Multi-objective Optimization Problem with Bounded Parameters
RAIRO - Operations Research - Recherche Opérationnelle, Volume 48 (2014) no. 4, pp. 545-558.

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.

DOI: 10.1051/ro/2014023
Classification: 90C25, 90C29, 90C30
Keywords: multi-objective optimization problem, efficient solution, optimality condition, interval valued convex function
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     title = {Multi-objective {Optimization} {Problem} with {Bounded} {Parameters}},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Bhurjee, Ajay Kumar; Panda, Geetanjali. Multi-objective Optimization Problem with Bounded Parameters. RAIRO - Operations Research - Recherche Opérationnelle, Volume 48 (2014) no. 4, pp. 545-558. doi : 10.1051/ro/2014023. http://archive.numdam.org/articles/10.1051/ro/2014023/

[1] A. Bhurjee and G. Panda, Efficient solution of interval optimization problem. Math. Meth. Oper. Res. 76 (2012) 273-288. | MR | Zbl

[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. | MR | Zbl

[3] M. Hladik, Computing the tolerances in multiobjective linear programming. Optim. Methods Softw. 23 (2008) 731-739. | MR | Zbl

[4] M. Inuiguchi and M. Sakawa, Possible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency test. Fuzzy Sets Syst. 78 (1996) 231-241. | MR | Zbl

[5] H. Ishibuchi and H. Tanaka, Multiobjective programming in optimization of the interval objective function. Eur. J. Oper. Res. 48 (1990) 219-225. | Zbl

[6] O. Mangasarian, Nonlinear Programming. New York: McGraw Hill (1969). | MR | Zbl

[7] R. Moore, Interval Analysis. Prentice-Hall (1966). | MR | Zbl

[8] C. Oliveira and C.H. Antunes, Multiple objective linear programming models with interval coefficients an illustrated overview. Eur. J. Oper. Res. 181 (2007) 1434-1463. | Zbl

[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. | MR

[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. | Zbl

[11] B. Urli and R. Nadeau, An interactive method to multiobjective linear programming problem with interval coefficients. INFOR 30 (1992) 127-137. | Zbl

[12] H.C. Wu, On interval-valued nonlinear programming problems. J. Math. Anal. Appl. 338 (2008) 299-316. | MR | Zbl

[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. | MR | Zbl

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