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

A. K. Ojha; Rashmi Ranjan Ota

RAIRO - Operations Research - Recherche Opérationnelle (2014)

  • Volume: 48, Issue: 4, page 429-453
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Ojha, A. K., and Ota, Rashmi Ranjan. "Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method." RAIRO - Operations Research - Recherche Opérationnelle 48.4 (2014): 429-453. <http://eudml.org/doc/275036>.

@article{Ojha2014,
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.},
author = {Ojha, A. K., Ota, Rashmi Ranjan},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {geometric programming; Karush-Kuhn-Tucker (KKT) condition; ϵ-constraint method; fuzzy programming; duality theorem; Pareto optimal solution; -constraint method},
language = {eng},
number = {4},
pages = {429-453},
publisher = {EDP-Sciences},
title = {Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method},
url = {http://eudml.org/doc/275036},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Ojha, A. K.
AU - Ota, Rashmi Ranjan
TI - Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 4
SP - 429
EP - 453
AB - 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.
LA - eng
KW - geometric programming; Karush-Kuhn-Tucker (KKT) condition; ϵ-constraint method; fuzzy programming; duality theorem; Pareto optimal solution; -constraint method
UR - http://eudml.org/doc/275036
ER -

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