Mathematical Programming: Series A and B
A branch and bound algorithm for the bilevel programming problem
SIAM Journal on Scientific and Statistical Computing
New branch-and-bound rules for linear bilevel programming
SIAM Journal on Scientific and Statistical Computing
Annals of Operations Research - Special issue on hierarchical optimization
Heuristic algorithms for delivered price spatially competitive network facility location problems
Annals of Operations Research - Special issue on hierarchical optimization
Annals of Operations Research - Special issue on hierarchical optimization
Descent approaches for quadratic bilevel programming
Journal of Optimization Theory and Applications
Bi-Level Optimisation Using Genetic Algorithm
ICAIS '02 Proceedings of the 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS'02)
A global optimization method for nonlinear bilevel programmingproblems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
On computational search for optimistic solutions in bilevel problems
Journal of Global Optimization
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In this paper, a special nonlinear bilevel programming problem (BLPP), in which the follower's problem is a convex quadratic programming in y, is transformed into an equivalent single-level programming problem by using Karush-Kuhn-Tucker(K-K-T) condition. To solve the equivalent problem effectively, firstly, a genetic algorithm is incorporated with Lemke algorithm. For x fixed, the optimal solution y of the follower's problem can be obtained by Lemke algorithm, then (x,y) is a feasible or approximately feasible solution of the transformed problem and considered as a point in the population; secondly, based on the best individuals in the population, a special crossover operator is designed to generate high quality individuals; finally, a new hybrid genetic algorithm is proposed for solving this class of bilevel programming problems. The simulation on 20 benchmark problems demonstrates the effectiveness of the proposed algorithm.