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Global optimization of mixed-integer bilevel programming problems

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  • Zeynep Gümüş
  • Christodoulos Floudas

Abstract

Two approaches that solve the mixed-integer nonlinear bilevel programming problem to global optimality are introduced. The first addresses problems mixed-integer nonlinear in outer variables and C 2 -nonlinear in inner variables. The second adresses problems with general mixed-integer nonlinear functions in outer level. Inner level functions may be mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in inner integer variables, and linear in inner continuous variables. This second approach is based on reformulating the mixed-integer inner problem as continuous via its vertex polyheral convex hull representation and solving the resulting nonlinear bilevel optimization problem by a novel deterministic global optimization framework. Computational studies illustrate proposed approaches. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Zeynep Gümüş & Christodoulos Floudas, 2005. "Global optimization of mixed-integer bilevel programming problems," Computational Management Science, Springer, vol. 2(3), pages 181-212, July.
    • Handle: RePEc:spr:comgts:v:2:y:2005:i:3:p:181-212
    DOI: 10.1007/s10287-005-0025-1
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    Cited by:

    1. Robbins, Matthew J. & Lunday, Brian J., 2016. "A bilevel formulation of the pediatric vaccine pricing problem," European Journal of Operational Research, Elsevier, vol. 248(2), pages 634-645.
    2. S. Dempe & F. Mefo Kue, 2017. "Solving discrete linear bilevel optimization problems using the optimal value reformulation," Journal of Global Optimization, Springer, vol. 68(2), pages 255-277, June.
    3. Florensa, Carlos & Garcia-Herreros, Pablo & Misra, Pratik & Arslan, Erdem & Mehta, Sanjay & Grossmann, Ignacio E., 2017. "Capacity planning with competitive decision-makers: Trilevel MILP formulation, degeneracy, and solution approaches," European Journal of Operational Research, Elsevier, vol. 262(2), pages 449-463.
    4. Wang, Guangmin & Gao, Ziyou & Xu, Meng, 2019. "Integrating link-based discrete credit charging scheme into discrete network design problem," European Journal of Operational Research, Elsevier, vol. 272(1), pages 176-187.
    5. Yuping Wang & Hong Li & Chuangyin Dang, 2011. "A New Evolutionary Algorithm for a Class of Nonlinear Bilevel Programming Problems and Its Global Convergence," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 618-629, November.
    6. Zhai, Wenyuan & Zhao, Yingzi & Lian, Xiangru & Yang, Mingming & Lu, Fadian, 2014. "Management planning of fast-growing plantations based on a bi-level programming model," Forest Policy and Economics, Elsevier, vol. 38(C), pages 173-177.
    7. G. Saharidis & I. Androulakis & M. Ierapetritou, 2011. "Model building using bi-level optimization," Journal of Global Optimization, Springer, vol. 49(1), pages 49-67, January.
    8. Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.
    9. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
    10. Soares, Inês & Alves, Maria João & Henggeler Antunes, Carlos, 2021. "A deterministic bounding procedure for the global optimization of a bi-level mixed-integer problem," European Journal of Operational Research, Elsevier, vol. 291(1), pages 52-66.
    11. Hecheng Li, 2015. "A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems," Annals of Operations Research, Springer, vol. 235(1), pages 543-558, December.
    12. Ghavamifar, Ali & Makui, Ahmad & Taleizadeh, Ata Allah, 2018. "Designing a resilient competitive supply chain network under disruption risks: A real-world application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 87-109.
    13. Jabarzare, Ziba & Zolfagharinia, Hossein & Najafi, Mehdi, 2020. "Dynamic interdiction networks with applications in illicit supply chains," Omega, Elsevier, vol. 96(C).
    14. Sharma, Bijay P. & Yu, Tun-Hsiang Edward & English, Burton C. & Boyer, Christopher M., 2018. "Analyzing the Economics of Renewable Jet Fuels Using a Game-theoretic Approach," 2018 Annual Meeting, August 5-7, Washington, D.C. 273787, Agricultural and Applied Economics Association.
    15. Losada, Chaya & Scaparra, M. Paola & O’Hanley, Jesse R., 2012. "Optimizing system resilience: A facility protection model with recovery time," European Journal of Operational Research, Elsevier, vol. 217(3), pages 519-530.

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