A Genetic Algorithm for Solving Linear-Quadratic Bilevel Program-Ming Problems
In this paper, we focus on a special linear-quadratic bilevel programming problem in which the follower’s problem is a convex-quadratic programming, whereas the leader’s functions are linear. At first, based on Karush-Kuhn-Tucher(K-K-T) conditions, the original problem is transformed into an equivalent nonlinear programming problem in which the objective and constraint functions are linear except for the complementary slack conditions. Then, a genetic algorithm is proposed to solve the equivalent problem. In the proposed algorithm, the individuals are encoded in two phases. Finally, the efficiency of the approach is demonstrated by an example.
Wenya Tian and Linli Xu
H. C. Li and Y. P. Wang, "A Genetic Algorithm for Solving Linear-Quadratic Bilevel Program-Ming Problems", Advanced Materials Research, Vol. 186, pp. 626-630, 2011