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Neural Computing and Applications
Erschienen in: Neural Computing and Applications 4/2018

17.08.2016 | Original Article

Nature-inspired computational intelligence integration with Nelder–Mead method to solve nonlinear benchmark models

verfasst von: Muhammad Asif Zahoor Raja, Aneela Zameer, Adiqa Kausar Kiani, Azam Shehzad, Muhammad Abdul Rehman Khan

Erschienen in: Neural Computing and Applications | Ausgabe 4/2018

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Abstract

In the present study, nature-inspired computing technique has been designed for the solution of nonlinear systems by exploiting the strength of particle swarm optimization (PSO) hybrid with Nelder–Mead method (NMM). Fitness function based on least square approximation theory is developed for the systems, while optimization of the design variables is performed with PSO, an efficient global search method, refined with NMM for rapid local convergence. Sixteen variants of the proposed hybrid scheme PSO-NMM have been evaluated on five benchmark nonlinear systems, namely interval arithmetic benchmark model, kinematic application model, neurophysiology problem, combustion model and chemical equilibrium system. Reliability and effectiveness of the proposed solver have been validated after comparison with the results of statistical analysis based on massive data generated for sufficiently large number of independent executions.
Vorheriger Artikel A hybrid advertising media selection model using AHP and fuzzy-based GA decision making

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Literatur
1.
Nazemi AR (2013) Solving general convex nonlinear optimization problems by an efficient neurodynamic model. Eng Appl Artif Intell 26:685–696CrossRef
2.
Nazemi AR (2014) A neural network model for solving convex quadratic programming problems with some applications. Eng Appl Artif Intell 32:54–62CrossRef
3.
Nazemi AR, Nazemi M (2014) A gradient-based neural network method for solving strictly convex quadratic programming problems. Cogn Comput 6:484–495CrossRef
4.
Khan JA, Raja MAZ, Syam MI, Tanoli SAK, Awan SE (2015) Design and application of nature inspired computing approach for non-linear stiff oscillatory problems. Neural Comput Appl 26(7):1763–1780. doi:10.​1007/​s00521-015-1841-z CrossRef
5.
6.
Raja MAZ, Ahmad SUI, Samar R (2014) Solution of the 2-dimensional Bratu problem using neural network, swarm intelligence and sequential quadratic programming. Neural Comput Appl 25:1723–1739. doi:10.​1007/​s00521-014-1664-3 CrossRef
7.
Nazemi AR, Omidi F (2012) A capable neural network model for solving the maximum flow problem. J Comput Appl Math 236:3498–3513MathSciNetCrossRefMATH
8.
9.
Mall S, Chakraverty S (2014) Chebyshev neural network based model for solving Lane–Emden type equations. Appl Math Comput 247:100–114MathSciNetMATH
10.
11.
Raja MAZ, Samar R, Haroon T, Shah SM (2015) Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery–Hamel problem. Appl Math Mech 36(12):1611–1638MathSciNetCrossRef
12.
Mall Susmita, Chakraverty S (2015) Numerical solution of nonlinear singular initial value problems of Emden–Fowler type using Chebyshev Neural Network method. Neurocomputing 149:975–982CrossRef
13.
Raja MAZ, Khan JA, Behloul D, Haroon T, Siddiqui AM, Samar R (2015) Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation. Appl Soft Comput 26:244–256. doi:10.​1016/​j.​asoc.​2014.​10.​009 CrossRef
14.
Raja MAZ, Khan JA, Shah SM, Bhahoal D, Samar R (2015) Comparison of three unsupervised neural network models for first Painlevé Transcendent. Neural Comput Appl 26(5):1055–1071. doi:10.​1007/​s00521-014-1774-y CrossRef
15.
Mall S, Chakraverty S (2015) Multi layer versus functional link single layer neural network for solving nonlinear singular initial value problems. In: Proceedings of the third international symposium on women in computing and informatics (pp 678–683). ACM
16.
17.
18.
Raja MAZ, Farooq U, Chaudhary NI, Wazwaz AM (2016) Stochastic numerical solver for nanofluidic problems containing multi-walled carbon nanotubes. Appl Soft Comput 38:561–586CrossRef
19.
Raja MAZ, Shah FH, Khan AA, Khan NA (2016) Design of bio-inspired computational intelligence technique for solving steady thin film flow of Johnson-Segalman fluid on vertical cylinder for drainage problems. J Taiwan Inst Chem Eng 60:59–75CrossRef
20.
Li Min (2014) A Polak–Ribière–Polyak method for solving large-scale nonlinear systems of equations and its global convergence. Appl Math Comput 248:314–322MathSciNetMATH
21.
Amat S, Hernández-Verón MA, Rubio MJ (2014) Improving the applicability of the secant method to solve nonlinear systems of equations. Appl Math Comput 247:741–752MathSciNetMATH
22.
Sharma JR, Arora H, Petković MS (2014) An efficient derivative free family of fourth order methods for solving systems of nonlinear equations. Appl Math Comput 235:383–393MathSciNetMATH
23.
Ortega JM, Rheinboldt WC (1970) Iterative solution of nonlinear equations in several variables, vol 30. Siam, PhiladelphiaMATH
24.
Kelley CT (2003) Solving nonlinear equations with Newton’s method, vol 1. Siam, PhiladelphiaCrossRefMATH
25.
26.
27.
Darvishi MT, Barati A (2007) A fourth order method from quadrature formulae to solve the system of nonlinear equations. Appl Math Comput 188:257–261MathSciNetMATH
28.
Knoll DA, Keyes DE (2004) Jacobian free Newton–Krylov methods: a survey of approaches and applications. J Comput Phys 193:357–397MathSciNetCrossRefMATH
29.
30.
Jafari H, Gejji VD (2006) Revised Adomian decomposition method for solving a system of nonlinear equation. J Appl Math Comput 175:1–7MathSciNetCrossRefMATH
31.
Abbasbandy S (2005) Extended Newton method for a system on non linear equations by modified domain decomposition method. J Appl Math Comput 170:648–656CrossRefMATH
32.
Vahidi AR, Javadi S, Khorasani SM (2012) Solving system of nonlinear equations by restarted Adomain’s method. J Appl Math Comput 6:509–516MATH
33.
Sharma JR, Guha RK, Gupta P (2013) Improved King’s methods with optimal order of convergence based on rational approximations. Appl Math Lett 26(4):473–480MathSciNetCrossRefMATH
34.
Sharma JR, Gupta P (2014) An efficient fifth order method for solving systems of nonlinear equations. Comput Math Appl 67(3):591–601MathSciNetCrossRefMATH
35.
36.
Sharma JR, Arora H (2014) An efficient family of weighted-Newton methods with optimal eighth order convergence. Appl Math Lett 29:1–6MathSciNetCrossRefMATH
37.
38.
Abu O (2015) Arqub, adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations. Neural Comput Appl. doi:10.​1007/​s00521-015-2110-x
39.
Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415MathSciNetCrossRefMATH
40.
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Perth, Australia, vol 4. IEEE Service Center, Piscataway, pp 1942–1948
41.
Trelea IC (2003) The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf Process Lett 85(6):317–325MathSciNetCrossRefMATH
42.
Ping Tian D (2013) A review of convergence analysis of particle swarm optimization. Int J Grid Distrib Comput 6(6):117–128CrossRef
43.
44.
García-Gonzalo E, Fernández-Martínez JL (2012) A brief historical review of particle swarm optimization (PSO). J Bioinform Intell Control 1(1):3–16CrossRef
45.
46.
Jiang S, Wang Y, Ji Z (2015) A new design method for adaptive IIR system identification using hybrid particle swarm optimization and gravitational search algorithm. Nonlinear Dyn 79(4):2553–2576MathSciNetCrossRef
47.
Lu Y et al (2015) Improved particle swarm optimization algorithm and its application in text feature selection. Appl Soft Comput 35:629–636CrossRef
48.
Saeid S, Sadeghi MT, Marvas MA (2014) High reliability estimation of product quality using support vector regression and hybrid meta-heuristic algorithms. J Taiwan Inst Chem Eng 45:2225–2232CrossRef
49.
Prawin J, Rao ARM, Lakshmi K (2016) Nonlinear parametric identification strategy combining reverse path and hybrid dynamic quantum particle swarm optimization. Nonlinear Dyn 84(2):797–815MathSciNetCrossRef
50.
Liu X (2016) Optimization design on fractional order PID controller based on adaptive particle swarm optimization algorithm. Nonlinear Dyn 84(1):379–386MathSciNetCrossRef
51.
52.
Dennis JE, Woods DJ (1987) Optimization on microcomputers: the Nelder-Mead simplex algorithm. In: Wouk A (ed) New computing environments: microcomputers in large-scale computing. SIAM, Philadelphia, pp 116–122
53.
Grosan Crina, Abraham Ajith (2008) A new approach for solving nonlinear equations systems. IEEE Trans Syst Man Cybern Part A Syst Hum 38(3):698–714CrossRef
54.
Grosan Crina, Abraham Ajith (2008) Multiple solutions for a system of nonlinear equations. Int J Innov Comput Inf Control 4(9):2161–2170
55.
Van Hentenryck P, McAllester D, Kapur D (1997) Solving polynomial systems using a branch and prune approach. SIAM J Numer Anal 34(2):797–827MathSciNetCrossRefMATH
56.
57.
Meintjes K, Morgan AP (1990) Chemical equilibrium systems as numerical test problems. ACM Trans Math Softw 16(2):143–151CrossRefMATH
58.
Verschelde J, Verlinden P, Cools R (1994) Homotopies exploiting Newton polytopes for solving sparse polynomial systems. SIAM J Numer Anal 31(3):915–930MathSciNetCrossRefMATH
59.
Morgan AP (1987) Solving polynomial system using continuation for scientific and engineering problems. Prentice-Hall, Englewood CliffsMATH
60.
Pires ES, Machado JT, de Moura Oliveira PB, Cunha JB, Mendes L (2010) Particle swarm optimization with fractional-order velocity. Nonlinear Dyn 61(1–2):295–301CrossRefMATH
61.
Couceiro MS, Rocha RP, Ferreira NF, Machado JT (2012) Introducing the fractional-order Darwinian PSO. Signal Image Video Process 6(3):343–350CrossRef
62.
Couceiro MS, Martins FM, Rocha RP, Ferreira NM, Sivasundaram S (2012) Introducing the fractional order robotic Darwinian PSO. In: AIP conference proceedings, American institute of physics, vol 1493, no 1, p 242
63.
Pires EJS, Machado JAT, de Moura Oliveira PB (2013) Entropy diversity in multi-objective particle swarm optimization. Entropy 15(12):5475–5491CrossRefMATH
64.
Couceiro M, Ghamisi P (2016) Fractional-order Darwinian PSO. In: Merkle D (ed) Fractional order Darwinian particle swarm optimization. Springer, Berlin, pp 11–20CrossRef
Metadaten
Titel
Nature-inspired computational intelligence integration with Nelder–Mead method to solve nonlinear benchmark models
verfasst von
Muhammad Asif Zahoor Raja
Aneela Zameer
Adiqa Kausar Kiani
Azam Shehzad
Muhammad Abdul Rehman Khan
Publikationsdatum
17.08.2016
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 4/2018
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-016-2523-1

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