Parametric approach for an absolute value linear fractional programming with interval coefficients in the objective function

2014 ◽  
Author(s):  
M. Borza ◽  
A. S. Rambely ◽  
M. Saraj
Keyword(s):  
Objective Function ◽  
Fractional Programming ◽  
Parametric Approach ◽  
Linear Fractional Programming ◽  
Absolute Value ◽  
Interval Coefficients

scholarly journals A New Global Optimization Algorithm for a Class of Linear Fractional Programming

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 867 ◽  
Author(s):  
X. Liu ◽  
Y.L. Gao ◽  
B. Zhang ◽  
F.P. Tian
Keyword(s):  
Global Optimization ◽  
Lower Bound ◽  
Objective Function ◽  
Programming Problem ◽  
Optimization Algorithm ◽  
Fractional Programming ◽  
Original Problem ◽  
Global Optimization Algorithm ◽  
Linear Fractional Programming ◽  
Advantages And Disadvantages

In this paper, we propose a new global optimization algorithm, which can better solve a class of linear fractional programming problems on a large scale. First, the original problem is equivalent to a nonlinear programming problem: It introduces p auxiliary variables. At the same time, p new nonlinear equality constraints are added to the original problem. By classifying the coefficient symbols of all linear functions in the objective function of the original problem, four sets are obtained, which are I i + , I i − , J i + and J i − . Combined with the multiplication rule of real number operation, the objective function and constraint conditions of the equivalent problem are linearized into a lower bound linear relaxation programming problem. Our lower bound determination method only needs e i T x + f i ≠ 0 , and there is no need to convert molecules to non-negative forms in advance for some special problems. A output-space branch and bound algorithm based on solving the linear programming problem is proposed and the convergence of the algorithm is proved. Finally, in order to illustrate the feasibility and effectiveness of the algorithm, we have done a series of numerical experiments, and show the advantages and disadvantages of our algorithm by the numerical results.

scholarly journals An Approach for Solving Multi-Objective Linear Fractional Programming Problem with fully Rough Interval Coefficients

2021 ◽  
Vol 23 (07) ◽  
pp. 94-109
Author(s):  
Mohamed Solomon ◽  
◽  
Hegazy Zaher ◽  
Naglaa Ragaa ◽  
◽  
...  
Keyword(s):  
Fractional Programming ◽  
Efficient Solution ◽  
The Other ◽  
Regular Simplex ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Interval Coefficients ◽  
Rough Interval ◽  
Single Objective ◽  
Linear Fractional Programming Problem

In this paper, a multi-objective linear fractional programming (MOLFP) problem is considered where all of its coefficients in the objective function and constraints are rough intervals (RIs). At first, to solve this problem, we will construct two MOLFP problems with interval coefficients. One of these problems is a MOLFP where all of its coefficients are upper approximations of RIs and the other is a MOLFP where all of its coefficients are lower approximations of RIs. Second, the MOLFP problems are transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally, the single objective LP problem is solved by a regular simplex method which yields an efficient solution of the original MOLFP problem. A numerical example is given to demonstrate the results.

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.

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