Abstract
In this paper, we consider a shortest path network interdiction problem with incomplete information and multiple levels of interdiction intensity. The evader knows the attacker’s decision on the network arcs that have been interdicted. However, the extent of damage on each arc depends on the interdiction intensity and the amount of budget spent for interdiction. We consider two cases in which the evader has incomplete information about both the intensity of attack on the interdicted arcs and the additional cost imposed for traversing those arcs. In the first case, the evader’s perception of this cost falls in an interval of uncertainty. In the second case, it is assumed that the evader estimates a relative frequency for each level of interdiction intensity. This gives rise to multiple uncertainty sets for the evader’s estimates of the additional cost. To handle the uncertainty that arises in both cases, a robust optimization approach is employed to derive the mathematical formulation of underlying bilevel optimization problem. For each case, we first take the well-known duality-based approach to reformulate the problem as a single-level model. We show that this method does not always end up with an integer solution or fails in achieving a solution within the time limit. Therefore, we develop an alternative algorithm based on the decomposition approach. Computational results show that the proposed algorithm outperforms the duality-based method to obtain the optimal solution. Last, a real case study is presented to show the applicability of the studied problem.
Similar content being viewed by others
Notes
"Department of Defense Dictionary of Military and Associated Terms," Joint Publication 1–02, Nov. 8, 2010 (As Amended Through Aug. 15, 2012), p. 96..
National Research Council. (1999). Assessment of two cost-effectiveness studies on cocaine control policy.
Fiegel, B. (2021). Narco-drones: a new way to transport drugs. Criminal Drone Evolution: Cartel Weaponization of Aerial IEDS, 7.
References
Albert, L. A., Nikolaev, A., & Jacobson, S. H. (2022). Homeland security research opportunities. IISE Transactions, 55(1), 22–31.
Assimakopoulos, N. (1987). A network interdiction model for hospital infection control. Computers in Biology and Medicine, 17(6), 413–422.
Baycik, N. O., Sharkey, T. C., & Rainwater, C. E. (2018). Interdicting layered physical and information flow networks. IISE Transactions, 50(4), 316–331.
Baycik, N. O., & Sullivan, K. M. (2019). Robust location of hidden interdictions on a shortest path network. IISE Transactions, 51(12), 1332–1347.
Bayrak, H., & Bailey, M. D. (2008). Shortest path network interdiction with asymmetric information. Networks: An International Journal, 52(3), 133–140.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53.
Bertsimas, D., & Thiele, A. (2006). Robust and data-driven optimization: modern decision making under uncertainty. In M. P. Johnson, B. Norman, N. Secomandi, P. Gray, & H. J. Greenberg (Eds.), Models, methods, and applications for innovative decision making (pp. 95–122). INFORMS. https://doi.org/10.1287/educ.1063.0022
Borrero, J. S., Prokopyev, O. A., & Sauré, D. (2015). Sequential shortest path interdiction with incomplete information. Decision Analysis, 13(1), 68–98.
Borrero, J. S., Prokopyev, O. A., & Sauré, D. (2019). Sequential interdiction with incomplete information and learning. Operations Research, 67(1), 72–89.
Brown, G., Carlyle, M., Salmerón, J., & Wood, K. (2006). Defending critical infrastructure. Interfaces, 36(6), 530–544.
Brown, G. G., Carlyle, W. M., Harney, R. C., Skroch, E. M., & Wood, R. K. (2009). Interdicting a nuclear-weapons project. Operations Research, 57(4), 866–877.
Cormican, K. J., Morton, D. P., & Wood, R. K. (1998). Stochastic network interdiction. Operations Research, 46(2), 184–197.
Fakhry, R., Hassini, E., Ezzeldin, M., & El-Dakhakhni, W. (2021). Tri-level mixed-binary linear programming: Solution approaches and application in defending critical infrastructure. European Journal of Operational Research, 298(3), 1114–1131.
Ghaffarinasab, N., & Atayi, R. (2018). An implicit enumeration algorithm for the hub interdiction median problem with fortification. European Journal of Operational Research, 267(1), 23–39.
Giommoni, L., Aziani, A., & Berlusconi, G. (2017). How do illicit drugs move across countries? A network analysis of the heroin supply to Europe. Journal of Drug Issues, 47(2), 217–240.
Goldberg, N. (2017). Non-zero-sum nonlinear network path interdiction with an application to inspection in terror networks. Naval Research Logistics (NRL), 64(2), 139–153.
Hemmecke, R., Schultz, R., & Woodruff, D. L. (2003). Interdicting stochastic networks with binary interdiction effort. In D. L. Woodruff (Ed.), Network interdiction and stochastic integer programming (pp. 69–84). Boston: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48109-X_4
Holzmann, T., & Smith, J. C. (2021). The shortest path interdiction problem with randomized interdiction strategies: Complexity and algorithms. Operations Research, 69(1), 82–99.
Israeli, E., & Wood, R. K. (2002). Shortest-path network interdiction. Networks An International Journal, 40(2), 97–111.
Jenelius, E., Petersen, T., & Mattsson, L. G. (2006). Importance and exposure in road network vulnerability analysis. Transportation Research Part A: Policy and Practice, 40(7), 537–560.
Lei, X., Shen, S., & Song, Y. (2018). Stochastic maximum flow interdiction problems under heterogeneous risk preferences. Computers & Operations Research, 90, 97–109.
Losada, C., Scaparra, M. P., Church, R. L., & Daskin, M. S. (2012). The stochastic interdiction median problem with disruption intensity levels. Annals of Operations Research, 201(1), 345–365.
Magliocca, N. R., McSweeney, K., Sesnie, S. E., Tellman, E., Devine, J. A., Nielsen, E. A., Pearson, Z., & Wrathall, D. J. (2019). Modeling cocaine traffickers and counterdrug interdiction forces as a complex adaptive system. Proceedings of the National Academy of Sciences, 116(16), 7784–7792. https://doi.org/10.1073/pnas.1812459116
Malaviya, A., Rainwater, C., & Sharkey, T. (2012). Multi-period network interdiction problems with applications to city-level drug enforcement. IIE Transactions, 44(5), 368–380.
Morton, D. P., Pan, F., & Saeger, K. J. (2007). Models for nuclear smuggling interdiction. IIE Transactions, 39(1), 3–14.
Nandi, A. K., & Medal, H. R. (2016). Methods for removing links in a network to minimize the spread of infections. Computers & Operations Research, 69, 10–24.
Nandi, A. K., Medal, H. R., & Vadlamani, S. (2016). Interdicting attack graphs to protect organizations from cyber attacks: A bi-level defender–attacker model. Computers & Operations Research, 75, 118–131.
Nguyen, D. H., & Smith, J. C. (2022a). Network interdiction with asymmetric cost uncertainty. European Journal of Operational Research, 297(1), 239–251.
Nguyen, D. H., & Smith, J. C. (2022). Asymmetric stochastic shortest-path interdiction under conditional value-at-risk. IISE Transactions. https://doi.org/10.1080/24725854.2022.2043570
Pan, F., Charlton, W. S., & Morton, D. P. (2003). A stochastic program for interdicting smuggled nuclear material. In D. L. Woodruff (Ed.), Network interdiction and stochastic integer programming (pp. 1–19). Boston: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48109-X_1
Pan, F., & Morton, D. P. (2008). Minimizing a stochastic maximum-reliability path. Networks: An International Journal, 52(3), 111–119.
Pay, B. S., Merrick, J. R., & Song, Y. (2019). Stochastic network interdiction with incomplete preference. Networks, 73(1), 3–22.
Price, A. N., Curtin, K. M., Magliocca, N. R., Turner, D., Mitchell, P., McSweeney, K., & Summers, D. L. (2022). A family of models in support of realistic drug interdiction location decision‐making. Transactions in GIS, 26(4), 1962–1980. https://doi.org/10.1111/tgis.12921
Sadeghi, S., Seifi, A., & Azizi, E. (2017). Trilevel shortest path network interdiction with partial fortification. Computers & Industrial Engineering, 106, 400–411.
Salmerón, J. (2012). Deception tactics for network interdiction: A multiobjective approach. Networks, 60(1), 45–58.
Smith, J. C., & Song, Y. (2019). A survey of network interdiction models and algorithms. European Journal of Operational Research, 283(3), 797–811.
Sullivan, K. M., Morton, D. P., Pan, F., & Cole Smith, J. (2014). Securing a border under asymmetric information. Naval Research Logistics (NRL), 61(2), 91–100.
Wei, N., & Walteros, J. L. (2022). Integer programming methods for solving binary interdiction games. European Journal of Operational Research., 302(2), 456–469.
Wei, N., Walteros, J. L., & Pajouh, F. M. (2021). Integer programming formulations for minimum spanning tree interdiction. INFORMS Journal on Computing, 33(4), 1461–1480.
Wood, R. K. (1993). Deterministic network interdiction. Mathematical and Computer Modelling, 17(2), 1–18.
Yates, J., & Sanjeevi, S. (2013). A length-based, multiple-resource formulation for shortest path network interdiction problems in the transportation sector. International Journal of Critical Infrastructure Protection, 6(2), 107–119.
Zhang, C., & Ramirez-Marquez, J. E. (2013). Protecting critical infrastructures against intentional attacks: A two-stage game with incomplete information. IIE Transactions, 45(3), 244–258.
Zheng, K., & Albert, L. A. (2019). Interdiction models for delaying adversarial attacks against critical information technology infrastructure. Naval Research Logistics (NRL), 66(5), 411–429.
Funding
This study had no funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The first author declares she has no conflict of interest. The second author declares he has no conflict of interest.
Ethical approval
This article does not contain any studies with human participants performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Azizi, E., Seifi, A. Shortest path network interdiction with incomplete information: a robust optimization approach. Ann Oper Res 335, 727–759 (2024). https://doi.org/10.1007/s10479-023-05350-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-023-05350-1