Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T16:09:03.976Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-objective Optimization Problem with BoundedParameters

Published online by Cambridge University Press:  11 July 2014

Ajay Kumar Bhurjee  and
Geetanjali Panda
Ajay Kumar Bhurjee
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, India.. geetanjali@maths.iitkgp.ernet.in
Geetanjali Panda
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, India.. geetanjali@maths.iitkgp.ernet.in
Get access

Abstract

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

Keywords

Multi-objective optimization problemefficient solutionoptimality conditioninterval valued convex function
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 4 , October 2014 , pp. 545 - 558
Copyright
© EDP Sciences, ROADEF, SMAI 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bhurjee, A. and Panda, G., Efficient solution of interval optimization problem. Math. Meth. Oper. Res. 76 (2012) 273–288. Google Scholar
Gong, D., Sun, J. and Ji, X., Evolutionary algorithms with preference polyhedron for interval multi-objective optimization problems. Inform. Sci. 233 (2013) 141–161. Google Scholar
Hladik, M., Computing the tolerances in multiobjective linear programming. Optim. Methods Softw. 23 (2008) 731–739. Google Scholar
Inuiguchi, M. and Sakawa, M., Possible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency test. Fuzzy Sets Syst. 78 (1996) 231–241. Google Scholar
Ishibuchi, H. and Tanaka, H., Multiobjective programming in optimization of the interval objective function. Eur. J. Oper. Res. 48 (1990) 219–225. Google Scholar
O. Mangasarian, Nonlinear Programming. New York: McGraw Hill (1969).
R. Moore, Interval Analysis. Prentice-Hall (1966).
Oliveira, C. and Antunes, C.H., Multiple objective linear programming models with interval coefficients an illustrated overview. Eur. J. Oper. Res. 181 (2007) 1434–1463. Google Scholar
Rivaz, S. and Yaghoobi, M., Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients. Central Eur. J. Oper. Res. 21 (2013) 625–649. Google Scholar
Soares, G., Parreiras, R., Jaulin, L., Vasconcelos, J. and Maia, C., Interval robust multi-objective algorithm. Nonlinear Anal. Theor. Meth. Appl. 71 (2009) 1818–1825. Google Scholar
Urli, B. and Nadeau, R., An interactive method to multiobjective linear programming problem with interval coefficients. INFOR 30 (1992) 127–137. Google Scholar
Wu, H.C., On interval-valued nonlinear programming problems. J. Math. Anal. Appl. 338 (2008) 299–316. Google Scholar
Wu, H.C., The karush-kuhn-tucker optimality conditions in multiobjective programming problems with interval-valued objective functions. Eur. J. Oper. Res. 196 (2009) 49–60. Google Scholar