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Volumn 38, Issue 3, 2008, Pages 698-714

A new approach for solving nonlinear equations systems

Author keywords

Computational intelligence; Evolutionary multiobjective optimization; Metaheuristics; Nonlinear equation systems

Indexed keywords

EVOLUTIONARY ALGORITHMS; HEURISTIC METHODS; NONLINEAR EQUATIONS; OPTIMIZATION; PROBLEM SOLVING;

EID: 43249120401     PISSN: 10834427     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCA.2008.918599     Document Type: Article
Times cited : (225)

References (50)
  • 1
    • 33749867996 scopus 로고    scopus 로고
    • A distributed cooperative coevolutionary algorithm for multiobjective optimization
    • K. C. Tan Y. J. Yang C. K. Goh A distributed cooperative coevolutionary algorithm for multiobjective optimization IEEE Trans. Evol. Comput. 10 5 527 549 Oct. 2006
    • (2006) IEEE Trans. Evol. Comput. , vol.10 , Issue.5 , pp. 527-549
    • Tan, K.C.1    Yang, Y.J.2    Goh, C.K.3
  • 2
    • 0028449799 scopus 로고
    • Homotopies exploiting Newton polytopes for solving sparse polynomial systems
    • J. Verschelde P. Verlinden R. Cools Homotopies exploiting Newton polytopes for solving sparse polynomial systems SIAM J. Numer. Anal. 31 3 915 930 Jun. 1994
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.3 , pp. 915-930
    • Verschelde, J.1    Verlinden, P.2    Cools, R.3
  • 3
    • 33746251985 scopus 로고    scopus 로고
    • Evolutionary Multiobjective Optimization: Theoretical Advances and Applications
    • Springer-Verlag New York
    • Evolutionary Multiobjective Optimization: Theoretical Advances and Applications 2005 Springer-Verlag New York
    • (2005)
  • 4
    • 33744773216 scopus 로고    scopus 로고
    • Multiobjective evolutionary algorithms for electric power dispatch problem
    • M. A. Abido Multiobjective evolutionary algorithms for electric power dispatch problem IEEE Trans. Evol. Comput. 10 3 315 329 Jun. 2006
    • (2006) IEEE Trans. Evol. Comput. , vol.10 , Issue.3 , pp. 315-329
    • Abido, M.A.1
  • 5
    • 34249862706 scopus 로고    scopus 로고
    • Multi-objective optimization using modified differential evolution (MDE)
    • R. Angira B. V. Babu Multi-objective optimization using modified differential evolution (MDE) Int. J. Math. Sci. 5 2 371 387 2006
    • (2006) Int. J. Math. Sci. , vol.5 , Issue.2 , pp. 371-387
    • Angira, R.1    Babu, B.V.2
  • 6
    • 20344404492 scopus 로고    scopus 로고
    • Multiobjective differential evolution (MODE) for optimization of adiabatic styrene reactor
    • B. V. Babu P. G. Chakole J. H. Syed Mubeen Multiobjective differential evolution (MODE) for optimization of adiabatic styrene reactor Chem. Eng. Sci. 60 17 4822 4837 Sep. 2005
    • (2005) Chem. Eng. Sci. , vol.60 , Issue.17 , pp. 4822-4837
    • Babu, B.V.1    Chakole, P.G.2    Syed Mubeen, J.H.3
  • 7
    • 33745465892 scopus 로고    scopus 로고
    • Tensor–Krylov methods for solving large-scale systems of nonlinear equations
    • B. W. Bader Tensor–Krylov methods for solving large-scale systems of nonlinear equations SIAM J. Numer. Anal. 43 3 1321 1347 2005
    • (2005) SIAM J. Numer. Anal. , vol.43 , Issue.3 , pp. 1321-1347
    • Bader, B.W.1
  • 8
    • 33744770997 scopus 로고    scopus 로고
    • Evolutionary multiobjective industrial design: The case of a racing car tire-suspension system
    • A. Benedetti M. Farina M. Gobbi Evolutionary multiobjective industrial design: The case of a racing car tire-suspension system IEEE Trans. Evol. Comput. 10 3 230 244 Jun. 2006
    • (2006) IEEE Trans. Evol. Comput. , vol.10 , Issue.3 , pp. 230-244
    • Benedetti, A.1    Farina, M.2    Gobbi, M.3
  • 9
    • 0003866523 scopus 로고    scopus 로고
    • Projection Methods for Systems of Equations
    • Elsevier The Netherlands, Amsterdam
    • C. Brezinski Projection Methods for Systems of Equations 1997 Elsevier The Netherlands, Amsterdam
    • (1997)
    • Brezinski, C.1
  • 10
    • 84968510937 scopus 로고
    • A class of methods for solving nonlinear simultaneous equations
    • C. G. Broyden A class of methods for solving nonlinear simultaneous equations Math. Comput. 19 92 577 593 Oct. 1965
    • (1965) Math. Comput. , vol.19 , Issue.92 , pp. 577-593
    • Broyden, C.G.1
  • 11
    • 33847325781 scopus 로고    scopus 로고
    • A diversified multiobjective GA for optimizing reservoir rule curves
    • L. Chen J. McPhee W. G. Yeh A diversified multiobjective GA for optimizing reservoir rule curves Adv. Water Res. 30 5 1082 1093 May 2007
    • (2007) Adv. Water Res. , vol.30 , Issue.5 , pp. 1082-1093
    • Chen, L.1    McPhee, J.2    Yeh, W.G.3
  • 12
    • 0003951723 scopus 로고    scopus 로고
    • Trust-Region Methods
    • SIAM PA, Philadelphia
    • A. R. Conn N. I. M. Gould P. L. Toint Trust-Region Methods 2000 SIAM PA, Philadelphia
    • (2000)
    • Conn, A.R.1    Gould, N.I.M.2    Toint, P.L.3
  • 13
    • 0003866267 scopus 로고    scopus 로고
    • Multi-Objective Optimization Using Evolutionary Algorithms
    • Wiley New York
    • K. Deb Multi-Objective Optimization Using Evolutionary Algorithms 2001 Wiley New York
    • (2001)
    • Deb, K.1
  • 14
    • 4644246639 scopus 로고    scopus 로고
    • Towards a better understanding of the epoxy-polymerization process using multi-objective evolutionary computation
    • K. Deb K. Mitra R. Dewri S. Majumdar Towards a better understanding of the epoxy-polymerization process using multi-objective evolutionary computation Chem. Eng. Sci. 59 20 4261 4277 Oct. 2004
    • (2004) Chem. Eng. Sci. , vol.59 , Issue.20 , pp. 4261-4277
    • Deb, K.1    Mitra, K.2    Dewri, R.3    Majumdar, S.4
  • 15
    • 43249110906 scopus 로고
    • On Newton's method and nonlinear simultaneous replacements
    • J. E. Denis On Newton's method and nonlinear simultaneous replacements SIAM J. Numer. Anal. 4 103 108 1967
    • (1967) SIAM J. Numer. Anal. , vol.4 , pp. 103-108
    • Denis, J.E.1
  • 16
    • 0012706890 scopus 로고
    • On Newton like methods
    • J. E. Denis On Newton like methods Numer. Math. 11 4 324 330 May 1968
    • (1968) Numer. Math. , vol.11 , Issue.4 , pp. 324-330
    • Denis, J.E.1
  • 17
    • 84968469596 scopus 로고
    • On the convergence of Broyden's method for nonlinear systems of equations
    • J. E. Denis On the convergence of Broyden's method for nonlinear systems of equations Math. Comput. 25 115 559 567 Jul. 1971
    • (1971) Math. Comput. , vol.25 , Issue.115 , pp. 559-567
    • Denis, J.E.1
  • 18
    • 0027684527 scopus 로고
    • Least change secant methods, sizing, and shifting
    • J. E. Denis H. Wolkowicz Least change secant methods, sizing, and shifting SIAM J. Numer. Anal. 30 1291 1314 1993
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1291-1314
    • Denis, J.E.1    Wolkowicz, H.2
  • 19
    • 0033413991 scopus 로고    scopus 로고
    • A trust-region algorithm for least-squares solutions of nonlinear systems of equalities and inequalities
    • J. E. Denis M. El Alem K. Williamson A trust-region algorithm for least-squares solutions of nonlinear systems of equalities and inequalities SIAM J. Opt. 9 2 291 315 1999
    • (1999) SIAM J. Opt. , vol.9 , Issue.2 , pp. 291-315
    • Denis, J.E.1    El Alem, M.2    Williamson, K.3
  • 20
    • 26044448330 scopus 로고    scopus 로고
    • A new method for solving a system of the nonlinear equations
    • S. Effati A. R. Nazemi A new method for solving a system of the nonlinear equations Appl. Math. Comput. 168 2 877 894 Sep. 2005
    • (2005) Appl. Math. Comput. , vol.168 , Issue.2 , pp. 877-894
    • Effati, S.1    Nazemi, A.R.2
  • 21
    • 0002565825 scopus 로고
    • Biases in the crossover landscape
    • L. J. Eshelman R. A. Caruna J. D. Schaffer Biases in the crossover landscape Proc. Int. Conf. Genetic Algorithms 10 19 Proc. Int. Conf. Genetic Algorithms 1989
    • (1989) , pp. 10-19
    • Eshelman, L.J.1    Caruna, R.A.2    Schaffer, J.D.3
  • 22
    • 0003722376 scopus 로고
    • Genetic Algorithms in Search, Optimization and Machine Learning
    • Addison-Wesley MA, Reading
    • D. E. Goldberg Genetic Algorithms in Search, Optimization and Machine Learning 1989 Addison-Wesley MA, Reading
    • (1989)
    • Goldberg, D.E.1
  • 23
    • 30244518538 scopus 로고
    • The implicit function theorem for solving systems of nonlinear equations in R2
    • T. N. Grapsa M. N. Vrahatis The implicit function theorem for solving systems of nonlinear equations in R2 Int. J. Comput. Math. 28 14 171 181 1989
    • (1989) Int. J. Comput. Math. , vol.28 , Issue.14 , pp. 171-181
    • Grapsa, T.N.1    Vrahatis, M.N.2
  • 24
    • 30244504687 scopus 로고
    • A dimension-reducing method for solving systems of nonlinear equations in $R^{n}$
    • T. N. Grapsa M. N. Vrahatis A dimension-reducing method for solving systems of nonlinear equations in $R^{n}$ Int. J. Comput. Math. 32 3/4 205 216 1990
    • (1990) Int. J. Comput. Math. , vol.32 , Issue.3/4 , pp. 205-216
    • Grapsa, T.N.1    Vrahatis, M.N.2
  • 25
    • 30244552391 scopus 로고
    • Solving systems of nonlinear equations in $R^{n}$ using a rotating hyperplane in $R^{n + 1}$
    • T. N. Grapsa M. N. Vrahatis T. C. Bountis Solving systems of nonlinear equations in $R^{n}$ using a rotating hyperplane in $R^{n + 1}$ Int. J. Comput. Math. 35 14 133 151 1990
    • (1990) Int. J. Comput. Math. , vol.35 , Issue.14 , pp. 133-151
    • Grapsa, T.N.1    Vrahatis, M.N.2    Bountis, T.C.3
  • 26
    • 0029709294 scopus 로고    scopus 로고
    • A dimension-reducing method for unconstrained optimization
    • T. N. Grapsa M. N. Vrahatis A dimension-reducing method for unconstrained optimization J. Comput. Appl. Math. 66 1/2 239 253 Jan. 1996
    • (1996) J. Comput. Appl. Math. , vol.66 , Issue.1/2 , pp. 239-253
    • Grapsa, T.N.1    Vrahatis, M.N.2
  • 27
    • 85177110440 scopus 로고    scopus 로고
    • T. N. Grapsa M. N. Vrahatis Dimension reducing methods for systems of nonlinear equations and unconstrained optimization: A review Recent Advances in Mechanics and Related Fields 215 225 2003
    • (2003) , pp. 215-225
    • Grapsa, T.N.1    Vrahatis, M.N.2
  • 28
    • 0000524439 scopus 로고    scopus 로고
    • Solving polynomial systems using a branch and prune approach
    • P. Van Hentenryck D. McAllester D. Kapur Solving polynomial systems using a branch and prune approach SIAM J. Numer. Anal. 34 2 797 827 Apr. 1997
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.2 , pp. 797-827
    • Van Hentenryck, P.1    McAllester, D.2    Kapur, D.3
  • 30
    • 0000300972 scopus 로고
    • Safe starting regions by fixed points and tightening
    • H. Hong V. Stahl Safe starting regions by fixed points and tightening Computing 53 3/4 323 335 Sep. 1994
    • (1994) Computing , vol.53 , Issue.3/4 , pp. 323-335
    • Hong, H.1    Stahl, V.2
  • 31
    • 0038411679 scopus 로고
    • Continuous Optimization: The State of the Art
    • Algorithms for solving nonlinear systems of equations Kluwer MA, Norwell
    • J. M. Martinez Continuous Optimization: The State of the Art 81 108 1994 Kluwer MA, Norwell Algorithms for solving nonlinear systems of equations
    • (1994) , pp. 81-108
    • Martinez, J.M.1
  • 32
    • 33846027145 scopus 로고    scopus 로고
    • A multiobjective evolutionary approach for linearly constrained project selection under uncertainty
    • A. L. Medaglia S. B. Graves J. L. Ringuest A multiobjective evolutionary approach for linearly constrained project selection under uncertainty Eur. J. Oper. Res. 179 3 869 894 Jun. 2007
    • (2007) Eur. J. Oper. Res. , vol.179 , Issue.3 , pp. 869-894
    • Medaglia, A.L.1    Graves, S.B.2    Ringuest, J.L.3
  • 33
    • 0025448634 scopus 로고
    • Chemical equilibrium systems as numerical test problems
    • K. Meintjes A. P. Morgan Chemical equilibrium systems as numerical test problems ACM Trans. Math. Softw. 16 2 143 151 Jun. 1990
    • (1990) ACM Trans. Math. Softw. , vol.16 , Issue.2 , pp. 143-151
    • Meintjes, K.1    Morgan, A.P.2
  • 34
    • 33750731956 scopus 로고    scopus 로고
    • Searching for multiobjective preventive maintenance schedules: Combining preferences with evolutionary algorithms
    • G. Quan G. W. Greenwood D. Liu S. Hu Searching for multiobjective preventive maintenance schedules: Combining preferences with evolutionary algorithms Eur. J. Oper. Res. 177 3 1969 1984 Mar. 2007
    • (2007) Eur. J. Oper. Res. , vol.177 , Issue.3 , pp. 1969-1984
    • Quan, G.1    Greenwood, G.W.2    Liu, D.3    Hu, S.4
  • 35
    • 33845720006 scopus 로고    scopus 로고
    • Using interactive archives in evolutionary multiobjective optimization: A case study for long-term groundwater monitoring design
    • P. Reed J. B. Kollat V. K. Devireddy Using interactive archives in evolutionary multiobjective optimization: A case study for long-term groundwater monitoring design Environ. Model. Softw. 22 5 683 692 May 2007
    • (2007) Environ. Model. Softw. , vol.22 , Issue.5 , pp. 683-692
    • Reed, P.1    Kollat, J.B.2    Devireddy, V.K.3
  • 36
    • 0004087274 scopus 로고
    • Methods for Solving Systems of Equations
    • SIAM PA, Philadelphia
    • W. C. Rheinboldt Methods for Solving Systems of Equations 1974 SIAM PA, Philadelphia
    • (1974)
    • Rheinboldt, W.C.1
  • 37
    • 33646145079 scopus 로고    scopus 로고
    • Order reduction of large scale second-order systems using Krylov subspace methods
    • B. Salimbahrami B. Lohmann Order reduction of large scale second-order systems using Krylov subspace methods Lin. Alg. Appl. 415 2/3 385 405 Jun. 2006
    • (2006) Lin. Alg. Appl. , vol.415 , Issue.2/3 , pp. 385-405
    • Salimbahrami, B.1    Lohmann, B.2
  • 38
    • 0002109912 scopus 로고
    • An adaptive crossover distribution mechanism for genetic algorithms
    • NJ
    • J. D. Schaffer A. Morishima An adaptive crossover distribution mechanism for genetic algorithms Proc. Int. Conf. Genetic Algorithms 36 40 Proc. Int. Conf. Genetic Algorithms Hillsdale NJ 1987
    • (1987) , pp. 36-40
    • Schaffer, J.D.1    Morishima, A.2
  • 39
    • 0003023194 scopus 로고
    • On the virtues of uniform crossover
    • W. M. Spears K. A. De Jong On the virtues of uniform crossover Proc. Int. Conf. Genetic Algorithms 230 236 Proc. Int. Conf. Genetic Algorithms 1991
    • (1991) , pp. 230-236
    • Spears, W.M.1    De Jong, K.A.2
  • 40
    • 0002881568 scopus 로고
    • Uniform crossover in genetic algorithms
    • CA
    • G. Syswerda Uniform crossover in genetic algorithms Proc. Conf. Genetic Algorithms 2 9 Proc. Conf. Genetic Algorithms Los Altos CA 1989
    • (1989) , pp. 2-9
    • Syswerda, G.1
  • 41
    • 0003709653 scopus 로고
    • Multiple Criteria Optimization. Theory, Computation, and Application
    • Wiley New York
    • R. E. Steuer Multiple Criteria Optimization. Theory, Computation, and Application Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics 1986 Wiley New York
    • (1986)
    • Steuer, R.E.1
  • 42
    • 0029532734 scopus 로고
    • A new dimension-reducing method for solving systems of nonlinear equations
    • T. N. Grapsa M. N. Vrahatis A new dimension-reducing method for solving systems of nonlinear equations Int. J. Comput. Math. 55 3/4 235 244 1995
    • (1995) Int. J. Comput. Math. , vol.55 , Issue.3/4 , pp. 235-244
    • Grapsa, T.N.1    Vrahatis, M.N.2
  • 43
    • 0003717416 scopus 로고
    • Methods and Applications of Interval Analysis
    • SIAM PA, Philadelphia
    • R. E. Moore Methods and Applications of Interval Analysis 1979 SIAM PA, Philadelphia
    • (1979)
    • Moore, R.E.1
  • 44
    • 45949116959 scopus 로고
    • Computing all solutions to polynomial systems using homotopy continuation
    • A. P. Morgan Computing all solutions to polynomial systems using homotopy continuation Appl. Math. Comput. 24 2 115 138 Nov. 1987
    • (1987) Appl. Math. Comput. , vol.24 , Issue.2 , pp. 115-138
    • Morgan, A.P.1
  • 45
    • 0003633233 scopus 로고
    • Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems
    • Prentice-Hall NJ, Englewood Cliffs
    • A. P. Morgan Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems 1987 Prentice-Hall NJ, Englewood Cliffs
    • (1987)
    • Morgan, A.P.1
  • 46
    • 0346119927 scopus 로고    scopus 로고
    • A null space method for solving system of equations
    • P. Y. Nie A null space method for solving system of equations Appl. Math. Comput. 149 1 215 226 Feb. 2004
    • (2004) Appl. Math. Comput. , vol.149 , Issue.1 , pp. 215-226
    • Nie, P.Y.1
  • 47
    • 33644664672 scopus 로고    scopus 로고
    • An SQP approach with line search for a system of nonlinear equations
    • P. Y. Nie An SQP approach with line search for a system of nonlinear equations Math. Comput. Model. 43 3/4 368 373 Feb. 2006
    • (2006) Math. Comput. Model. , vol.43 , Issue.3/4 , pp. 368-373
    • Nie, P.Y.1
  • 48
    • 0033322289 scopus 로고    scopus 로고
    • On the kinematic analysis of robotic mechanisms
    • J. Nielson B. Roth On the kinematic analysis of robotic mechanisms Int. J. Robot. Res. 18 12 1147 1160 Dec. 1999
    • (1999) Int. J. Robot. Res. , vol.18 , Issue.12 , pp. 1147-1160
    • Nielson, J.1    Roth, B.2
  • 49
    • 0003602606 scopus 로고
    • Iterative Solution of Nonlinear Equations in Several Variables
    • Academic New York
    • J. M. Ortega W. C. Rheinboldt Iterative Solution of Nonlinear Equations in Several Variables 1970 Academic New York
    • (1970)
    • Ortega, J.M.1    Rheinboldt, W.C.2
  • 50
    • 0004161838 scopus 로고    scopus 로고
    • Numerical Recipes in C: The Art of Scientific Computing
    • Cambridge Univ. Press U.K., Cambridge
    • W. H. Press S. A. Teukolsky W. T. Vetterling B. P. Flannery Numerical Recipes in C: The Art of Scientific Computing 2002 Cambridge Univ. Press U.K., Cambridge
    • (2002)
    • Press, W.H.1    Teukolsky, S.A.2    Vetterling, W.T.3    Flannery, B.P.4


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