Advertisement

Districting and Routing for Security Control

  • Michael Prischink
  • Christian KloimüllnerEmail author
  • Benjamin Biesinger
  • Günther R. Raidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9668)

Abstract

Regular security controls on a day by day basis are an essential and important mechanism to prevent theft and vandalism in business buildings. Typically, security workers patrol through a set of objects where each object requires a particular number of visits on all or some days within a given planning horizon, and each of these visits has to be performed in a specific time window. An important goal of the security company is to partition all objects into a minimum number of disjoint clusters such that for each cluster and each day of the planning horizon a feasible route for performing all the requested visits exists. Each route is limited by a maximum working time, must satisfy the visits’ time window constraints, and any two visits of one object must be separated by a minimum time difference. We call this problem the Districting and Routing Problem for Security Control. In our heuristic approach we split the problem into a districting part where objects have to be assigned to districts and a routing part where feasible routes for each combination of district and period have to be found. These parts cannot be solved independently though. We propose an exact mixed integer linear programming model and a routing construction heuristic in a greedy like fashion with variable neighborhood descent for the routing part as well as a districting construction heuristic and an iterative destroy & recreate algorithm for the districting part. Computational results show that the exact algorithm is only able to solve small routing instances and the iterative destroy & recreate algorithm is able to reduce the number of districts significantly from the starting solutions.

References

  1. 1.
    Ascheuer, N., Fischetti, M., Grötschel, M.: Solving the asymmetric travelling salesman problem with time windows by branch-and-cut. Math. Program. 90(3), 475–506 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Baldacci, R., Mingozzi, A., Roberti, R.: New state-space relaxations for solving the traveling salesman problem with time windows. INFORMS J. Comput. 24(3), 356–371 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cheng, C.B., Mao, C.P.: A modified ant colony system for solving the travelling salesman problem with time windows. Math. Comput. Model. 46(9), 1225–1235 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Da Silva, R.F., Urrutia, S.: A general VNS heuristic for the traveling salesman problem with time windows. Discrete Optim. 7(4), 203–211 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gambardella, L.M., Taillard, E., Agazzi, G.: MACS-VRPTW: A multiple ant colony system for vehicle routing problems with time windows. In: Corne, D., Dorigo, M., Glover, F., Dasgupta, D., Moscato, P., Poli, R., Price, K.V. (eds.) New Ideas in Optimization, Chap. 5, pp. 63–76. McGraw-Hill Ltd., Maidenhead (1999)Google Scholar
  6. 6.
    López-Ibáñez, M., Blum, C.: Beam-ACO for the travelling salesman problem with time windows. Comput. Oper. Res. 37(9), 1570–1583 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    López-Ibáñez, M., Blum, C., Ohlmann, J.W., Thomas, B.W.: The travelling salesman problem with time windows: Adapting algorithms from travel-time to makespan optimization. Appl. Soft Comput. 13(9), 3806–3815 (2013)CrossRefGoogle Scholar
  8. 8.
    Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. ACM 7(4), 326–329 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Mladenović, N., Todosijević, R., Urošević, D.: An efficient GVNS for solving traveling salesman problem with time windows. Electron. Notes Discrete Math. 39, 83–90 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Nagata, Y., Bräysy, O.: A powerful route minimization heuristic for the vehicle routing problem with time windows. Oper. Res. Lett. 37(5), 333–338 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Nagata, Y., Bräysy, O., Dullaert, W.: A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows. Comput. Oper. Res. 37(4), 724–737 (2010)CrossRefzbMATHGoogle Scholar
  12. 12.
    Ohlmann, J.W., Thomas, B.W.: A compressed-annealing heuristic for the traveling salesman problem with time windows. INFORMS J. Comput. 19(1), 80–90 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Prescott-Gagnon, E., Desaulniers, G., Rousseau, L.M.: A branch-and-price-based large neighborhood search algorithm for the vehicle routing problem with time windows. Networks 54(4), 190–204 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Savelsbergh, M.W.P.: The vehicle routing problem with time windows: Minimizing route duration. ORSA J. Comput. 4(2), 146–154 (1992)CrossRefzbMATHGoogle Scholar
  15. 15.
    Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Vidal, T., Crainic, T.G., Gendreau, M., Prins, C.: A hybrid genetic algorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows. Comput. Oper. Res. 40(1), 475–489 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Michael Prischink
    • 1
    • 2
  • Christian Kloimüllner
    • 1
    Email author
  • Benjamin Biesinger
    • 1
  • Günther R. Raidl
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsTU WienViennaAustria
  2. 2.Research Industrial Systems EngineeringSchwechatAustria

Personalised recommendations