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2018 | OriginalPaper | Chapter

A New Solution Method for a Class of Fuzzy Random Bilevel Programming Problems

Authors : Aihong Ren, Xingsi Xue

Published in: Advances in Intelligent Information Hiding and Multimedia Signal Processing

Publisher: Springer International Publishing

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Abstract

This paper investigates a kind of bilevel programming with fuzzy random variable coefficients in both objective functions and the right hand side of constraints. On the basis of the notion of Er-expected value of fuzzy random variable, the upper and lower level objective functions can be replaced with their corresponding Er-expected values. In terms of probability over defuzzified operator, fuzzy stochastic constraints can be converted into the equivalent forms. Based on these, the fuzzy random bilevel programming problem can be transformed into its deterministic one. Then we suggest differential evolution algorithm to solve the final crisp problem. Finally, a numerical example is given to illustrate the proposed method.

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Literature
1.
Zhang, G.Q., Gao, Y., Lu, J.: Competitive strategic bidding optimization in electricity markets using bilevel programming and swarm technique. IEEE Trans. Industr. Electron. 58(6), 2138–2146 (2011)CrossRef
2.
Gzara, F.: A cutting plane approach for bilevel hazardous material transport network design. Oper. Res. Lett. 41(1), 40–46 (2013)MathSciNetCrossRefMATH
3.
Fontaine, P., Minner, S.: Benders decomposition for discrete-continuous linear bilevel problems with application to traffic network design. Transp. Res. Part B Methodol. 70, 163–172 (2014)CrossRef
4.
Cecchini, M., Ecker, J., Kupferschmid, M., Leitch, R.: Solving nonlinear principal-agent problems using bilevel programming. Eur. J. Oper. Res. 230(2), 364–373 (2013)MathSciNetCrossRefMATH
5.
Dempe, S.: Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52(3), 333–359 (2003)MathSciNetCrossRefMATH
6.
7.
8.
Bard, J.F.: Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers, Dordrecht, Boston, London (1998)CrossRefMATH
9.
Dempe, S.: Foundations of Bilevel Programming. Kluwer Academic Publishers, Dordrecht, Boston, London (2002)MATH
10.
Dempe, S., Kalashnikov, V., Pérez-Valdés, G.A., Kalashnykova, N.: Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks. Kluwer Academic Publishers, Springer, Berlin (2015)
11.
Zhang, G.Q., Lu, J., Dillon, T.: Fuzzy linear bilevel optimization: solution concepts, approaches and applications. Stud. Fuzziness Soft Comput. 215, 351–379 (2007)MathSciNetCrossRefMATH
12.
Gao, Y., Zhang, G.Q., Ma, J., Lu, J.: A \(\lambda \)-cut and goal-programming-based algorithm for fuzzy-linear multiple-objective bilevel optimization. IEEE Trans. Fuzzy Syst. 18(1), 1–13 (2010)CrossRef
13.
Sakawa, M., Katagiri, H.: Interactive fuzzy programming based on fractile criterion optimization model for two-level stochastic linear programming problems. Cybern. Syst. 41(7), 508–521 (2010)CrossRefMATH
14.
Yano, H.: Hierarchical Multiobjective stochastic linear programming problems considering both probability maximization and fractile optimization. IAENG Int. J. Appl. Mathe. 42(2), 91–98 (2012)MathSciNet
15.
16.
Sakawa, M., Katagiri, H.: Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization. CEJOR 20, 101–117 (2012)MathSciNetCrossRefMATH
17.
Sakawa, M., Katagiri, H.: Interactive fuzzy random cooperative two-level linear programming through level sets based probability maximization. Expert Syst. Appl. 40, 1400–1406 (2013)CrossRef
18.
Ren, A., Wang, Y.P.: Optimistic Stackelberg solutions to bilevel linear programming with fuzzy random variable coefficients. Knowl.-Based Syst. 67, 206–217 (2014)CrossRef
19.
20.
21.
Eshghi, K., Nematian, J.: Special classes of mathematical programming models with fuzzy random variables. J. Intell. Fuzzy Syst. 19(2), 131–140 (2008)MATH
22.
23.
24.
Aiche, F., Abbas, M., Dubois, D.: Chance-constrained programming with fuzzy stochastic coefficients. Fuzzy Optim. Decis. Making 12, 125–152 (2013)MathSciNetCrossRef
25.
Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)MathSciNetCrossRefMATH
26.
Ren, A.H., Wang, Y.P.: An interval programming approach for bilevel linear programming problem with fuzzy random coefficients. In: 2013 IEEE Congress on Evolutionary Computation (CEC2013), pp. 462–469 (2013)
Metadata
Title
A New Solution Method for a Class of Fuzzy Random Bilevel Programming Problems
Authors
Aihong Ren
Xingsi Xue
Copyright Year
2018
Book
Advances in Intelligent Information Hiding and Multimedia Signal Processing

Print ISBN: 978-3-319-63855-3

Electronic ISBN: 978-3-319-63856-0

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-63856-0_29

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