Share This Article:

Alienor Method for Nonlinear Multi-Objective Optimization

Abstract Full-Text HTML Download Download as PDF (Size:2107KB) PP. 217-224
DOI: 10.4236/am.2011.22023    5,053 Downloads   10,166 Views   Citations

ABSTRACT

This paper deals with the Alienor method to tackle multiobjective nonlinear optimization problems. In this approach, the multiple criteria of the optimization problem are aggregated into a single one using weighted sums. Then, the resulting single objective nonlinear optimization problem is solved using the Alienor method associated with the Optimization Preserving Operators technique which has proved to be suitable for (nonlinear) optimization problems with a large number of variables (see [1]). The proposed approach is evaluated through test problems. The results show that the approach provides good approximations of the Pareto front while requiring small computational time, even for large instances.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Maimos, B. Konfe, S. Koussoube and B. Some, "Alienor Method for Nonlinear Multi-Objective Optimization," Applied Mathematics, Vol. 2 No. 2, 2011, pp. 217-224. doi: 10.4236/am.2011.22023.

References

[1] B. O. Konf, “Nouvelles Mthodes Mathmatiques Alienor et Adomian, pour la Biomdecine,” Thse de l’Universit de Ouagadougou, Ouagadougou, 2005.
[2] T. El-Ghazali, “Metaheuristics: From Design to Implementation,” John Wiley and Sons, Inc., Hoboken, 2009.
[3] M. Maimos, Y. Cherruault, B. Konf and N. A. Massamba, “Alienor Method to Solve Multi-Objective Linear Programming,” Kybernetes, Vol. 36, No. 5, 2009, pp. 789-799. doi:10.1108/03684920910962678
[4] B. O. Konf, Y. Cherruault and B. Som, “Solving Constrained Global Optimization Problems without Penalty Parameters,” Kybernetes, Vol. 34, No. 7-8, 2005, pp. 1090-1103. doi:10.1108/03684920510605902
[5] Y. Cherruault and G. Mora, “Optimisation Globale: Thorie des Courbes α-Denses,” Economica, Paris, 2005.
[6] Y. Cherruault, “Optimisation: Methodes Locales et Globales,” Presses Universitaires de France (P. U. F), Paris, 1999.
[7] Y. Cherruault, “Modles et Mthodes Mathmatiques pour les Sciences du Vivant,” Presses Universitaires de France (P. U. F), Paris, 1998.
[8] B. O. Konf, Y. Cherruault and T. Benneouala, “A Global Optimization Method for Large Number of Variables (Variant of Alienor Method),” Kybernetes, Vol. 34, No. 7-8, 2005, pp. 1070-1083. doi:10.1108/03684920510605885
[9] T. Benneouala and Y. Cherruault, “Alienor Method for Global Optimization with a Large Number of Variables,” Kybernetes, Vol. 34, No. 7-8, 2005, pp. 1104-1111. doi:10.1108/03684920510605911
[10] G. Mora, Y. Cherruault and A. Benabidallah, “Global Optimization-Preserving Operators,” Kybernetes, Vol. 32, No. 9-10, pp. 1473-1480.
[11] B. O. Konf, Y. Cherruault, B. Som and T. Benneouala, “A New ‘Optimization-Preserving-Operateur’ Applied to Global Optimization,” Kybernetes, Vol. 34, No. 7-8, 2005, pp. 1112-1124. doi:10.1108/03684920510605920
[12] S. Elaoud, T. Loukil and J. Teghem, “The Pareto Fitness Genetic Algorithm: Test Function Study,” European Journal of Opertional Research, Vol. 177, No. 3, 2007, pp. 1703-1719. doi:10.1016/j.ejor.2005.10.018
[13] V. Barichard, M. Ehrgott, X. Gandibleu, V. T’kindt, “Multiobjective Programming and Goal Programming,” Springer, Berlin, 2009. doi:10.1007/978-3-540-85646-7
[14] V. Barichard, “Approches Hybrides pour les Problmes Multiobjectifs,” Thse de l’Universit d’Angers, Angers, 2003.
[15] P. Siarry, and Z. Michalewicz, “Advances in Methheu- ristics for Hard Optimization,” Springer, Berlin, 2008. doi:10.1007/978-3-540-72960-0

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.