In the recent years, the bi-level and tri-level programming problems (TLPP) are interested by many researchers and TLPP is known as an appropriate tool to solve the real problems in several areas such as economic, traffic, finance, management, and so on. Also, it has been proven that the general TLPP is an NP-hard problem. The literature shows a few attempts for solving using TLPP. In this paper, we attempt to develop two effective approaches, one based on Taylor theorem and the other based on the hybrid algorithm by combining the penalty function and the line search algorithm for solving the linear TLPP. In these approaches, by using Karush-Kuhn-Tucker conditions, TLP Pischanged to non-smooth single problem, and then it is smoothed by proposed functions. Finally, the smoothed problem is solved using both of the proposed approaches. The presented approaches achieve an efficient and feasible solution in an appropriate time which has been evaluated by comparing to references and test problems.
