scholarly journals PENDEKATAN ALGORITMA GENETIKA DALAM MENYELESAIKAN PERMASALAHAN FUZZY LINEAR PROGRAMMING

2011 ◽  
Vol 5 (3) ◽  
pp. 36
Author(s):  
Siska Dewi Lestari ◽  
Subanar Subanar
Keyword(s):  
Genetic Algorithm ◽  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Number ◽  
Fitness Function ◽  
Fuzzy Linear Programming ◽  
Right Hand ◽  
Fuzzy Constraint ◽  
Linear Programming Problems ◽  
Genetic Algorithm Approach

Fuzzy linear programming is one of the linear programming developments which able to accommodate uncertainty in the real world. Genetic algorithm approach in solving linear programming problems with fuzzy constraints has been introduced by Lin (2008) by providing a case which consists of two decision variables and three constraint functions. Other linear programming problem arise with the presence of some coefficients which are fuzzy in linear programming problems, such as the coefficient of the objective function, the coefficient of constraint functions, and right-hand side coefficients constraint functions. In this study, the problem studied is to explain the genetic algorithm approach to solve linear programming problems where the objective function coefficients and right-hand sides are fuzzy constraint functions.PT Dakota Furniture study case provides a linear programming formulation with a given objective function coefficients and right-hand side coefficients are fuzzy constraint functions. This study describes the use of genetic algorithm approach to solve the problem of linear programming of PT Dakota to maximize the mean income. The genetic algorithm approach is done by simulate every fuzzy number and each fuzzy numbers by distributing them on certain partition points. Then genetic algorithm is used to evaluate the value for each partition point. As a result, the Final Value represents the coefficient of fuzzy number.  Fitness function is done by calculating the value of the objective function of linear programming problems. Empirical results indicated that the genetic algorithm approach can provide a very good solution by giving some limitations on each fuzzy coefficient.Genetic algorithm approach can be extended not only to resolve the case of PT Dakota Furniture, but can also be used to solve other linear programming case with some coefficients in the objective function and constraint functions are fuzzy.Keywords : Genetic Algorithm, Fuzzy Linear Programming, Linear Programming, Two-Phase Simplex Method

scholarly journals Penalty method for fuzzy linear programming with trapezoidal numbers

2009 ◽  
Vol 19 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Bogdana Stanojevic ◽  
Milan Stanojevic
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Number ◽  
Penalty Method ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Constraint Violation ◽  
Deterministic Problem ◽  
Multi Objective Programming ◽  
Linear Programming Problems

In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints.

scholarly journals Comparing different ranking functions for solving fuzzy linear programming problems with fuzzy cost coefficients

2021 ◽  
Vol 4 (2) ◽  
pp. 3-17
Author(s):  
Betsabé Pérez Garrido ◽  
Szabolcs Szilárd Sebrek ◽  
Viktoriia Semenova
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Ranking Functions ◽  
Statistical Software ◽  
Linear Programming Problems ◽  
Fuzzy Cost ◽  
The Cost ◽  
Cost Vector

In many applications of linear programming, the lack of exact information results in various problems. Nevertheless, these types of problems can be handled using fuzzy linear programming. This study aims to compare different ranking functions for solving fuzzy linear programming problems in which the coefficients of the objective function (the cost vector) are fuzzy numbers. A numerical example is introduced from the field of tourism and then solved using five ranking functions. Computations were carried out using the FuzzyLP package implemented in the statistical software R.

scholarly journals On multi-objective linear programming problems with inexact rough interval-fuzzy coefficients

2015 ◽  
Vol 14 (5) ◽  
pp. 5742-5758
Author(s):  
E. E. Ammar ◽  
M. L. Hussein ◽  
A. M. Khalifa
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Fuzzy Number ◽  
Linear Programming Problem ◽  
Solution Procedure ◽  
Modeling Framework ◽  
Multi Objective ◽  
Interval Solution ◽  
Linear Programming Problems ◽  
Rough Interval

This paper deals with a multi-objective linear programming problem with an inexact rough interval fuzzy coefficients IRFMOLP. This problem is considered by incorporating an inexact rough interval fuzzy number in both the objective function and constrains. The concept of "Rough interval" is introduced in the modeling framework to represent dualuncertain parameters. A suggested solution procedure is given to obtain rough interval solution for IRFLP(w) problem. Finally,two numerical example is given to clarify the obtained results in this paper.

scholarly journals Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yi-hua Zhong ◽  
Yan-lin Jia ◽  
Dandan Chen ◽  
Yan Yang
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Fuzzy Number ◽  
Simplex Method ◽  
Interior Point Method ◽  
Large Scale ◽  
Ranking Function ◽  
Point Method ◽  
Fuzzy Linear Programming ◽  
Linear Programming Problems

Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.

Solving Vibration Control Problems Using Reduced Order Models for Flexible Structures: A Genetic Algorithm Approach

1997 ◽  
Author(s):  
Sourav Kundu ◽  
Kentaro Kamagata ◽  
Shigeru Sugino ◽  
Takeshi Minowa ◽  
Kazuto Seto
Keyword(s):  
Genetic Algorithm ◽  
Vibration Control ◽  
Controller Design ◽  
Fitness Function ◽  
Flexible Structures ◽  
Design Solution ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Fitness Value ◽  
Genetic Algorithm Approach

Abstract A Genetic Algorithm (GA) based approach for solution of optimal control design of flexible structures is presented in this paper. The method for modeling flexible structures with distributed parameters as reduced-order models with lumped parameters, which has been developed previously, is employed. Due to some restrictions on controller design it is necessary to make a reduced-order model of the structure. Once the model is established the design of flexible structures is considered as a feedback search procedure where a new solution is assigned some fitness value for the GA and the algorithm iterates till some satisfactory design solution is achieved. We propose a pole assignment method to determine the evaluation (fitness) function to be used by the GA to find optimal damping ratios in passive elements. This paper demonstrates the first results of a genetic algorithm approach to solution of the vibration control problem for practical control applications to flexible tower-like structures.

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