Abstract
In this study, we formulate a double layer neural network based hybrid method to solve the quadratic bi-level programming problem. Our proposed algorithm comprises an improved artificial bee colony algorithm, a Hopfield network, and a Boltzmann machine in order to effectively and efficiently solve such problems. The improved artificial bee colony algorithm is developed for dealing with the upper level problem. The experiment results indicate that compared with other methods, the proposed double layer neural network based hybrid method is capable of achieving better optimal solutions for the quadratic bi-level programming problem.
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References
Bard, J.F., Moore, J.T.: A branch and bound algorithm for the bilevel programming problem. SIAM J. Sci. Stat. Comp. 11(2), 281–292 (1990)
Bard, J.F., Plummer, J., Sourie, J.C.: A bilevel programming approach to determining tax credits for biofuel production. Eur. J. Oper. Res. 120(1), 30–46 (2000)
Bard, J.F.: Practical Bilevel Optimization: Algorithms and Applications, vol. 30, 476 pages. Springer (1998)
Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Ann. Oper. Res. 153(1), 235–256 (2007)
Colson, B., Marcotte, P., Savard, G.: Bilevel programming: a survey. OR 43(2), 87–107 (2005)
Dempe, S.: Foundations of Bilevel Programming. Springer (2002)
Dempe, S.: Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optim.: J. Math. Progr. Oper. Res. 52(3), 333–359 (2003)
Fortuny-Amat, J., McCarl, B.: A representation and economic interpretation of a two-level programming problem. J. Oper. Res. Soc. 32(9), 783–792 (1981)
Hansen, P., Jaumard, B., Savard, G.: New branch-and-bound rules for linear bilevel programming. SIAM J. Sci. Stat. Comput. 13(5), 1194–1217 (1992)
Hobbs, B.F., Carolyn, B.M., Pang, J.S.: Strategic gaming analysis for electric power systems: an MPEC approach. IEEE Trans. Power Syst. 15(2), 638–645 (2000)
Li, H., Jiao, Y., Zhang, L.: Orthogonal genetic algorithm for solving quadratic bilevel programming problems. J. Syst. Eng. Electr. 21(5), 763–770 (2010)
Li, J., Watada, J., Yaakob, S.B.: A genetic algorithm based double layer neural network for solving quadratic bilevel programming problem. In: 2014 International Joint Conference on Neural Networks (IJCNN), pp. 382–389. IEEE (2014)
Lv, Y., Tiesong, H., Wang, G., Wan, Z.: A neural network approach for solving nonlinear bilevel programming problem. Comput. Math. Appl. 55(12), 2823–2829 (2008)
Lv, Y., Chen, Z., Wan, Z.: A neural network for solving a convex quadratic bilevel programming problem. J. Comput. Appl. Math. 234(2), 505–511 (2010)
Marcotte, P., Gilles, S.: Bilevel programming: a combinatorial perspective. In: Graph Theory and Combinatorial Optimization, pp. 191–217. Springer US (2005)
Muu, L.D., Van Quy, N.: Global optimization method for solving convex quadratic bilevel programming problems. J. Global Optim. 26(2), 199–219 (2003)
Savard, G., Gauvin, J.: The steepest descent direction for the nonlinear bilevel programming problem. Oper. Res. Lett. 15(5), 265–272 (1994)
Sherali, H.D., Soyster, A.L., Murphy, F.H.: Stackelberg-Nash-Cournot equilibria: characterizations and computations. Oper. Res. 31(2), 253–276 (1983)
Shih, H.-S., Wen, U.-P., Lee, S., Lan, K.-M., Hsiao, H.-C.: A neural network approach to multiobjective and multilevel programming problems. Comput. Math. Appl. 48(1), 95–108 (2004)
Vicente, L.N., Calamai, P.H.: Bilevel and multilevel programming: a bibliography review. J. Global Optim. 5(3), 291–306 (1994)
Vicente, L., Savard, G., Judice, J.: Discrete linear bilevel programming problem. J. Optim. Theory Appl. 89(3), 597–614 (1996)
Watada, J., Oda, K.: Formulation of a two-layered Boltzmann machine for portfolio selection. Int. J. Fuzzy Syst. 2(1), 39–44 (2001)
Yaakob, S.B., Watada, J., Fulcher, J.: Structural learning of the Boltzmann machine and its Application to life cycle management.Neurocomputing 74(12–13), 2193–2200 (2011)
Yang, Hai, Bell, M.G.H.: Models and algorithms for road network design: a review and some new developments. Transp. Rev. 18(3), 257–278 (1998)
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Watada, J., Ding, H. (2016). A Double Layer Neural Network Based on Artificial Bee Colony Algorithm for Solving Quadratic Bi-Level Programming Problem. In: Czarnowski, I., Caballero, A., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies 2016. IDT 2016. Smart Innovation, Systems and Technologies, vol 56. Springer, Cham. https://doi.org/10.1007/978-3-319-39630-9_37
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DOI: https://doi.org/10.1007/978-3-319-39630-9_37
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