Fuzzy optimization
Seyedeh Maedeh Mirmohseni; Seyed Hadi Nasseri; Mohammad Hossein Khaviari
Abstract
In this paper, dynamic programming for sequencing weighted jobs on a single machine to minimizing total tardiness is focused, to significance of fuzzy numbers field, and importance of that for decision makers who are facing on uncertain data, combination of dynamic programming and fuzzy numbers is applied. ...
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In this paper, dynamic programming for sequencing weighted jobs on a single machine to minimizing total tardiness is focused, to significance of fuzzy numbers field, and importance of that for decision makers who are facing on uncertain data, combination of dynamic programming and fuzzy numbers is applied. A random scheduling problem with fuzzy processing times is given and solved. In addition, algorithm consuming time during solving same category problem and different sizes are analyzed that for large problem CPU time usage is extremely unaffordable. Therefore demonstration of near-exact heuristic method such as Genetic Algorithm (GA) appears. In this paper sufficient discussion around solving this kind of problems and their algorithms analysis and a combination between Dynamic Programming (DP) and genetic algorithm as a newly born method is proposed that stand on DP performance and genetic algorithm search power, and finally comparison on the recent developed method has been held. Then this method can deal with real-world problem easily. Thus, decision makers actually can use this modification of dynamic programming for coping with un-crisp problem.
Fuzzy optimization
Seyed Hadi Nasseri; Hadi Zavieh; Seyedeh Maedeh Mirmohseni
Abstract
In this paper, we generalize a linear programming problem with symmetric trapezoidal fuzzy number which is introduced by Ganesan and et al. in [3] to a general kind of trapezoidal fuzzy number. In this way, we first establish a new arithmetic operation for multiplication of two trapezoidal ...
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In this paper, we generalize a linear programming problem with symmetric trapezoidal fuzzy number which is introduced by Ganesan and et al. in [3] to a general kind of trapezoidal fuzzy number. In this way, we first establish a new arithmetic operation for multiplication of two trapezoidal fuzzy numbers. Then in order to preparing a method for solving the fuzzy linear programming as well as the primal simplex algorithm, we use a general linear ranking function as a convenient approach in the literature. In fact, our main contribution in this work is based on 3 items: 1) Extending the current fuzzy linear program to a general kind which is not essentially including the symmetric trapezoidal fuzzy numbers , 2) Defining a new multiplication role of two trapezoidal fuzzy numbers, 3) Establishing a fuzzy primal simplex algorithm for solving the generalized model. We in particular emphasize that this study can be used for establishing fuzzy dual simplex algorithm, fuzzy primal-dual simplex algorithm, fuzzy multi objective linear programming and the other similar methods which are appeared in the literature.