scholarly journals An Exact Method for a Discrete Multiobjective Linear Fractional Optimization

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed El-Amine Chergui ◽  
Mustapha Moulaï
Keyword(s):  
Fractional Programming ◽  
Feasible Solution ◽  
Efficient Solutions ◽  
Branch And Cut ◽  
Multiple Objective ◽  
Objective Functions ◽  
Linear Fractional Programming ◽  
Fractional Optimization ◽  
Important Field ◽  
Linear Fractional Programming Problem

Integer linear fractional programming problem with multiple objective (MOILFP) is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.

scholarly journals An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Meriem Ait Mehdi ◽  
Mohamed El-Amine Chergui ◽  
Moncef Abbas
Keyword(s):  
Branching Process ◽  
Feasible Solution ◽  
Linear Program ◽  
Branch And Cut ◽  
Objective Functions ◽  
Improved Method ◽  
Linear Fractional Programming ◽  
Linear Fractional Program ◽  
Linear Fractional Programming Problem ◽  
General Step

We describe an improvement of Chergui and Moulaï’s method (2008) that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality) one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

scholarly journals Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs

2012 ◽  
Vol 22 (1) ◽  
pp. 41-50 ◽  
Author(s):  
B. Stanojevic ◽  
I.M. Stancu-Minasian
Keyword(s):  
Linear Programming ◽  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Triangular Fuzzy Numbers ◽  
Linear Fractional Programming ◽  
Numerical Examples ◽  
Fractional Programs ◽  
Linear Fractional Programming Problem

In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm.

scholarly journals Crisp-linear-and Models in Fuzzy Multiple Objective Linear Fractional Programming

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Bogdana Stanojevic ◽  
Simona Dzitac ◽  
Ioan Dzitac
Keyword(s):  
Objective Function ◽  
Fractional Programming ◽  
Linear Models ◽  
Multiple Objective ◽  
Membership Functions ◽  
Tolerance Limits ◽  
Linear Fractional Programming ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Linear Fractional Programming Problem

The aim of this paper is to introduce two crisp linear models to solve fuzzy multiple objective linear fractional programming problems. In a novel manner we construct two piece-wise linear membership functions to describe the fuzzy goal linked to a linear fractional objective. They are related to the numerator and denominator of the fractional objective function; and we show that using the fuzzy-and operator to aggregate them a convenient description of the original fractional fuzzy goal is obtained. Further on, with the help of the fuzzy-and operator we aggregate all fuzzy goals and constraints, formulate a crisp linear model, and use it to provide a solution to the initial fuzzy multiple objective linear fractional programming problem. The second model embeds in distinct ways the positive and negative information, the desires and restrictions respectively; and aggregates in a bipolar manner the goals and constraints. The main advantage of using the new models lies in the fact that they are linear, and can generate distinct solutions to the multiple objective problem by varying the thresholds and tolerance limits imposed on the fuzzy goals.

scholarly journals GOAL PROGRAMMING APPROACH TO CHANCE CONSTRAINED MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM BASED ON TAYLOR’S SERIES APPROXIMATION

2012 ◽  
Vol 2 (2) ◽  
pp. 77-80
Author(s):  
Durga Banerjee ◽  
Surapati Pramanik
Keyword(s):  
Programming Problem ◽  
Goal Programming ◽  
Fractional Programming ◽  
Random Variables ◽  
Optimal Solution ◽  
Programming Approach ◽  
Objective Functions ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Linear Fractional Programming Problem

This paper deals with goal programming approach to chance constrained multi-objective linear fractional programming problem based on Taylor’s series approximation. We consider the constraints with right hand parameters as the random variables of known mean and variance. The random variables are transformed into standard normal variables with zero mean and unit variance. We convert the chance constraints with known confidence level into equivalent deterministic constraints. The goals of linear fractional objective functions are determined by optimizing it subject to the equivalent deterministic system constraints. Then the fractional objective functions are transformed into equivalent linear functions at the optimal solution point by using first order Taylor polynomial series. In the solution process, we use three minsum goal programming models and identify the most compromise optimal solution by using Euclidean distance function.

scholarly journals Additive Algorithm for Solving 0-1 Integer Linear Fractional Programming Problem

2013 ◽  
Vol 61 (2) ◽  
pp. 173-178
Author(s):  
Md Rajib Arefin ◽  
Touhid Hossain ◽  
Md Ainul Islam
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Integer Linear Programming ◽  
Fractional Programming ◽  
Feasible Solution ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Fractional Programming Problem

In this paper, we present additive algorithm for solving a class of 0-1 integer linear fractional programming problems (0-1 ILFP) where all the coefficients at the numerator of the objective function are of same sign. The process is analogous to the process of solving 0-1 integer linear programming (0-1 ILP) problem but the condition of fathoming the partial feasible solution is different from that of 0-1 ILP. The procedure has been illustrated by two examples. DOI: http://dx.doi.org/10.3329/dujs.v61i2.17066 Dhaka Univ. J. Sci. 61(2): 173-178, 2013 (July)

GOAL PROGRAMMING APPROACH TO CHANCE CONSTRAINED MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEM BASED ON TAYLOR’S SERIES APPROXIMATION

2012 ◽  
Vol 2 (2) ◽  
pp. 77-80 ◽  
Author(s):  
Durga Banerjee ◽  
Surapati Pramanik
Keyword(s):  
Programming Problem ◽  
Goal Programming ◽  
Fractional Programming ◽  
Random Variables ◽  
Optimal Solution ◽  
Programming Approach ◽  
Objective Functions ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Linear Fractional Programming Problem

This paper deals with goal programming approach to chance constrained multi-objective linear fractional programming problem based on Taylor’s series approximation. We consider the constraints with right hand parameters as the random variables of known mean and variance. The random variables are transformed into standard normal variables with zero mean and unit variance. We convert the chance constraints with known confidence level into equivalent deterministic constraints. The goals of linear fractional objective functions are determined by optimizing it subject to the equivalent deterministic system constraints. Then the fractional objective functions are transformed into equivalent linear functions at the optimal solution point by using first order Taylor polynomial series. In the solution process, we use three minsum goal programming models and identify the most compromise optimal solution by using Euclidean distance function.

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