Fuzzy Goal Programming to Optimization the Multi-Objective Problem
Science Journal of Applied Mathematics and Statistics
Volume 2, Issue 1, February 2014, Pages: 14-19
Received: Nov. 13, 2013; Published: Feb. 20, 2014
Views 3528      Downloads 386
Azzabi Lotfi, LASQUO/ISTIA/ University of Angers France
Ayadi Dorra, LASQUO/ISTIA/ University of Angers France
Bachar Kaddour, ESSCA Angers France
Kobi Abdessamad, LASQUO/ISTIA/ University of Angers France
Article Tools
Follow on us
Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.
Multicriteria Approach, Multi-Objective Optimization Problems, Fuzzy Goal Programming
To cite this article
Azzabi Lotfi, Ayadi Dorra, Bachar Kaddour, Kobi Abdessamad, Fuzzy Goal Programming to Optimization the Multi-Objective Problem, Science Journal of Applied Mathematics and Statistics. Vol. 2, No. 1, 2014, pp. 14-19. doi: 10.11648/j.sjams.20140201.12
B F. Blake, BA. McCarl., "Goal Programming via Multidimensional Scaling Applied to Sengalese Subsistence Farming: A Reply," American Journal of Agricultural Economics. 65 (1983):832-33.
M. Baltes, R. Schneider, C. Sturm, and M. Reuss., "Optimal experimental design for parameter estimation in unstructured growth models," Biotechnology Progress, 10, 480}488(1994).
LT. Biegler, J J. Damiano. GE. Blau., "Nonlinear parameter estimation: A case study comparison," A.I.Ch.E. Journal, 32, 29}45(1986).
K. Deb., " Optimization for engineering design: Algorithms and examples." Prentice-Hall, New Delhi, India (1995).
C M. Fonseca, P J. Fleming., " An overview of evolutionary algorithms in multiobjective optimization," Evolutionary Computation, 3:1–16 (1995).
J. Horn, N. Nafploitis, and D E. Goldberg., " A niched Pareto genetic algorithm for multiobjective optimization, " In Michalewicz, Z., editor, Proceedings of the First IEEE Conference on Evolutionary Computation, pages 82–87, IEEE Service Center, Piscataway, New Jersey, (1994).
N. Srinivas, K. Deb., "Multi-Objective function optimization using non-dominated sorting genetic algorithms," Evolutionary Computation, 2(3):221–248, (1995).
E. Zitzler, L. Thiele., "Multiobjective optimization using evolutionary algorithms—A comparative case study,. " In Eiben, A. E., B¨ack, T., Schoenauer, M. and Schwefel, H.-P., editors, Parallel Problem Solving from Nature, V, pages 292–301, Springer, Berlin, Germany, (1998).
J. Teng, G. Tzeng., "A multiobjective programming approach for selecting non-independent transportation investment alternatives," Transportation Research-B, 30(4):201–307, 1996, (1996).
M. Ehrgott., "Multicriteria optimization," LNEMS 491. Springer, Berlin, 2005.
L A. Zadeh,. " Fuzzy Sets, Information and Control, " 8, 1965, pp. 338–353.
M. Belmokaddem, M. Mekidiche , A. Sahed.," Application of a fuzzy GOAL PROGRAMMING approach with different importance and priorities to aggregate production planning," Journal of Applied Quantitative Methods, (2009).
HJ. Zimmermen., "Fuzzy programming and linear programming with several objective functions, " Fuzzy Sets and Systems, 1, 1978, pp. 45–56, 1978.
HJ. Zimmermann., "Applications of fuzzy sets theory to mathematical programming," Information Science, 35, 1985, pp. 29-58, (1985).
E.L, Hannan., "Linear programming with multiple fuzzy goals," Fuzzy Sets and Systems, 6,1981-a, pp. 235-248, (1981).
E.L, Hannan., "On Fuzzy Goal Programming, " Decision Sciences 12, 1981-b, pp. 522–531, (1981).
H. Leberling., "On finding compromise solutions in multi criteria problems using the fuzzy min-operator, " Fuzzy Sets and Systems, 6, 1981, pp. 105–118, (1981).
MK. Luhandjula., "Compensatory operations in fuzzy programming with multiple objectives, " Fuzzy Sets and Systems, 8, 1982, pp. 245–252, (1982).
PA. Rubin, R. Narasimhan., "Fuzzy goal programming with nested priorities," Fuzzy Sets and Systems, 14, 1984, pp. 115–129, (1984).
R N. Tiwari, S. Dharmar, and J R. Rao., "Fuzzy goal programming – An additive model," Fuzzy Sets and Systems, 24, 1987, pp. 27–34, (1987) .
H F. Wang, C. C, Fu., "A generalization of fuzzy goal programming with preemptive structure,"Computers and Operations Research, 24, 1997, pp. 819–828, (1997).
L H. Chen, F C. Tsai., "Fuzzy goal programming with different importance and priorities, " European Journal of Operational Research, 133, 2001, pp. 548–556, (2001).
M A. Yaghoobi, M. Tamiz., " A method for solving fuzzy goal programming problems based on MINMAX approach,"European Journal of Operational Research, 177, pp. 1580–1590, (2007).
B. Aouni, O. Kettani., "Goal Programming Model: A Glorious History and a Promising Future", European Journal of Operational Research, Vol. 133, No. 2, 1-7, (2001).
J-M. Martel, B. Aouni., "Incorporating the Decision-maker’s Preferences in the Goal Programming Model", Journal of Operational Research Society, Vol.41, 1121-1132, (1990).
J M. Martel, B. Aouni., "Incorporating the Decision-maker’s Preferences in the Goal Programming Model with Fuzzy Goals Values: A new Formulation", Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, (1996).
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186