A Hybrid Approach for Solving Nonlinear Bilevel Programming Problems Using Genetic Algorithms

The paper focuses on a special nonlinear bilevel programming problem(BLPP), and its characteristic is that the follower's programming is convex and quadratic, whereas there are no any additional requirements for the leader's functions. In order to solve the complex problem efficiently, it is first converted into an equivalent single-level programming by using Karush-Kuhn-Tucher (K-K-T) conditions, and then a hybrid genetic algorithm(HGA), combined with an enumeration technique of the bases, is proposed to solve the equivalent problem. At first, a mixed encoding scheme is given, involving the leader's variables and the bases of the follower's linear complementarity system, In addition, we present a fitness function which consists of the leader's objective and a penalty term, and by which the feasible and infeasible individuals can be identified. In order to illustrate the efficiency of HGA, 10 test problems selected from literature are solved, and the computational results show that the proposed algorithm is efficient and robust.