International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.3, Jun. 2015, Pub. Date: May 16, 2015
Smoothing and Solving Linear Quad-Level Programming Problem Using Mathematical Theorems
[01] Eghbal Hosseini, Payamenur University of Tehran, Department of Mathematics, Tehran, Iran.
[02] Isa Nakhai Kamalabadi, University of Kurdistan, Department of Industy, Sanandaj, Iran.
The multi-level programming problems are attractive for many researchers because of their application in several areas such as economic, traffic, finance, management, computer science, informatics, transportation and so on. Among these, the quad-level programming problem (QLPP) is an appropriate tool to model these real problems because many real problems have four levels. It has been proven that even the general bi-level programming problem is an NP-hard problem, so the multi-level problem are practical and complicated problems therefore solving these problem would be significant. The literature shows several algorithms to solve different forms of the bi-level programming problems (BLPP). Not only there is no any algorithm for solving QLPP, but also it has not been studied by any researcher. The most important part in this paper is presentation and studying of a new model (QLPP) of multi-level problems. Also we attempt for developing two applied problems which would be modeled to the linear QLPP, then we attempt for developing an effective approach based on analyze theorems for solving the linear QLPP. In this approach, by using the heuristic method the QLPP is converted to a linear single problem. Finally, the single level problem is solved using the enumeration algorithm. The presented approach achieves an efficient and feasible solution in an appropriate time which has been evaluated by solving test problems.
Linear Quad-Level Programming Problem, Heuristic Method, Enumeration Algorithm
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