Keywords:-
Article Content:-
Abstract
Our previous work has proved the performance of the MOMA method to solve multiobjective optimization problems [1]. More precisely the best approximation of the Pareto optimal solutions of linear and nonlinear probl ems in continuous variables [2,3]. But the results were mixed on some kids of problems. Thus, this present work presents an improvement of the performances of the MOMA method to the resolution of problems of multiobjective optimization. This improvement consists in remplacing in the MOMA method, OPO (Operator Preserving the Optimum) by the strategy of the simplex algorithm of Nelder-Mead. This new procedure has been named MOMA-Plus[1] and makes it possible to obtain solutions at least as good as those of MOMA. Numerical exper iment s on a dozen benchmarks proved the effectiveness of this new version, MOMA-Plus. 2010 Mathematics Subject Classification: 90C29, 90C30, 49M30, 49M37
References:-
References
Kounhinir Som´e. ”Nouvelle m´ethode m´etaheuristique bas´ee sur la m´ethode Ali´enor pour
la r´esolution des probl`emes d’optmisation multiobjectif : Th´eorie et Applications.”, Th`ese de
doctorat unique, 2013, Universit´e de Ouadougou, Burkina Faso.
Kounhinir Som´e, Oliver Wenddabo Sawadogo, Berthold Ulungu, Blaise Som´e. ”A theoretical
f o u n d a t i o n m e t a h e u r i s t i c method to solve some multiobjective optimization problems,
International Journal of Applied Mathematical Research, volume 2 (4) (2013), page 464-475.
Kounhinir Som´e, Berthold Ulungu, Ibrahim Himidi Mohamed, Blaise Som´e. ”A new Method
for solving NonLinear Multiobjective Optimization Problems, JP Journal of Mathematical
Sciences, Volume 2, Issue1 et 2, 2011, page 1-18.
Mohsen EJDAY, Optimisation multiobjectif à base de m´etamod`ele pour le proc´ed´es de mise en
forme. Th`ese de doctorat, Paris Tech, France, 2011.
C. A. Coello coello, G. B. Lamont, D. A. V. Veldhuizen, Evolut ionna r y algorithme f o r
solving multiobjective probl em, s e cond Edi t ion, Springer, 2007.
Balira O.Konf´e, Nouvelles m´ethodes math´ematiques Alienor et Adomian, pour la biom´edecine.
Th`ese de doctorat pr´esent´ee `a l’Universit´e de Ouagadougou 2004-2005.
T. Benneoula, and Y. Cherruault, Alienor method for Global optimization with a large number
of variable, Kybernetes 34(7/8)(2005), 1104-1111.
Y. Cherruault, G. Mora, O p t i m i z a t i o n global: Th´eorie des courbes α−denses, Ed.
Economica, 2005. 9. B.O.Konf´e, Y.Cherruaul t , B.Som´e, T.Benneouala, A new optimization preserving
operator, applied to global optimization. Kybernet Mars 2004.
M. A. Luersen, GBNM: Un algorithme d’optimisation par la recherche directe - Application `a
la conception de Monopalmes de nage, th`ese de doctoract, l’Universit´e de Rouen, France
K. Deb, Multi-Objective Optimization using Evolutionary Al g o r i t hms , Edited by Wiley and
sons, Chichester, 2001.
Jacques Teghem, Programmation lin´eaire. Edition de l’Universit´e de Bruxelles (´edition
Ellipse), 1996.
Steur R, Multicriteria optimization: Theorie, computation and application, Wiley, New York.
Edition 1986.
J. Nelder, R. Mead, A simplex method for function minimization, Computer Journal, vol. 7,
n◦4, 1965, p.308-31