Multi-objective Geometric Programming Problem Research Articles

Multi Objective Geometric Programming with Interval Coefficients: A Parametric Approach

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.

Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems

Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example

An Alternative Approach to the Solution of Multi-Objective Geometric Programming Problems

The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.

Bi-level multiobjective geometric programming (BL-MOGP) problem under fuzziness

Bi-level multiobjective geometric programming (BL-MOGP) problem under fuzziness

MULTI-OBJECTIVE GEOMETRIC PROGRAMMING WITH VARYING PARAMETERS: APPLICATION IN WASTE WATER TREATMENT SYSTEM

In this paper a general multi-objective geometric programming problem with interval parameters is proposed, and a methodology is developed to derive its solution. The model is transformed into a general geometric programming problem, and relation between the original problem and the transformed problem is established. Application of this discussion is illustrated in a waste water treatment model.

Multi-objective geometric programming approach in multivariate stratified sample survey with quadratic cost function

ABSTRACTThe problem of optimum allocation in multivariate stratified sample surveys where the total cost () of the survey is quadratic in with significant travel cost has been formulated of as a Multi-Objective Geometric Programming Problem (MOGPP). The fuzzy programming approach has been described for converting the (MOGPP) into Single Objective Geometric Programming Problem (SOGPP) with the use of the membership function. The formulated SOGPP has been solved with the help of LINGO [LINGO User's Guide. Published by Lindo Systems Inc., 1415 North Dayton Street, Chicago, Illinois-60622; 2013.] Software and the dual solution is obtained. The optimum allocations of sample sizes are obtained with the help of dual solutions and the primal–dual relationship theorem. A numerical example is given to illustrate the procedure.

A hybrid method for solving multi-objective geometric programming problem

A multi–objective geometric programming problem contains more than one objective that needs to be achieved simultaneously. Such problems arise in many applications where two or more, sometimes conflicting objective functions have to be minimised concurrently. In this paper a new adaptive strategy called hybrid method proposed to find Pareto optimal solutions of the multi–objective geometric programming problem. Using geometric programming technique, a global best optimal solution is obtained from a set of Pareto optimal solution having a great impact on convergence of solution. The discussed hybrid method having a goal to enhance the optimisers over all performance by combining different optimisation techniques. In the proposed method we have combined e–constraint and weighted mean method and finally the result so obtained compared with the result obtained by fuzzy programming method. The solution procedure of the proposed hybrid method is illustrated by the numerical examples.

A comparative study on optimization techniques for solving multi-objective geometric programming problems

Various optimization techniques are there for mathematical modeling and design of many non-linear problems related to the various eld of science and engineering. The real world engineering problems are occurring in the form of multi-criteria having certain constraints. Till now, no such single optimization method exist which could optimize all objective functions simultaneously. In this paper, weighted sum method has been discussed to solve multi-objective geometric programming problem(MOGPP) and the result so obtained by weighted sum method has been compared with fuzzy programming method. Illustrative examples are presented to demonstrate the correctness of proposed model.

Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition usingϵ-constraint method

Optimization is an important tool widely used in formulation of the mathematical model and design of various decision making problems related to the science and engineering. Generally, the real world problems are occurring in the form of multi-criteria and multi-choice with certain constraints. There is no such single optimal solution exist which could optimize all the objective functions simultaneously. In this paper, ϵ -constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used to solve multi-objective Geometric programming problems(MOGPP) for searching a compromise solution. To find the suitable compromise solution for multi-objective Geometric programming problems, a brief solution procedure using ϵ -constraint method has been presented. The basic concept and classical principle of multi-objective optimization problems with KKT condition has been discussed. The result obtained by ϵ -constraint method with help of KKT condition has been compared with the result so obtained by Fuzzy programming method. Illustrative examples are presented to demonstrate the correctness of proposed model.

Fuzzy Geometric Programming in Multivariate Stratified Sample Surveys in Presence of Non-Response with Quadratic Cost Function

In this paper, the problem of non-response with significant travel costs in multivariate stratified sample surveys has been formulated of as a Multi-Objective Geometric Programming Problem (MOGPP). The fuzzy programming approach has been described for solving the formulated MOGPP. The formulated MOGPP has been solved with the help of LINGO Software and the dual solution is obtained. The optimum allocations of sample sizes of respondents and non respondents are obtained with the help of dual solutions and primal-dual relationship theorem. A numerical example is given to illustrate the procedure.

Multi-objective geometric programming problem with ∊-constraint method

In multi-objective geometric programming problem there are more than one objective functions. There is no single optimal solution which simultaneously optimizes all the objective functions. Under these conditions the decision makers always search for the most “preferred” solution, in contrast to the optimal solution. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper ∊-constraint method has been applied to find the non-inferior solution. A brief solution procedure of ∊-constraint method has been presented to find the non-inferior solution of the multi-objective programming problems. Further, the multi-objective programming problems is solved by the fuzzy programming technique to find the optimal compromise solution. Finally, two numerical examples are solved by both the methods and compared with their obtained solutions.

On Multi-Objective Geometric Programming Problems with a Negative Degree of Difficulty

تعد درجة الصعوبة مبدأ مهماً في نظرية البرمجة الهندسية الكلاسيكية. والمسألة المقابلة غالبا ما تكون غير مقبولة عند درجة الصعوبة السالبة وبما أن البحوث المنشورة في هذا المجال قليلة جدا.فان هذا البحث سيقدم الأفكار والمبادئ الأساسية للبرمجة الهندسية متعددة أهداف؛ فقد تم تطوير إجراء عددي لحل مسألة البرمجة الهندسية متعددة الأهداف ذات درجة الصعوبة السالبة مستخدمين طريقة الأوزان للحصول على حل بمستوى مقبول واستخدام تقنية المبسطة للتأكد من معقولية المسألة المقابلة؛ وذلك بإضافة حد ثابت لدالة الهدف الأساسية.

Multi-objective geometric programming problem and its applications

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.

Multi-item imperfect production lot size model with hybrid number cost parameters

In this study we have developed a multi-item finite production lot size model with reworking of imperfect quality items. When production stops, defected items are assumed to rework at a constant rate. The cost parameters in this model are taken here as hybrid numbers (i.e. some of the costs are fuzzy numbers as well as random variables). Then the model is converted into a multi-objective geometric programming (GP) problem. A numerical example is given to support the problem. A sensitivity analysis has given to study the nature of the objective functions.

Fuzzy programming technique to solve multi-objective geometric programming problems

Abstract In this paper fuzzy programming technique is used to solve a multi-objective geometric programming problem as a vector minimum problem. A fuzzy membership function is defined for the multi-objective geometric programming problem. Two numerical examples are presented to illustrate the method.

Fuzzy geometric programming with several objective functions

The theory of fuzzy sets is employed to solve the multiobjective geometric programming problem. It is emphasized that the product operator reduces the degree of difficulty.