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Solving multi-period interdiction via generalized Bender’s decomposition

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Abstract

This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem. Computational experiences denote reasonable consistency with expectations.

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References

  1. Department of Homeland Security (DHS). A roadmap for cybersecurity research. Department of Homeland Security (DHS), Technical Report, November, 2009

    Google Scholar 

  2. Allende, G.B., Still, G. Solving bilevel programs with the KKT-approach. Math. Program., Ser. A, 138: 309–332 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chang, C.T. An efficient linearization approach for mixed-integer problems. European Journal of Operational Research, 123(3): 652–659 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Corely, H.W., Sha, D.Y. Most vital links and nodes in weighted network. Operations Research Letters, 1: 157–160 (1982)

    Article  MathSciNet  Google Scholar 

  5. Cormican, K.J., Morton, D.P., Wood, R.K. Stochastic network interdiction. Operations Research, 46: 184–197 (1998)

    Article  MATH  Google Scholar 

  6. DeNegre, S. Interdiction and discrete bilevel linear programming. Doctoral disssertation, Lehigh University, 2011

    Google Scholar 

  7. Fulkerson, D.R., Harding, G.C. Maximizing the minimum source-sink path subject to budget constraint. Mathematical Programming, 13: 116–118 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  8. Geoffrion, A.M. Generalized Benders decomposition. Journal of Optimization Theory and Applications, 10(4): 237–260 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  9. Glover, F. Improved linear integer programming formulations of nonlinear integer problems. Management Science, 22(4): 455469 (1975)

    Article  MathSciNet  Google Scholar 

  10. Golden, B. A problem in network interdiction. Naval Research Logistics Quarterly, 25: 711–713 (1978)

    Article  MATH  Google Scholar 

  11. Israeli, E., Wood, R.K. Shortest-path network interdiction. Networks, 40(2): 97–111 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gm, H.Z., Floudas, A.C. Global optimization of mixed-integer bilevel programming problems. Computational Management Science, 2(3): 181–212 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kettani, O. Oral, M. Equivalent formulations of nonlinear integer problems for efficient optimization. Management Science, 36(1): 115119 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  14. Klaus, C. Network design for reliablity and resilience to attack. Doctoral disssertation, Naval Postgraduate School, 2014

    Google Scholar 

  15. Larsson, T., Yuan, D. An augmente lagrangean algorithm for large scale multicommodity routing. Computational Optimization and Applications, 27 (2): 187–215 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Malaviya, A., Rainwater, C., Sharkey, T. Multi-period network interdiction problems with applications to city-level drug enforcement. IIE Transactions, 44: 368–380 (2012)

    Article  Google Scholar 

  17. McMasters, A.W., Mustin, T.M. Optimal interdiction of a supply network. Naval Research Logistics Quarterly, 17: 261–268 (1970)

    Article  MATH  Google Scholar 

  18. Saharidis, G.K. Ierapetritou, M.G. Resolution method for mixed integer bi-level linear problems based on decomposition technique. J. Glob. Optim., 44: 20–51 (2008)

    MathSciNet  MATH  Google Scholar 

  19. Stackelberg, H. The Theory of the Market Economy. William Hodge and Co., London, U.K., 1952

    Google Scholar 

  20. Sterbenz, J.P.G., Hutchison, D., Cetinkaya, E.K., Jabbar, A., Rohrer, J.P., Scholler, M., Smith, P. Resilience and survivability in communication networks: strategies, principles, and survey of disciplines. Computer Networks, 54(8): 12451265 (2010)

    Article  MATH  Google Scholar 

  21. Wen, U. Yang, Y. Algorithms for solving the mixed integer two-level linear programming problem. Comput. Oper. Res., 17: 133–142 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wollmer, R.D. Removing arcs from a network. Operations Research, 12: 934–940 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wood, R.K. Deteministic network interdiction. Mathematical and Computer Modeling, 17: 1–18 (1993)

    Article  MATH  Google Scholar 

  24. Woodruff, D.L. Network interdiction and stochastic integer programming. Kluwer Academic Publishers, 2003

    Book  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank Azarbaijan Shahid Madani University for supporting this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Maryam Soleimani-Alyar & Alireza Ghaffari-Hadigheh

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  1. Maryam Soleimani-Alyar
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  2. Alireza Ghaffari-Hadigheh
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Correspondence to Maryam Soleimani-Alyar.

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Supported by Azarbaijan Shahid Madani University.

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Soleimani-Alyar, M., Ghaffari-Hadigheh, A. Solving multi-period interdiction via generalized Bender’s decomposition. Acta Math. Appl. Sin. Engl. Ser. 33, 633–644 (2017). https://doi.org/10.1007/s10255-017-0687-9

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  • DOI: https://doi.org/10.1007/s10255-017-0687-9

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