Mathematical Programming: Series A and B
Computational difficulties of bilevel linear programming
Operations Research
Descent approaches for quadratic bilevel programming
Journal of Optimization Theory and Applications
A Survey of Optimization by Building and Using Probabilistic Models
Computational Optimization and Applications
From Recombination of Genes to the Estimation of Distributions I. Binary Parameters
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
Bi-Level Optimisation Using Genetic Algorithm
ICAIS '02 Proceedings of the 2002 IEEE International Conference on Artificial Intelligence Systems (ICAIS'02)
Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms (Studies in Fuzziness and Soft Computing)
Optimization of limited network capacity with toll settings
Information Sciences: an International Journal
A bi-level programming for logistics network design with system-optimized flows
Information Sciences: an International Journal
Model, solution concept, and Kth-best algorithm for linear trilevel programming
Information Sciences: an International Journal
Practical Bilevel Optimization: Algorithms and Applications
Practical Bilevel Optimization: Algorithms and Applications
Applied Soft Computing
INFORMS Journal on Computing
A simulated annealing method based on a specialised evolutionary algorithm
Applied Soft Computing
Estimation of particle swarm distribution algorithms: Combining the benefits of PSO and EDAs
Information Sciences: an International Journal
On bilevel multi-follower decision making: General framework and solutions
Information Sciences: an International Journal
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
A global optimization method for nonlinear bilevel programmingproblems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A comparative study of population-based optimization algorithms for turning operations
Information Sciences: an International Journal
Optimization of cutting parameters in multi-pass turning using artificial bee colony-based approach
Information Sciences: an International Journal
An artificial bee colony algorithm for the maximally diverse grouping problem
Information Sciences: an International Journal
A new hybrid artificial bee colony algorithm for robust optimal design and manufacturing
Applied Soft Computing
Information Sciences: an International Journal
Bilevel direct search method for leader-follower problems and application in health insurance
Computers and Operations Research
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In this paper, a novel evolutionary algorithm called estimation of distribution algorithm (EDA) is proposed for solving a special class of nonlinear bilevel programming problems (BLPPs) in which the lower level problem is a convex programming problem for each given upper level decision. This special type of BLPP is transformed into a equivalent single-level constrained optimization problem using the Karush-Kuhn-er conditions of the lower level problem. Then, we propose an EDA based on the statistical information of the superior candidate solutions to solve the transformed problem. We stress that the new population of individuals is sampled from the probabilistic distribution of those superior solutions. Thus, one of the main advantages of EDA over most other meta-heuristics is its ability to adapt the operators to the structure of the problem, although adaptation in EDA is usually limited by the initial choice of the probabilistic model. In addition, two specific rules are established in the initialization procedure to make use of the hierarchical structure of BLPPs and to handle the constraints. Moreover, without requiring the differentiability of the objective function, or the convexity of the search space of the equivalent problem, the proposed algorithm can address nonlinear BLPPs with non-differentiable or non-convex upper level objective function and upper level constraint functions. Finally, the proposed algorithm has been applied to 16 benchmark problem; in five of these problems, all of the upper level variables and lower level variables are 10-dimensional. The numerical results compared with those of other methods reveal the feasibility and effectiveness of the proposed algorithm.