Multi-objective Optimization Problem with Bounded Parameters

Ajay Kumar Bhurjee; Geetanjali Panda

RAIRO - Operations Research - Recherche Opérationnelle (2014)

  • Volume: 48, Issue: 4, page 545-558
  • ISSN: 0399-0559

Abstract

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In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.

How to cite

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Bhurjee, Ajay Kumar, and Panda, Geetanjali. "Multi-objective Optimization Problem with Bounded Parameters." RAIRO - Operations Research - Recherche Opérationnelle 48.4 (2014): 545-558. <http://eudml.org/doc/275004>.

@article{Bhurjee2014,
abstract = {In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.},
author = {Bhurjee, Ajay Kumar, Panda, Geetanjali},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {multi-objective optimization problem; efficient solution; optimality condition; interval valued convex function; nonlinear multi-objective optimization problems; interval parameters; interval-valued convex function},
language = {eng},
number = {4},
pages = {545-558},
publisher = {EDP-Sciences},
title = {Multi-objective Optimization Problem with Bounded Parameters},
url = {http://eudml.org/doc/275004},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Bhurjee, Ajay Kumar
AU - Panda, Geetanjali
TI - Multi-objective Optimization Problem with Bounded Parameters
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 4
SP - 545
EP - 558
AB - In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.
LA - eng
KW - multi-objective optimization problem; efficient solution; optimality condition; interval valued convex function; nonlinear multi-objective optimization problems; interval parameters; interval-valued convex function
UR - http://eudml.org/doc/275004
ER -

References

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  2. [2] D. Gong, J. Sun and X. Ji, Evolutionary algorithms with preference polyhedron for interval multi-objective optimization problems. Inform. Sci.233 (2013) 141–161. Zbl1284.90099MR3036834
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  9. [9] S. Rivaz and M. Yaghoobi, Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients. Central Eur. J. Oper. Res.21 (2013) 625–649. MR3092851
  10. [10] G. Soares, R. Parreiras, L. Jaulin, J. Vasconcelos and C. Maia, Interval robust multi-objective algorithm. Nonlinear Anal. Theor. Meth. Appl.71 (2009) 1818–1825. Zbl1238.90140
  11. [11] B. Urli and R. Nadeau, An interactive method to multiobjective linear programming problem with interval coefficients. INFOR30 (1992) 127–137. Zbl0760.90084
  12. [12] H.C. Wu, On interval-valued nonlinear programming problems. J. Math. Anal. Appl.338 (2008) 299–316. Zbl1278.90392MR2386417
  13. [13] H.C. Wu, The karush-kuhn-tucker optimality conditions in multiobjective programming problems with interval-valued objective functions. Eur. J. Oper. Res.196 (2009) 49–60. Zbl1190.90198MR2477727

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