Bi-Level Multi-Objective Large Scale Integer Quadratic Programming Problem with Symmetric Trapezoidal Fuzzy Numbers in the Objective Functions

O. E. Emam

Department of Information Systems, Faculty of Computer Science and Information, Helwan University, P.O.Box 11795, Egypt.

E. Fathy

Department of Mathematics, Faculty of Science, Helwan University, P.O.Box 11795, Egypt.

A. A. Abdullah *

Department of Information Systems, Higher Institute of Computer Science and Information Systems, Fifth Avenue - New Cairo, Egypt.

*Author to whom correspondence should be addressed.


Abstract

This paper focuses on the solution of a Bi-Level Multi-Objective Large Scale Integer Quadratic Programming (BLMOLSIQP) problem, where all the decision parameters in the objective functions are symmetric trapezoidal fuzzy numbers, and have block angular structure of the constraints. The suggested algorithm based on α-level sets of fuzzy numbers, weighted sum method, Taylor’s series, Decomposition algorithm, and also the Branch and Bound method is used to find a compromised solution for the problem under consideration. Then, the proposed algorithm is compared to Frank and Wolfe algorithm to demonstrate its effectiveness. Moreover, the theoretical results are illustrated with the help of a numerical example.

Keywords: Large scale, integer programming, quadratic programming, multi-objective, fuzzy programming, bi-level programming.


How to Cite

Emam, O. E., Fathy, E., & Abdullah, A. A. (2018). Bi-Level Multi-Objective Large Scale Integer Quadratic Programming Problem with Symmetric Trapezoidal Fuzzy Numbers in the Objective Functions. Journal of Advances in Mathematics and Computer Science, 27(2), 1–15. https://doi.org/10.9734/JAMCS/2018/40808

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