A Genetic Algorithm for Solving a Special Class of Nonlinear Bilevel Programming Problems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Application of particle swarm optimization algorithm for solving bi-level linear programming problem
Computers & Mathematics with Applications
An adaptive penalty formulation for constrained evolutionary optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Solving a type of biobjective bilevel programming problem using NSGA-II
Computers & Mathematics with Applications
Constructing test problems for bilevel evolutionary multi-objective optimization
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Bilevel multi-objective optimization problem solving using progressively interactive EMO
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
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A hierarchical particle swarm optimization for solving bilevel programming problems
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
PRICAI'12 Proceedings of the 12th Pacific Rim international conference on Trends in Artificial Intelligence
Evolutionary bilevel optimization
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
Estimation of distribution algorithm for a class of nonlinear bilevel programming problems
Information Sciences: an International Journal
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Integrated Computer-Aided Engineering
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In this paper, a special nonlinear bilevel programming problem (nonlinear BLPP) is transformed into an equivalent single objective nonlinear programming problem. To solve the equivalent problem effectively, we first construct a specific optimization problem with two objectives. By solving the specific problem, we can decrease the leader's objective value, identify the quality of any feasible solution from infeasible solutions and the quality of two feasible solutions for the equivalent single objective optimization problem, force the infeasible solutions moving toward the feasible region, and improve the feasible solutions gradually. We then propose a new constraint-handling scheme and a specific-design crossover operator. The new constraint-handling scheme can make the individuals satisfy all linear constraints exactly and the nonlinear constraints approximately. The crossover operator can generate high quality potential offspring. Based on the constraint-handling scheme and the crossover operator, we propose a new evolutionary algorithm and prove its global convergence. A distinguishing feature of the algorithm is that it can be used to handle nonlinear BLPPs with nondifferentiable leader's objective functions. Finally, simulations on 31 benchmark problems, 12 of which have nondifferentiable leader's objective functions, are made and the results demonstrate the effectiveness of the proposed algorithm.