Fuzzy programming technique to solve multi-objective geometric programming problems

1992 ◽  
Vol 51 (1) ◽  
pp. 67-71 ◽  
Author(s):  
M.P. Biswal
Keyword(s):  
Geometric Programming ◽  
Fuzzy Programming ◽  
Programming Technique ◽  
Multi Objective

scholarly journals Multi-Objective Capacitated Solid Transportation Problem with Uncertain Variables

2021 ◽  
Vol 6 (5) ◽  
pp. 1406-1422
Author(s):  
Vandana Y. Kakran ◽  
Jayesh M. Dhodiya
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Solid Transportation Problem ◽  
Programming Technique ◽  
Distance Method ◽  
Multi Objective ◽  
Uncertain Variables ◽  
Value Model ◽  
Single Objective

This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.

scholarly journals Multi-Objective Faculty Course Assignment Problem with Result and Feedback Based Uncertain Preferences

2021 ◽  
Vol 6 (4) ◽  
pp. 1055-1075
Author(s):  
Sunil B. Bhoi ◽  
Jayesh M Dhodiya
Keyword(s):  
Deterministic Model ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Programming Technique ◽  
Feedback Analysis ◽  
Multi Objective ◽  
Ranking Criteria ◽  
Uncertain Preferences ◽  
Single Objective ◽  
Optimistic Value

In this paper, a multi-objective faculty course allocation problem with result analysis and feedback analysis based on uncertain preferences mathematical model is presented. To deal with an uncertain model, three different ranking criteria are being used to develop: a) Expected value, b) Optimistic value, c) Dependent optimistic value criterion. These mathematical models are transformed into their corresponding deterministic forms using the basic concepts of uncertainty theory. The deterministic model of DOCM consists of fractional objectives which are converted into their linear form using Charnes and Cooper’s transformation. These deterministic formulations MOFCAP are converted into a single objective problem by using the fuzzy programming technique with linear and exponential membership functions. Further, the single objective problem for all the defined models is solved in the Lingo 18.0 software to derive the Pareto-optimal solution. The sensitivity of the models is also performed to examine the variation in the objective function due to the variation in parameters. Finally, a numerical example is given to exhibit the application and algorithm of the models.

scholarly journals Multi-objective geometric programming problem and its applications

2010 ◽  
Vol 20 (2) ◽  
pp. 213-227 ◽  
Author(s):  
Sahidul Islam
Keyword(s):  
Programming Problem ◽  
Geometric Programming ◽  
Optimization Technique ◽  
Real Life ◽  
Fuzzy Optimization ◽  
Solution Procedure ◽  
Programming Technique ◽  
Multi Objective ◽  
Numerical Example ◽  
Multiobjective Problem

In this paper, we have discussed constrained posynomial Multi-Objective Geometric Programming Problem. Here we shall describe the fuzzy optimization technique (through Geometric Programming technique) In order to solve the above multiobjective problem. The solution procedure of the fuzzy technique is illustrated by a numerical example and real life applications.

scholarly journals Multi Objective Geometric Programming with Interval Coefficients: A Parametric Approach

2019 ◽  
pp. 395-407
Author(s):  
Zeinab Mousavi ◽  
Mansour Saraj
Keyword(s):  
Engineering Design ◽  
Geometric Programming ◽  
Nonlinear Problems ◽  
Optimization Techniques ◽  
Programming Technique ◽  
Design Problems ◽  
Multi Objective ◽  
Engineering Design Problems ◽  
Interval Valued Function ◽  
The Right

When we talk of optimization in industry we need to pay attention in searching for very powerful and flexible optimization techniques. One of such techniques which has attracted the interest of many researchers in the last few decades is called geometric programming that provides a powerful tool for solving nonlinear problems. As we know in the real world, many applications of geometric programming are engineering design problems. Generally, engineering design problems deal with multi-objective functions, in which their objectives are often in conflicts with each other. This paper considers a solution method when the cost, the constraint coefficients, and the right-hand sides in the multi-objective geometric programming problems are imprecise and represented as interval values. This problem is reduced with the method of weighted sum to a single objective function and further by applying interval-valued function, we solve the problem by geometric programming technique. The ability of calculating the bounds of the objective value developed in this paper might help lead to more realistic modeling efforts in engineering optimization areas. Finally a numerical example is given to illustrate the methodology of solution and efficiency of the present approach.

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