Presentation and Solving Non-Linear Quad-Level Programming Problem Utilizing a Heuristic Approach Based on Taylor Theorem

Document Type : Original Manuscript


Department of Mathematics, University of Raparin, Ranya, Kurdistan Region, Iraq


The multi-level programming problems are attractive for many researchers because of their application in several areas such as economic, traffic, finance, management, transportation, information technology, engineering and so on. It has been proven that even the general bi-level programming problem is an NP-hard problem, so the multi-level problems are practical and complicated problems therefore solving these problems 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 quad-level programming problem, but also it has not been studied by any researcher.  The most important part of this paper is presentation and studying of a new model of non-linear multi-level problems.Then we attempt to develop an effective approach based on Taylor theorem for solving the non-linear quad-level programming problem. In this approach, by using aproposedsmoothing method the quad-level programming problem is converted to a linear single problem. Finally, the single level problem is solved using the algorithm based on Taylor algorithm. The presented approach achieves an efficient and feasible solution in an appropriate time which has been evaluated by solving test problems. 


  • Proposing and studying of a new model of multi-level name quad-level programming problem.
  • Smoothing of the non-linear quad-level programming problem.
  • Linearization of the proposed non-linear problem.
  • Presentation of a new algorithm based on Taylor algorithm.
  • Proposing and solving of examples by the method.


Main Subjects