حل مسألة البرمجة ثنائية المستوى (الخطية-التربيعية ) بتطبيق الخوارزمية الجينية

1-Bard, J. F., Plummer, J., & Sourie, J. C (2000)." A bilevel programming approach to determining tax credits for biofuel production". European Journal of Operational Research, 120(1), 30-46.‏

2-Colson, B., Marcotte, P., & Savard, G. (2007). "An overview of bilevel optimization". Annuls of operations research, 153(1), 235-256.‏ DOI: https://doi.org/10.1007/s10479-007-0176-2

3- Dempe, S., & Zemkoho, A. B. (2012). "On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem". Nonlinear Analysis: Theory, Methods & Applications, 75(3), 1202-1218.‏ DOI: https://doi.org/10.1016/j.na.2011.05.097

4-Dempe, S., Mordukhovich, B. S., & Zemkoho, A. B. (2014). "Necessary optimality conditions in pessimistic bilevel programming". Optimization, 63(4), 505-533 DOI: https://doi.org/10.1080/02331934.2012.696641

5-Edmunds, T. A., & Bard, J. F. (1991)." Algorithms for nonlinear bilevel mathematical programs". IEEE transactions on Systems, Man, and Cybernetics, 21(1), 83-89. DOI: https://doi.org/10.1109/21.101139

6-Eghbal Hosseini,Isa Nakhai kamalabadi (2013) "(a genetic approach for solving bi-level programming problems)" AMO-Advanced modeling and optimization,volume15, Number 3, 2013.

7-Frederick S.Hiller ,Gerald j.Lieberman "(introduction to operations research )" ninth edition(2010).published by McGraw-Hill cobyright 2010.

8-Fricke, C. (2003). "An Introduction to Bilevel Programming". Departement of Mathematics and Statistics, University of Melbourne.

9-G.Z.wang ,wan,x.wang,y.lv, "Genetic algorithm based on simplex method for solving linear-quadratic bi-level programming problem", computers and mathematics with applications , 2550-2555, 2008

10-Ghadimi, S., & Wang, M. (2018). "Approximation Methods for Bilevel Programming".Cornell university. arXiv:1802.0224 vl[math.oc] 6 Feb 2018. ‏

11- H.I.Calvete,c. cale, "Apenalty method for solving bi-level linear-fractional linear programming problems", Asia-pacific journal of operational research 207-224, 2004.

12-Hamdy Taha ,"Operations Research: An Introduction (8thEdition)"and(9th Edition). Published by Prentice Hall (2007)

13-Hansen, P., Jaumard, B., & Sa-vard, G. (1992)." New branch-and-bound rules for linear bilevel programming". SIAM Journal on scientific and Statistical Computing, 13(5), 1194-1217. DOI: https://doi.org/10.1137/0913069

14-Hosseini, E., & Kamalabadi, I. N. (2015). "Two approach to solve nonlinear bilevelfor solving non-linear bi-level programming problem". Advances in Computer Science: an International Journal.‏

15- Lv, Y., Hu, T., Wang, G., & Wan, Z. (2008). "A neural network approach for solving nonlinear bilevel programming problem". Computers & Mathematics with Applications, 55(12), 2823-2829. DOI: https://doi.org/10.1016/j.camwa.2007.09.010

16-Ma, S. (2016)." A nonlinear bi-level programming approach for product portfolio management". SpringerPlus, 5(1), 727.‏ DOI: https://doi.org/10.1186/s40064-016-2421-0

17-Marcotte, P. (1986). "Network design problem with congestion effects: A case of bilevel programming". Mathematical programming, 34(2), 142-162. DOI: https://doi.org/10.1007/BF01580580

18-Marcotte, P., Savard, G., & Zhu, D. L. (2001). "A trust region algorithm for nonlinear bilevel programming". Operations research letters, 29(4), 171-179.‏ DOI: https://doi.org/10.1016/S0167-6377(01)00092-X

19-Migdalas, A. (1995). "Bilevel programming in traffic planning: Models, methods and challenge". Journal of global optimization, 7(4), 381-405. DOI: https://doi.org/10.1007/BF01099649

20-Moore, J. T., & Bard, J. F. (1990)." The mixed integer linear bilevel programming problem". Operations research, 38(5), 911-921. DOI: https://doi.org/10.1287/opre.38.5.911

21-Pal, B. B., & Moitra, B. N. (2003)." A fuzzy goal programming procedure for solving quadratic bilevel programming problems". International Journal of Intelligent Systems, 18(5), 529-540.‏ DOI: https://doi.org/10.1002/int.10102

22-Sahin, K. H., & Ciric, A. R. (1998)." A dual temperature simulated annealing approach for solving bilevel programming problems". Computers & chemical engineering, 23(1), 11-25. DOI: https://doi.org/10.1016/S0098-1354(98)00267-1

23-Savard, G., & Gauvin, J. (1994). "The steepest descent direction for the nonlinear bilevel programming problem". Operations Research Letters, 15(5), 265-272. DOI: https://doi.org/10.1016/0167-6377(94)90086-8

24-Sinha, A., Malo, P., & Deb, K. (2017)." A review on bilevel optimization: From classical to evolutionary approaches and applications". IEEE Transactions on Evolutionary Computation, 22(2), 276-295. DOI: https://doi.org/10.1109/TEVC.2017.2712906