Decompostion The Parametric Space in Stochastic Multiobjective Programming Problem
Main Article Content
Abstract
In this paper, we introduce an approach for decomposing the parametric space in stochastic multiobjective programming problem (SMOPP) with random parameters in both the objective functions and in the constraints.
An algorithm based on determine a stability set of the first kind is proposed to decompose the parametric space of SMOPP.
An illustrative example is driven to discuss the proposed algorithm.
Downloads
Article Details
References
B. I. Bayoumi, A.A. El-Sawy, N.L. Baseley, I.K. Yousef, A.M. Widyan, Determining the efficient solutions for bicriteria programming problems with random variables in both the objective functions and the constraints, J. of KSIAM Vol. 9. No. 1, (2005) 1-12.
B. I. Bayoumi, A.A. El-Sawy, N.L. Baseley, I.K. Yousef, A.M. Widyan, Decompostion the parametric space in stochastic bicriteria programming problem, Sci Bull. , Faculty of Engineering, Ain Shams University, Vol 46, No. 3, (2005).
M. A. Kassem, Stability of Multiobjective nonlinear programming problems with random variables in the objective functions, Fuzzy sets and Systems 102 (1999) 247-252.
Andrzej Ruszczynski, Artur Swietanowski, Accelerating the regularized decomposition method for two stage stochastic linear problem. European Journal of Operational Research 101 (1997) 328-342
Andrzej Ruszczynski, Decomposition methods in stochastic programming, Mathematical Programming 79 (1997) 333-353.
Rudiger Schultz, Some Aspects of Stability in Stochastic Programming, Annals of Operations Research 100 (2000) 55 -84.
I. L. Averbakh, An Iterative Decomposition method in single-stage stochastic integer-programming problems, U.S.S.R. Comput. Maths. Math. phys., Vol. 30, No. 5, (1990) 133-139.
Hercules Vladimirou, Computational assessment of distributed decomposition methods for stochastic linear programs, European Journal of Operational Research 108 (1998) 653-670.
Adel M. Widyan, Obtaining the Efficient Solutions for Multcriterion Programming Problems With Stochastic Parameters, Journal of Natural Sciences and Mathematics Vol. 9, No. 1, (2016) 17-25.
Omar M. Saad, Mohamed Tamer B. Farag, On the Solution of Chance-Constrained Multiobjective Integer Quadratic Programming Problem with Some Stability Notions, Gen. Math. Notes, Vol. 20, No. 2, (2014) 111-124.
Mohmoud A. Abo-Sinna, A. H. Amer, Hend H. El Sayed, An interactive algorithm for decomposing the parametric space in fuzzy multiobjective dynamic programming problem, Applied Mathematics and Computation 174 (2006) 684-699.
M. A. Abo-Sinna, M. L. Hussein, An algorithm for decomposing the parametric space in multiobjective dynamic programming problems, European Journal of Operational Research 73 (1994) 532-538.
M. A. Kassem, Stability of possibilistic multiobjective nonlinear programming problems without differentiability, Fuzzy sets and Systems 94 (1998) 239-246.
M. A. Abo-Sinna, Generating -Pareto optimal solution to multiobjective nonlinear programming problems with fuzzy parameters: a decomposition method, The Journal of fuzzy Mathematics10 (1) (2002) 423-439..
Schrage, L., Optimization Modeling with LINGO, 6th. ed. Chicago, IL: LINDO Systems Inc., (2006).