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

Published online by Cambridge University Press:  10 June 2014

A.K. Ojha  and
Rashmi Ranjan Ota
A.K. Ojha
Affiliation:
School of Basic Sciences, Indian Institute of Technology, Bhubaneswar, 751013 Bhubaneswar, Odisha, India.. akojha57@yahoo.com; akojha@iitbbs.ac.in
Rashmi Ranjan Ota
Affiliation:
Department of Mathematics, ITER, SOA University, 751030 Bhubaneswar, Odisha, India.; otamath@yahoo.co.in
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Abstract

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.

Keywords

Geometric ProgrammingKarush−Kuhn−Tucker (KKT) conditionϵ-constraint methodfuzzy programmingduality theoremPareto optimal solution
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 4 , October 2014 , pp. 429 - 453
Copyright
© EDP Sciences, ROADEF, SMAI 2014

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