Taylor Approach for Solving Non-Linear Bi-level ProgrammingProblem

In recent years the bi-level programming problem (BLPP)is interested by many researchers and it is known as anappropriate tool to solve the real problems in several areassuch as computer science, engineering, economic, traffic,finance, management and so on. Also it has been provedthat the general BLPP is an NP-hard problem. Theliterature shows a few attempts for using approximatemethods. In this paper we attempt to develop an effectiveapproach based on Taylor theorem to obtain anapproximate solution for the non-linear BLPP. In thisapproach using the Karush-Kuhn–Tucker, the BLPP hasbeen converted to a non-smooth single problem, and then itis smoothed by the Fischer – Burmeister function. Finallythe smoothed problem is solved using an approach basedon Taylor theorem. The presented approach achieves anefficient and feasible solution in an appropriate time whichhas been is evaluated by comparing to references and testproblems.

کلیدواژه ها:

Non-linear bi-level programming problem ، Taylortheorem ، Karush-Kuhn–Tucker conditions ، smoothing methods