Solving linear-quadratic bi-level programming and linear-fractional bi-level programming problems using genetic algorithm

The bi-level programming problem (BLPP) is a suitable method for solving the real and complex problems in applicable areas. There are several forms of the BLPP as an NP-hard problem. The linear-quadratic bi-level programming (LQBP) and the linear-fractional bi-level programming (LFBP) problems are two important forms of the BLPP. In this article, we show an effective method based on genetic algorithm (GA) for solving such problems. To obtain efficient upper bounds and lower bounds we use the Karush-Kuhn-Tucker (KKT) conditions for transforming the LQBP and the LFBP into single level problems. Thus by using the proposed GA, the single problems are solved. The proposed approach achieves efficient and feasible solutions and they are evaluated by comparing with references and test problems.