Mathematical Programming: Series A and B
Annals of Operations Research - Special issue on hierarchical optimization
Descent approaches for quadratic bilevel programming
Journal of Optimization Theory and Applications
Global Optimization of Nonlinear Bilevel Programming Problems
Journal of Global Optimization
Bi-Level Optimisation Using Genetic Algorithm
ICAIS '02 Proceedings of the 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS'02)
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
An Evolutionary Algorithm for Global Optimization Based on Level-Set Evolution and Latin Squares
IEEE Transactions on Evolutionary Computation
A global optimization method for nonlinear bilevel programmingproblems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Estimation of distribution algorithm for a class of nonlinear bilevel programming problems
Information Sciences: an International Journal
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When the leader's objective function of a nonlinear bilevel programming problem is nondifferentiable and the follower's problem of it is nonconvex, the existing algorithms cannot solve the problem. In this paper, a new effective evolutionary algorithm is proposed for this class of nonlinear bilevel programming problems. First, based on the leader's objective function, a new fitness function is proposed that can be easily used to evaluate the quality of different types of potential solutions. Then, based on Latin squares, an efficient crossover operator is constructed that has the ability of local search. Furthermore, a new mutation operator is designed by using some good search directions so that the offspring can approach a global optimal solution quickly. To solve the follower's problem efficiently, we apply some efficient deterministic optimization algorithms in the MATLAB Toolbox to search for its solutions. The asymptotically global convergence of the algorithm is proved. Numerical experiments on 25 test problems show that the proposed algorithm has a better performance than the compared algorithms on most of the test problems and is effective and efficient.