Skip to main content
SpringerLink
Log in

A Matheuristic for Leader-Follower Games Involving Facility Location-Protection-Interdiction Decisions

  • Chapter
Metaheuristics for Bi-level Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 482))

Abstract

The topic of this chapter is the application of a matheuristic to the leaderfollower type of games—also called static Stackelberg games—that occur in the context of discrete location theory. The players of the game are a system planner (the leader) and an attacker (the follower). The decisions of the former are related to locating/relocating facilities as well as protecting some of those to provide service. The attacker, on the other hand, is interested in destroying (interdicting) facilities to cause the maximal possible disruption in service provision or accessibility. The motivation in the presented models is to identify the facilities that are most likely to be targeted by the attacker, and to devise a protection plan to minimize the resulting disruption on coverage as well as median type supply/demand or service networks. Stackelberg games can be formulated as a bilevel programming problem where the upper and the lower level problems with conflicting objectives belong to the leader and the follower, respectively. In this chapter, we first discuss the state of the art of the existing literature on both facility and network interdiction problems. Secondly, we present two fixed-charge facility location-protection-interdiction models applicable to coverage and median-type service network design problems. Out of these two, we focus on the latter model which also involves initial capacity planning and post-attack capacity expansion decisions on behalf of the leader. For this bilevel model, we develop a matheuristic which searches the solution space of the upper level problem according to tabu search principles, and resorts to a CPLEXbased exact solution technique to tackle the lower level problem. In addition, we also demonstrate the computational efficiency of using a hash function, which helps to uniquely identify and record all the solutions visited, thereby avoids cycling altogether throughout the tabu search iterations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aksen, D., Aras, N.: A bilevel fixed charge location model for facilities under imminent attack. Comp. Oper. Res. 39(7), 1364–1381 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aksen, D., Piyade, N., Aras, N.: The budget constrained r-interdiction median problem with capacity expansion. Central European Journal of Operations Research 18(3), 269–291 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aksen, D., Aras, N., Piyade, N.: A bilevel p-median model for the planning and protection of critical facilities. Journal of Heuristics (2011), doi: 10.1007/s10732-011-9163-5

    Google Scholar 

  4. Aras, N., Aksen, D.: Locating collection centers for distance- and incentive-dependent returns. Int. J. Prod. Econ. 111(2), 316–333 (2008)

    Article  Google Scholar 

  5. Aras, N., Aksen, D., Tanuğur, A.G.: Locating collection centers for incentive-dependent returns under a pick-up policy with capacitated vehicles. Eur. J. Oper. Res. 191(3), 1223–1240 (2008)

    Article  MATH  Google Scholar 

  6. Arroyo, J.M., Galiana, F.D.: On the solution of the bilevel programming formulation of the terrorist threat problem. IEEE Trans. Power Systems 20(2), 789–797 (2005)

    Article  Google Scholar 

  7. Bayrak, H., Bailey, M.D.: Shortest path network interdiction with asymmetric information. Networks 52(3), 133–140 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. BBC News UK, Arsonists target ambulance station. BBC Online Network (1999), http://news.bbc.co.uk/2/hi/uk_news/378254.stm (cited November 12, 2011)

  9. Berman, O., Krass, D., Drezner, Z.: The gradual covering decay location problem on a network. Eur. J. Oper. Res. 151, 474–480 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Berman, O., Drezner, T., Drezner, Z., Wesolowsky, G.O.: A defensive maximal covering problem on a network. International Transactions in Operational Research 16(1), 69–86 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Berman, O., Gavious, A.: Location of terror response facilities: a game between state and terrorist. European Journal of Operational Research 177(2), 1113–1133 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Berman, O., Gavious, A., Huang, R.: Location of response facilities: a simultaneous game between state and terrorist. International Journal of Operational Research 10(1), 102–120 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cappanera, P., Scaparra, M.P.: Optimal allocation of protective resources in shortest-path networks. Transportation Science 45(1), 64–80 (2011)

    Article  Google Scholar 

  14. Chalk, P., Hoffman, B., Reville, R., Kasupski, A.: Trends in terrorism. RAND Center for Terrorism Risk Management Policy (2005), http://www.rand.org/content/dam/rand/pubs/monographs/2005/RAND_MG393.pdf (cited November 12, 2011)

  15. Church, R.L., ReVelle, C.: The maximal covering location problem. Papers in Regional Science 32(1), 101–118 (1974)

    Article  Google Scholar 

  16. Church, R.L., Scaparra, M.P.: Protecting critical assets: the r-interdiction median problem with fortification. Geographical Analysis 39(2), 129–146 (2007)

    Article  Google Scholar 

  17. Church, R.L., Scaparra, M.P., Middleton, R.S.: Identifying critical infrastructure: the median and covering facility interdiction problems. Annals of the Association of American Geographers 94(3), 491–502 (2004)

    Article  Google Scholar 

  18. Cormican, K.J., Morton, D.P., Wood, R.K.: Stochastic network interdiction. Oper. Res. 46(2), 184–197 (1998)

    Article  MATH  Google Scholar 

  19. Floudas, C.A.: Deterministic Global Optimization: Theory, Methods and Applications. Nonconvex Optimization and Its Applications, vol. 37. Kluwer Academic Publishers, Dordrecht (2000)

    Book  Google Scholar 

  20. Fulkerson, D.R., Harding, G.C.: Maximizing the minimum source-sink path subject to a budget constraint. Math Prog. 13(1), 116–118 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gendreau, M.: An introduction to tabu search. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp. 37–54. Kluwer Academic Publishers, Boston (2003)

    Google Scholar 

  22. Glover, F., Laguna, M.: Tabu search. Kluwer Academic Publishers, Dordrecht (1997)

    Book  MATH  Google Scholar 

  23. Glover, F., Laguna, M., Martí, R.: Principles of Tabu Search. In: Gonzalez, T. (ed.) Handbook on Approximation Algorithms and Metaheuristics. Chapman & Hall/CRC, Boca Raton (2007)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  25. Hecheng, L., Yuping, W.: Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems. Journal of Systems Engineering and Electronics 19(6), 1157–1164 (2008)

    Article  MATH  Google Scholar 

  26. Held, H., Woodruff, D.L.: Heuristics for multi-stage interdiction of stochastic networks. Journal of Heuristics 11(5–6), 483–500 (2005)

    Article  MATH  Google Scholar 

  27. Held, H., Hemmecke, R., Woodruff, D.L.: A decomposition algorithm applied to planning the interdiction of stochastic networks. Naval Res. Logistics 52(4), 321–328 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Hemmecke, R., Schultz, R., Woodruff, D.L.: Interdicting stochastic networks with binary interdiction effort. In: Woodruff, D.L. (ed.) Network Interdiction and Stochastic Integer Programming. Operations Research/Computer Science Interfaces Series, vol. 22, pp. 69–84. Kluwer, Boston (2003)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  30. Keçici, S., Aras, N., Verter, V.: Incorporating the threat of terrorist attacks in the design of public service facility networks. Optimization Letters (2011), doi:10.1007/s11590-011-0412-1

    Google Scholar 

  31. Khachiyan, L., Boros, E., Borys, K., Elbassioni, K., Gurvich, V., Rudolf, G., Zhao, J.: On short paths interdiction problems: total and node-wise limited interdiction. Theory of Computing Systems 43(2), 204–233 (2008)

    Article  MathSciNet  Google Scholar 

  32. Liberatore, F., Scaparra, M.P., Daskin, M.S.: Analysis of facility protection strategies against an uncertain number of attacks: The stochastic R-interdiction median problem with fortification. Comp. Oper. Res. 38(1), 357–366 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  33. Lim, C., Smith, J.C.: Algorithms for discrete and continuous multicommodity flow network interdiction problems. IIE Transactions 39(1), 15–26 (2007)

    Article  Google Scholar 

  34. Losada, C., Scaparra, M.P., O’Hanley, J.R.: Optimizing system resilience: a facility protection model with recovery time. Eur. J. Oper. Res. 217(3), 519–530 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  35. Maniezzo, V., Stützle, T., Voß, S. (eds.): Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Annals of Information Systems, vol. 10. Springer (2009)

    Google Scholar 

  36. Moore, J.T., Bard, J.F.: The mixed-integer linear bilevel programming problem. Oper. Res. 38(5), 911–921 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  37. Motto, A.L., Arroyo, J.M., Galiana, F.D.: MILP for the analysis of electric grid security under disruptive threat. IEEE Transactions on Power Systems 20(3), 1357–1365 (2005)

    Article  Google Scholar 

  38. Murray, A.T., Matisziw, T.C., Grubesic, T.H.: Critical network infrastructure analysis: interdiction and system flow. Journal of Geographical Systems 9(2), 103–117 (2007)

    Article  Google Scholar 

  39. O’Hanley, J.R., Church, R.L., Gilless, K.: Locating and protecting critical reserve sites to minimize expected and worst-case losses. Biological Conservation 134(1), 130–141 (2007)

    Article  Google Scholar 

  40. O’Hanley, J.R., Church, R.L.: Designing robust coverage to hedge against worst-case facility losses. Eur. J. Oper. Res. 209(1), 23–36 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  41. Perl, R.: Trends in terrorism: Congressional Research Service Report for Congress. The Library of Congress, Order Code: RL33555 (2006), http://www.dtic.mil/cgi-in/GetTRDoc?AD=ADA464744&Location=U2&doc=GetTRDoc.pdf (cited November 12, 2011)

  42. Radio Free Europe-Radio Liberty, Afghanistan Report: March 8, 2008. Afghanistan: Mobile-Phone Towers are Taliban’s New Target (2008), http://www.rferl.org/content/article/1347757.html (accessed November 12, 2011)

  43. Royset, J.O., Wood, R.K.: Solving the bi-objective maximum-flow network interdiction problem. INFORMS J. Computing 19(2), 175–184 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  44. Salmerón, J., Wood, K., Baldick, R.: Worst-case interdiction analysis of large-scale Electric power grids. IEEE Trans. Power Systems 24(1), 96–104 (2009)

    Article  Google Scholar 

  45. Scaparra, M.P., Church, R.L.: A bilevel mixed integer program for critical infrastructure protection planning. Comp. Oper. Res. 35(6), 1905–1923 (2008a)

    Article  MATH  Google Scholar 

  46. Scaparra, M.P., Church, R.L.: An exact solution approach for the interdiction median problem with fortification. Eur. J. Oper. Res. 189(1), 76–92 (2008b)

    Article  MATH  Google Scholar 

  47. Scaparra, M.P., Church, R.L.: Protecting supply systems to mitigate potential disaster: A model to fortify capacitated facilities. Kent Business School Working Paper No.209, University of Kent, Canterbury, UK (2010)

    Google Scholar 

  48. Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM Journal on Discrete Mathematics 3(3), 411–430 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  49. Sherali, H.D., Adams, W.P., Driscoll, P.J.: Exploiting special structures in constructing a hierarchy of relaxations for 0-1 mixed integer problems. Oper. Res. 46(3), 396–405 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  50. Smith, J.C.: Basic interdiction models. In: Cochran, J. (ed.) Wiley Encyclopedia of Operations Research and Management Science (EORMS), Wiley, New York (2010), http://eu.wiley.com/WileyCDA/Section/id-380764.html (accessed: November 12, 2011)

    Google Scholar 

  51. Smith, J.C., Lim, C.: Algorithms for network interdiction and fortification games. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds.) Pareto Optimality, Game Theory and Equilibria, pp. 609–644. Springer, New York (2008)

    Chapter  Google Scholar 

  52. Smith, J.C., Lim, C., Sudargho, F.: Survivable network design under optimal and heuristic interdiction scenarios. Journal of Global Optimization 38(2), 181–199 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  53. Snyder, L.V., Scaparra, M.P., Daskin, M.S., Church, R.L.: Planning for disruptions in supply chain networks. In: Greenberg, H.K. (ed.) TutORials in Operations Research, pp. 234–257. INFORMS, Baltimore (2006)

    Google Scholar 

  54. Sun, M.: Solving the uncapacitated facility location problem using tabu search. Comp. Oper. Res. 33(9), 2563–2589 (2006)

    Article  MATH  Google Scholar 

  55. Wollmer, R.: Removing arcs from a network. Oper. Res. 12(6), 934–940 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  56. Wood, R.K.: Deterministic network interdiction. Mathematical and Computer Modelling 17(2), 1–18 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  57. Woodruff, D.L., Zemel, E.: Hashing vectors for tabu search. Annals of Oper. Res. 41(2), 123–137 (1993)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Admin. Sciences and Economics, Koç University, İstanbul, Turkey

    Deniz Aksen

  2. Dept. of Industrial Engineering, Boğaziçi University, İstanbul, Turkey

    Necati Aras

Authors
  1. Deniz Aksen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Necati Aras
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Deniz Aksen .

Editor information

Editors and Affiliations

  1. , Cite Scientifique, University of Lille 1, Villeneuve d'Ascq, 59655, France

    El-Ghazali Talbi

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Aksen, D., Aras, N. (2013). A Matheuristic for Leader-Follower Games Involving Facility Location-Protection-Interdiction Decisions. In: Talbi, EG. (eds) Metaheuristics for Bi-level Optimization. Studies in Computational Intelligence, vol 482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37838-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37838-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37837-9

  • Online ISBN: 978-3-642-37838-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation