A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems
Joint Authors
Jia, Fei
Ren, Aihong
Wang, Yuping
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-13
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We propose a hybrid algorithm based on estimation of distribution algorithm (EDA) and Nelder-Mead simplex method (NM) to solve a class of nonlinear bilevel programming problems where the follower’s problem is linear with respect to the lower level variable.
The bilevel programming is an NP-hard optimization problem, for which EDA-NM is applied as a new tool aiming at obtaining global optimal solutions of such a problem.
In fact, EDA-NM is very easy to be implementedsince it does not require gradients information.
Moreover, the hybrid algorithm intends to produce faster and more accurate convergence.
In the proposed approach, for fixed upper level variable, we make use of the optimality conditions of linear programming to deal with the follower’s problem and obtain its optimal solution.
Further, the leader’s objective function is taken as the fitness function.
Based on these schemes, the hybrid algorithm is designed by combining EDA with NM.
To verify the performance of EDA-NM, simulations on some test problems are made, and the results demonstrate that the proposed algorithm has a better performance than the compared algorithms.
Finally, the proposed approach is used to solve a practical example about pollution charges problem.
American Psychological Association (APA)
Ren, Aihong& Wang, Yuping& Jia, Fei. 2013. A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-467331
Modern Language Association (MLA)
Ren, Aihong…[et al.]. A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems. Journal of Applied Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-467331
American Medical Association (AMA)
Ren, Aihong& Wang, Yuping& Jia, Fei. A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-467331
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-467331