Volume 17, Issue 3 (8-2020)
jor 2020, 17(3): 1-22 |
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Ghaznavi M, Azodi A, Ghorani M. A Primal-Dual Algorithm for Solving Multiobjective Linear Optimization Problems with Fuzzy Variables. jor 2020; 17 (3) :1-22
URL: http://jamlu.liau.ac.ir/article-1-1665-en.html
URL: http://jamlu.liau.ac.ir/article-1-1665-en.html
A Primal-Dual Algorithm for Solving Multiobjective Linear Optimization Problems with Fuzzy Variables
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Abstract: (2751 Views)
The fuzzy primal-dual simplex method is a new and efficient method for solving linear programming problems with fuzzy variables. This algorithm is based on duality results and, similar to the dual simplex method, begins with dual feasibility and proceeds to primal feasibility. An important difference between the dual simplex method and the primal-dual method is that in the primal-dual algorithm, it is not required that the dual feasible solution to be basic. In this paper, we develop the primal-dual simplex method for solving fuzzy multiobjective linear programming problems. To this end, we utilize the fuzzy weighted sum scalarization method to present a fuzzy single objective optimization problem related to the fuzzy multiobjective linear programming problem. Then, by partitioning the weights of the weighted sum problem, we generalize the single objective primal-dual algorithm to fuzzy multiobjective problems. By using the presented algorithm, we can find a set of fuzzy Pareto optimal solutions. Presenting a set of fuzzy Pareto optimal solutions to the decision maker, enables himher to select the best solution based on hisher preferences. Finally, we apply the proposed algorithm for solving a three-objective optimization problem with fuzzy variables and compare the results with some existing methods.
Keywords: Fuzzy Multiobjective Linear Programming, Primal-Dual Simplex, Fuzzy Ranking, Fuzzy Pareto Optimal Solution.
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