Stackelberg-Nash equilibrium for multilevel programming with multiple followers using genetic algorithms

Multilevel programming offers a means of studying decentralized noncooperative decision systems. Unfortunately, multilevel programming is lacking efficient algorithms due to its computational difficulties such as nonconvexity and NP-hardness. This paper will design a genetic algorithm for solving Stackelberg-Nash equilibrium of nonlinear multilevel programming with multiple followers in which there might be information exchange among the followers. As a byproduct, we obtain a means for solving classical minimax problems. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed genetic algorithm.