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
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Authors
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
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Abstract
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.
Keywords
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
References
[1]
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.
[2]
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).
[3]
LT. Biegler, J J. Damiano. GE. Blau., "Nonlinear parameter estimation: A case study comparison," A.I.Ch.E. Journal, 32, 29}45(1986).
[4]
K. Deb., " Optimization for engineering design: Algorithms and examples." Prentice-Hall, New Delhi, India (1995).
[5]
C M. Fonseca, P J. Fleming., " An overview of evolutionary algorithms in multiobjective optimization," Evolutionary Computation, 3:1–16 (1995).
[6]
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).
[7]
N. Srinivas, K. Deb., "Multi-Objective function optimization using non-dominated sorting genetic algorithms," Evolutionary Computation, 2(3):221–248, (1995).
[8]
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).
[9]
J. Teng, G. Tzeng., "A multiobjective programming approach for selecting non-independent transportation investment alternatives," Transportation Research-B, 30(4):201–307, 1996, (1996).
[10]
M. Ehrgott., "Multicriteria optimization," LNEMS 491. Springer, Berlin, 2005.
[11]
L A. Zadeh,. " Fuzzy Sets, Information and Control, " 8, 1965, pp. 338–353.
[12]
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).
[13]
HJ. Zimmermen., "Fuzzy programming and linear programming with several objective functions, " Fuzzy Sets and Systems, 1, 1978, pp. 45–56, 1978.
[14]
HJ. Zimmermann., "Applications of fuzzy sets theory to mathematical programming," Information Science, 35, 1985, pp. 29-58, (1985).
[15]
E.L, Hannan., "Linear programming with multiple fuzzy goals," Fuzzy Sets and Systems, 6,1981-a, pp. 235-248, (1981).
[16]
E.L, Hannan., "On Fuzzy Goal Programming, " Decision Sciences 12, 1981-b, pp. 522–531, (1981).
[17]
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).
[18]
MK. Luhandjula., "Compensatory operations in fuzzy programming with multiple objectives, " Fuzzy Sets and Systems, 8, 1982, pp. 245–252, (1982).
[19]
PA. Rubin, R. Narasimhan., "Fuzzy goal programming with nested priorities," Fuzzy Sets and Systems, 14, 1984, pp. 115–129, (1984).
[20]
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) .
[21]
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).
[22]
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).
[23]
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).
[24]
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).
[25]
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).
[26]
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).
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