A Multistart Alternating Tabu Search for Commercial Districting

  • Alex Gliesch
  • Marcus Ritt
  • Mayron C. O. Moreira
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10782)

Abstract

In this paper we address a class of commercial districting problems that arises in the context of the distribution of goods. The problem aims at partitioning an area of distribution, which is modeled as an embedded planar graph, into connected components, called districts. Districts are required to be mutually balanced with respect to node attributes, such as number of customers, expected demand, and service cost, and as geometrically-compact as possible, by minimizing their Euclidean diameters. To solve this problem, we propose a multistart algorithm that repeatedly constructs solutions greedily and improves them by two alternating tabu searches, one aiming at achieving feasibility through balancing and the other at maximizing district compactness. Computational experiments confirm the effectiveness of the different components of our method and show that it significantly outperforms the current state of the art, improving known upper bounds in almost all instances.

Keywords

Districting Territory design Tabu search Heuristic algorithm Compactness 

Notes

Acknowledgments

This research was supported by the Brazilian funding agencies CNPq (grant 420348/2016-6), FAPEMIG (grant TEC-APQ-02694-16) and by Google Research Latin America (grant 25111). We would also like to thank to support of the Fundação de Desenvolvimento Científico e Cultural (FUNDECC/UFLA).

References

  1. 1.
    Ricca, F., Scozzari, A., Simeone, B.: Political districting: from classical models to recent approaches. Ann. Oper. Res. 204(1), 271–299 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ricca, F., Simeone, B.: Local search algorithms for political districting. Eur. J. Oper. Res. 189(3), 1409–1426 (2008)CrossRefGoogle Scholar
  3. 3.
    Bozkaya, B., Erkut, E., Haight, D., Laporte, G.: Designing new electoral districts for the city of Edmonton. Interfaces 41(6), 534–547 (2011)CrossRefGoogle Scholar
  4. 4.
    Bação, F., Lobo, V., Painho, M.: Applying genetic algorithms to zone design. Soft. Comput. 9(5), 341–348 (2005)CrossRefGoogle Scholar
  5. 5.
    Ríos-Mercado, R.Z., Fernández, E.: A reactive GRASP for a commercial territory design problem with multiple balancing requirements. Comput. Oper. Res. 36(3), 755–776 (2009)CrossRefGoogle Scholar
  6. 6.
    Lei, H., Laporte, G., Liu, Y., Zhang, T.: Dynamic design of sales territories. Comput. Oper. Res. 56, 84–92 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ríos-Mercado, R.Z., Escalante, H.J.: GRASP with path relinking for commercial districting. Exp. Syst. Appl. 44, 102–113 (2016). (September 2015)CrossRefGoogle Scholar
  8. 8.
    Camacho-Collados, M., Liberatore, F., Angulo, J.M.: A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector. Eur. J. Oper. Res. 246(2), 674–684 (2015)CrossRefGoogle Scholar
  9. 9.
    Steiner, M.T.A., Datta, D., Steiner Neto, P.J., Scarpin, C.T., Rui Figueira, J.: Multi-objective optimization in partitioning the healthcare system of Parana State in Brazil. Omega 52, 53–64 (2015)CrossRefGoogle Scholar
  10. 10.
    Blais, M., Lapierre, S.D., Laporte, G.: Solving a home-care districting problem in an urban setting. J. Oper. Res. Soc. 54(11), 1141–1147 (2003)CrossRefGoogle Scholar
  11. 11.
    Gliesch, A., Ritt, M., Moreira, M.C.O.: A genetic algorithm for fair land allocation. In: Genetic and Evolutionary Computation Conference, pp. 793–800. ACM Press (2017)Google Scholar
  12. 12.
    Kalcsics, J.: Districting problems. In: Laporte, G., Nickel, S., da Gama, F.S. (eds.) Location Science, pp. 595–622. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-13111-5_23CrossRefGoogle Scholar
  13. 13.
    Salazar-Aguilar, M.A., Ríos-Mercado, R.Z., Cabrera-Ríos, M.: New models for commercial territory design. Netw. Spat. Econ. 11(3), 487–507 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Salazar-Aguilar, M.A., Ríos-Mercado, R.Z., González-Velarde, J.L.: GRASP strategies for a bi-objective commercial territory design problem. J. Heuristics 19(2), 179–200 (2013)CrossRefGoogle Scholar
  15. 15.
    Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8(2), 67–71 (1989)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Butsch, A., Kalcsics, J., Laporte, G.: Districting for arc routing. INFORMS J. Comput. 26(October), 809–824 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Glover, F.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13, 533–549 (1986)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Erkut, E., Ülküsal, Y., Yeniçerioğlu, O.: A comparison of p-dispersion heuristics. Comput. Oper. Res. 21(10), 1103–1113 (1994)CrossRefGoogle Scholar
  19. 19.
    Tarjan, R.E.: A note on finding the bridges of a graph. Inf. Process. Lett. 2(6), 160–161 (1974)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Ła̧cki, J., Sankowski, P.: Optimal decremental connectivity in planar graphs. Theory Comput. Syst. 61(4), 1037–1053 (2016)MathSciNetCrossRefGoogle Scholar
  21. 21.
    King, D.M., Jacobson, S.H., Sewell, E.C., Cho, W.K.T.: Geo-graphs: an efficient model for enforcing contiguity and hole constraints in planar graph partitioning. Oper. Res. 60(5), 1213–1228 (2012)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Shamos, M.I.: Computational Geometry. Ph.D. thesis (1978)Google Scholar
  23. 23.
    Har-Peled, S.: On the Expected Complexity of Random Convex Hulls, pp. 1–20, November 2011. http://arxiv.org/abs/1111.5340
  24. 24.
    Andrew, A.M.: Another efficient algorithm for convex hulls in two dimensions. Inf. Process. Lett. 9(5), 216–219 (1979)CrossRefGoogle Scholar
  25. 25.
    Overmars, M.H., van Leeuwen, J.: Maintenance of configurations in the plane. J. Comput. Syst. Sci. 23(2), 166–204 (1981)MathSciNetCrossRefGoogle Scholar
  26. 26.
    López-Ibáñez, M., Dubois-Lacoste, J., Pérez Cáceres, L., Birattari, M., Stützle, T.: The irace package: iterated racing for automatic algorithm configuration. Oper. Res. Perspect. 3, 43–58 (2016)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Chou, C., Kimbrough, S.O., Sullivan-Fedock, J., Woodard, C.J., Murphy, F.H.: Using interactive evolutionary computation (IEC) with validated surrogate fitness functions for redistricting. In: Genetic and Evolutionary Computation Conference, pp. 1071–1078 (2012)Google Scholar
  28. 28.
    Fernández, E., Kalcsics, J., Nickel, S.: The maximum dispersion problem. Omega 41(4), 721–730 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Alex Gliesch
    • 1
  • Marcus Ritt
    • 1
  • Mayron C. O. Moreira
    • 2
  1. 1.Federal University of Rio Grande do SulPorto AlegreBrazil
  2. 2.Federal University of LavrasLavrasBrazil

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