New technique for solving multivariate global optimization
DOI:
https://doi.org/10.33993/jnaat521-1287Abstract
In this paper, we propose an algorithm based on branch and bound method to underestimate the objective function and reductive transformation which is transformed the all multivariable functions on univariable functions. We also demonstrate several quadratic lower bound functions are proposed which they are better/preferable than the others well-known in literature. We obtain that our experimental results are more effective when we face different nonconvex functions.
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Aaid, Djamel., Noui, Amel., Le Thi, Hoai An., Zidna, Ahmed.: A modi ed classical algorithm ALPT4C for solving a capacitated four-index transportation problem, Acta Mathematica Vietnamica, 37(3) 379-390(2012).
AAID, Djamel.: Etude numerique comparative entre des methodes de resolution d'un probleme de transport a quatre indices avec capacites, these de l'universite de Constantine, (2010). http://bu.umc.edu.dz/theses/math/AAI5587.pdf
Aaid, Djamel., Noui,Amel., Ouanes, Mohand.: A Piecewise Quadratic Underestimation For Global Optimization Optimization, JSLAROMAD II Tiziouzou. Algeria, les 28, 29 and 30 octobre (2013).
A, Djamel., N, Amel., Z, Ahmed., O, Mohand.: A Quadratic Branch and Bound with Alienor Method for Global Optimization, MAGO'2014,Malaga,SPAIN, 1-4 September (2014).
Adjiman, C.S., Androulakis, I.P., Floudas, C.A.: A global optimization method, alpha BB, for general twice differentiable NLPs-II. Implementation and computational results, Computers & Chemical Engineering, 22(9) 1159-1179 (1998). DOI: https://doi.org/10.1016/S0098-1354(98)00218-X
A, Guillez.: Alienor fractal algorithm for multivariable mnimization problems, Mathematical and Computer Modelling, 14 245-247(1990). DOI: https://doi.org/10.1016/0895-7177(90)90184-O
Akrotirianakis, I.G., Floudas, C.A.: Computational experience with a new class of convex underestimators: box-constrained NLP problems, Journal of Global Optimization, 29(3) 249-264(2004). DOI: https://doi.org/10.1023/B:JOGO.0000044768.75992.10
Bendiab, Y. Cherruault.: A new method for global optimization in two dimensions, International Journal of Bio-Medical Computing, 38(1) 71-73(1995). DOI: https://doi.org/10.1016/0020-7101(94)01039-4
Caratzoulas, S., Floudas, C.A.: A trigonometric convex underestimator for the base functions in Fourier space, Journal of Optimization Theory and Applications, 124(2) 339-362(2005). DOI: https://doi.org/10.1007/s10957-004-0940-2
Ciarlet.P.G.: The Finite Element Method for Elliptic Problems, Studies in Mathematics and Its Application, (1979).
Crina Grosan, Ajith Abrahamy: On a Class of Global Optimization Test Functions,Neural network world, http://falklands.globat.com/softcomputing.net/nnw2009.pdf
De Boor, C.: A Practical Guide to Splines", Applied Mathematical Sciences, Springer Verlag, (1978). DOI: https://doi.org/10.1007/978-1-4612-6333-3
Djaouida, Guettal., Abdelkader, Ziadi.: Reducing transformation and global optimization, Applied Mathematics and Computation, 218 5848-5860(2012). DOI: https://doi.org/10.1016/j.amc.2011.11.053
Fadila, Leslous., Philippe, Marthon., Oukacha, Brahim., Ouanes, Mohand.: Non-convex optimization based on DC programming and DCA in the search of a global optimum of a nonconvex function, Journal of the Egyptian Mathematical Society, doi:10.1016/j.joems..08.002(2015).
Jordan, Ninin.: Methodes d'Optimisation Globale basees sur l'Analyse d'Intervalle pour la Resolution des Problemes avec Contraintes, These Doctorat universite De Toulouse , 8 Decembre (2010) . http://ethesis.inp-toulouse.fr/archive/00001477/01/Ninin.pdf
Le Thi.H.A, Ouanes,M.: Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint, RAIRO Operations Research, 40 285-302(2006). DOI: https://doi.org/10.1051/ro:2006024
Mohamed, Rahal, Abdalkader,Ziadi.: A new extention of Piyavski's method to Holder functions of sveral variables,Aplied mathematics and computation, 218 478-788(2012).
Mohand, Ouanes., Hoai. An, Le Thi., Trong, Phuc. Nguyen., Ahmed, Zidna.: New quadratic lower bound for multivariate functions in global optimization, Mathematics and Computers in Simulation , 109 197-211(2015). DOI: https://doi.org/10.1016/j.matcom.2014.04.013
Mohand,Ouanes.: The main diagonal method in C1 global optimization problem, International Journal of Applied Mathematics, 25 (5) 663-672(2012).
Mohand, Ouanes.: A new approach for nonconvex SIP, International Journal of Applied Mathematics, 81 (3) 479-486(2012).
Mohand, Ouanes.: A comined descent gradient method and descritization method for convex SIP, International Journal of Applied Mathematics, 25 (4) 503-513(2012).
Mohand,Ouanes.: New underestimator for multivariate global optimization with box costraints, International Journal of Pure and Applied Mathematics, 84 (1) (2013). DOI: https://doi.org/10.12732/ijpam.v84i1.5
Noui, Amel., and Aaid, Djamel., and Ouanes, Mohand.: An efficient algorithm for the Bernstein Polynomial Approach to Global Optimization.: JSLAROMAD II,Tiziouzou,Algeria les 28, 29 et 30 octobre (2013).
T,Benneouala, Y,Cherruault.: Alienor method for global optimization with a large number of variables, Kybernetes, 34 (7/8) 1104-1111( 2005) . DOI: https://doi.org/10.1108/03684920510605911
Yves, Cherruault., Gaspar, Mora.: Optimisation globale Theorie Des courbes alpha-dense, Economica, Paris, (2005).
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