCS.2008.930834 [50] S. M. Mousavi, S. Mirdamadi, A. Siadat, J. Dantan, R. Tavakkoli-Moghaddam, An intuitionistic fuzzy grey model for selection problems with an application to the inspection planningin manufacturing firms, Engineering Applications of Artificial Intelligence, 39 (2015), 157-167. https://doi.org/10.1016/j.engappai.2014.12.004 [51] A. R. Nazemi, A dynamic system model for solving convex nonlinear optimization problems, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 1696-1705. https://doi.org/10.1016/j.cnsns.2011. 08.035 [52] A. R. Nazemi, S. Effati, Anapplication of a merit function for solving convex programming problems, Computers and Industrial Engineering, 66 (2013), 212-221. https://doi.org/10.1016/j.cie.2013.07.017 [53] A. R. Nazemi, M. Mortezaee, A new gradient-based neural dynamic framework for solving constrained min-max optimization problems with an application in portfolio selection models, Applied Intelligence, 49 (2019), 396-419. https://doi.org/10.1007/s10489-018-1268-1 [54] A. R. Nazemi, A. Sabeghi, A new neural network framework for solving convex secondorder cone constrained variational inequality problems with an application in multi-finger robot hands, Journal of Experimental and Theoretical Artificial Intelligence, 32(2) (2019), 181-203. https://doi.org/10.1080/0952813X.2019.1647559 [55] A. Nikseresht, A. R. Nazemi, A novel neural network for solving semidefinite programming problems with some applications, Journal of Computational and Applied Mathematics, 350 (2019), 309-323. https://doi.org/10. 1016/j.cam.2018.10.025 [56] A. Nikseresht, A. R. Nazemi, A novel neural network model for solving a class of nonlinear semidefinite programming problems, Journal of Computational and Applied Mathematics, 338 (2018), 69-79. https://doi.org/10. 1016/j.cam.2018.01.023 [57] A. Nikseresht, A. R. Nazemi, A smoothing gradient-based neural network strategy for solving semidefinite programming problems, NET-Network: Computation in Neural Systems, 33(3-4) (2022), 187-213. https://doi.org/10. 1080/0954898X.2022.2104463 [58] J. Nocedal, S. Wright, Numerical optimization, Second ed., Springer-Verlag, Berlin, NewYork, 2006. https: //doi.org/10.1007/0-387-22742-3_18 [59] Z. Peng, J. Wang, Output-feedback path-following control of autonomous under water vehicles based on an extended state observer and projection neural networks, IEEE Transactions on Systems, Man, and Cybernetics, 48(4) (2018), 535-544. https://doi.org/10.1109/TSMC.2017.2697447 [60] S. Qin, X. Le, J. Wang, A neurodynamic optimization approach to bilevel quadratic programming, IEEE Transactions on Neural Networks and Learning Systems, 28 (2017), 2580-2591. https://doi.org/10.1109/TNNLS. 2016.2595489 [61] M. A. Z. Raja, M. A. Manzar, F. H. Shah, Intelligent computing for Mathieu’s systems for parameter excitation, vertically driven pendulum and dusty plasma models, Applied Soft Computing, 62 (2018), 359-372. https://doi. org/10.1016/j.asoc.2017.10.049 [62] D. Rani, A. Ebrahimnejad, G. Gupta, Generalized techniques for solving intuitionistic fuzzy multi-objective nonlinear optimization problems, Expert Systems with Applications, 202 (2022), 117264. https://doi.org/10. 1016/j.eswa.2022.117264 [63] M. Ranjbar, S. Effati, S. M. Miri, An artificial neural network for solving quadratic zero-one programming problems, Neurocomputing, 235 (2017), 192-198. https://doi.org/10.1016/j.neucom.2016.12.064
[64] S. Rao, Engineering optimization: Theory and practice, Fourth ed., John Wiley and Sons, Hoboken, NewJersey, 2009. https://doi.org/10.1002/9780470549124 [65] J. D. L. C. Sama, K. Some, Solving fuzzy nonlinear optimization problems using null set concept, International Journal of Fuzzy System, 26 (2023), 674-685. https://doi.org/10.1007/s40815-023-01626-7 [66] Y. Shi, W. Sheng, S. Li, B. Li, X. Sun, Neurodynamics for equality-constrained time-variant nonlinear optimization using discretization, IEEE Transactions on Industrial Informatics, 20 (2024), 2354-2364. https://doi.org/10. 1109/TII.2023.3290187 [67] Y. Shi, Q. Shi, X. Cao, B. Li, X. Sun, An advanced discrete-time RNN for handling discrete time-varying matrix inversion: Form model design to disturbance-suppression analysis, CAAI Transactions on Intelligence Technology, (2023), 607-621. https://doi.org/10.1049/cit2.12229 [68] Y. Shi, J. Wang, S. Li, B. Li, X. Sun, Tracking control of cable-driven planar robot based on discrete-time recurrent neural network with immediate discretization method, IEEE Transactions on Industrial Informatics, 19 (2023), 7414-7423. https://doi.org/10.1109/TII.2022.3210255 [69] Y. Shi, W. Zhao, S. Li, B. Li, X. Sun, Novel discrete-time recurrent neural network for robot manipulator: A direct discretization technical route, IEEE Transactions on Neural Networks and Learning Systems, 34 (2023), 2781-2790. https://doi.org/10.1109/TNNLS.2021.3108050 [70] G. Singh, A. Singh, Extension of particle swarm optimization algorithm for solving transportation problem in fuzzy environment, Applied Soft Computing, 110 (2021), 107619. https://https://doi.org/10.1016/j.asoc. 2021.107619 [71] L. Stefanini, L. Sorini, M. L. Guerra, Parametric representation of fuzzy numbers and application to fuzzy calculus, Fuzzy Sets and Systems, 157 (2006), 2423-2455. https://doi.org/10.1016/j.fss.2006.02.002 [72] J. Sun, J. S. Chen, C. H. Ko, Neural networks for solving second-order cone constrained variational inequality problem, Computational Optimization and Applications, 51 (2012), 623-648. https://doi.org/10.1007/ s10589-010-9359-x [73] J. Sun, L. Zhang, A globally convergent method based on Fischer-Burmeister operators for solving second-order coneconstrained variational inequality problems, Computational Optimization and Applications, 58 (2009), 1936- 1946. https://doi.org/10.1016/j.camwa.2009.07.084 [74] Y. R. Syau, On convex and concave fuzzy mappings, Fuzzy Sets and Systems, 103 (1999), 163-168. https: //doi.org/10.1016/S0165-0114(97)00210-8 [75] J. Tang, D. Wang, Modelling and optimization for a type of fuzzy nonlinear programming problems in manufacturing systems, in: Proceedings of the 35th IEEE Conference on Decision and Control, (1996), 4401-4405. https://doi.org/10.1109/CDC.1996.577485. [76] D. W. Tank, J. J. Hopfield, Simple neural optimization networks: An a/d converter, signal decisioncircuit, and a linear programming circuit, IEEE Transactions on Circuits and Systems, 33 (1986), 533-541. https://doi.org/ 10.1109/TCS.1986.1085953 [77] P. Vasant, Hybrid LS-SA-PS methods for solving fuzzy non-linear programming problems, Mathematical and Computer Modelling, 57 (2013), 180-188. https://doi.org/10.1016/j.mcm.2011.08.002 [78] G. Wang, C. Wu, Directional derivatives and sub-differential of convex fuzzy mappings and application in convex fuzzy programming, Fuzzy Sets and Systems, 138 (2003), 559-591. https://doi.org/10.1016/S0165-0114(02) 00440-2 [79] H. C. Wu, Evaluate fuzzy optimization problems based on biobjective programming problems, Computers and Mathematics with Applications, 47 (2004), 893-902. https://doi.org/10.1016/S0898-1221(04)90073-9 [80] C. W. Wu, M. Y. Liao, Fuzzy nonlinear programming approach for evaluating and ranking process yields with imprecise data, Fuzzy Sets and Systems, 246 (2014), 142-155. https://doi.org/10.1016/j.fss.2013.10.014 [81] Y. Xia, An extended neural network for constrained optimization, Neural Computation, 16 (2004), 863-883. https://doi.org/10.1162/089976604322860730 [82] Y. Xia, J. Wang, A recurrent neural network for solving linear projection equations, Neural Networks, 13 (2000), 337-350. https://doi.org/10.1016/S0893-6080(00)00019-8 [83] Y. Xia, J. Wang, A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints, IEEE Transactions on Circuits and Systems I: Regular Papers, 51(7) (2004), 1385-1394. https: //doi.org/10.1109/TCSI.2004.830694 [84] Y. Xia, J. Wang, A bi-projection neural network for solving constrained quadratic optimization problems, IEEE Transactions on Neural Networks and Learning Systems, 27(2) (2015), 214-224. https://doi.org/10.1109/ TNNLS.2015.2500618 [85] Y. Yang, X. Xu, The projection neural network for solving convex nonlinear programming, In: Huang D-S, Heutte L, Loog M (eds) ICIC 2007, LNAI, vol 4682. Springer-Verlag, Heidelberg, (2007), 174-181. https://doi.org/ 10.1007/978-3-540-74205-0_20 [86] J. Zhang, X. Chen, L. Li, X. Ma, Optimality conditions for fuzzy optimization problems under granular convexity concept, Fuzzy Sets and Systems, 447 (2022), 54-75. https://doi.org/10.1016/j.fss.2022.01.004 [87] H. Zhu, G. H. Huang, P. Guo, SIFNP: Simulation–based interval–fuzzy nonlinear programming for seasonal planning of stream water quality management, Water, Air, and Soil Pollution, 223 (2012), 2051-2072. https: //doi.org/10.1007/s11270-011-1004-5 [88] H. Zhu, G. H. Huang, P. Guo, X. S. Qin, A fuzzy robust nonlinear programming model for stream water quality management, Water Resources Management, 23 (2009), 2913-2940. https://doi.org/10.1007/ s11269-009-9416-3 | ||
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