Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 3690474, 13 pages
http://dx.doi.org/10.1155/2016/3690474
Research Article

A Comparison of Local Search Methods for the Multicriteria Police Districting Problem on Graph

1UC3M-BS Institute of Financial Big Data, Charles III University of Madrid, Getafe, 28903 Madrid, Spain
2Deputy Directorate for Operations, Spanish National Police Corps, 28010 Madrid, Spain
3Statistics and Operations Research Department, University of Granada, 18071 Granada, Spain

Received 8 June 2015; Revised 29 January 2016; Accepted 16 February 2016

Academic Editor: Francisco Chicano

Copyright © 2016 F. Liberatore and M. Camacho-Collados. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Camacho-Collados, F. Liberatore, and J. M. Angulo, “A multi-criteria police districting problem for the efficient and effective design of patrol sector,” European Journal of Operational Research, vol. 246, no. 2, pp. 674–684, 2015. View at Publisher · View at Google Scholar
  2. W. L. Perry, B. McInnis, C. C. Price, S. C. Smith, and J. S. Hollywood, Predictive Policing. The Role of Crime Forecasting in Law Enforcement Operations, RAND Corporation, Santa Monica, Calif, USA, 2013.
  3. M. Camacho-Collados and F. Liberatore, “A decision support system for predictive police patrolling,” Decision Support Systems, vol. 75, pp. 25–37, 2015. View at Publisher · View at Google Scholar
  4. A. Sarac, R. Batta, J. Bhadury, and C. Rump, “Reconfiguring police reporting districts in the city of Buffalo,” OR Insight, vol. 12, no. 3, pp. 16–24, 1999. View at Publisher · View at Google Scholar
  5. D. He and Y. L. Hong, “An improved tabu search algorithm based on grid search used in the antenna parameters optimization,” Mathematical Problems in Engineering, vol. 2015, Article ID 947021, 8 pages, 2015. View at Publisher · View at Google Scholar
  6. X. H. Zhang, S. Q. Zhong, Y. L. Liu, and X. L. Wang, “A framing link based tabu search algorithm for large-scale multidepot vehicle routing problems,” Mathematical Problems in Engineering, vol. 2014, Article ID 152494, 13 pages, 2014. View at Publisher · View at Google Scholar
  7. G. Lin, W. Zhu, and M. M. Ali, “A tabu search-based memetic algorithm for hardware/software partitioning,” Mathematical Problems in Engineering, vol. 2014, Article ID 103059, 15 pages, 2014. View at Publisher · View at Google Scholar
  8. Y. Z. Yang and X. S. Gu, “Cultural-based genetic tabu algorithm for multiobjective job shop scheduling,” Mathematical Problems in Engineering, vol. 2014, Article ID 230719, 14 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. E. Rolland, H. Pirkul, and F. Glover, “Tabu search for graph partitioning,” Annals of Operations Research, vol. 63, pp. 209–232, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. B. Ucar, C. Aykanat, K. Kaya, and M. Ikinci, “Task assignment in heterogeneous computing systems,” Journal of Parallel and Distributed Computing, vol. 66, no. 1, pp. 32–46, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. U. Benlic and J.-K. Hao, “An effective multilevel memetic algorithm for balanced graph partitioning,” in Proceedings of the 22nd International Conference on Tools with Artificial Intelligence (ICTAI '10), pp. 121–128, Arras, France, October 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. U. Benlic and J.-K. Hao, “A multilevel memetic approach for improving graph k-partitions,” IEEE Transactions on Evolutionary Computation, vol. 15, no. 5, pp. 624–642, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. U. Benlic and J.-K. Hao, “An effective multilevel tabu search approach for balanced graph partitioning,” Computers and Operations Research, vol. 38, no. 7, pp. 1066–1075, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. P. Galinier, Z. Boujbel, and M. Coutinho Fernandes, “An efficient memetic algorithm for the graph partitioning problem,” Annals of Operations Research, vol. 191, no. 1, pp. 1–22, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. P. S. Mitchell, “Optimal selection of police patrol beats,” The Journal of Criminal Law, Criminology, and Police Science, vol. 63, no. 4, article 577, 1972. View at Publisher · View at Google Scholar
  16. S. E. Bodily, “Police sector design incorporating preferences of interest groups for equality and efficiency,” Management Science, vol. 24, no. 12, pp. 1301–1313, 1978. View at Publisher · View at Google Scholar
  17. R. Benveniste, “Solving the combined zoning and location problem for several emergency units,” Journal of the Operational Research Society, vol. 36, no. 5, pp. 433–450, 1985. View at Publisher · View at Google Scholar · View at Scopus
  18. S. J. D'Amico, S.-J. Wang, R. Batta, and C. M. Rump, “A simulated annealing approach to police district design,” Computers & Operations Research, vol. 29, no. 6, pp. 667–684, 2002. View at Publisher · View at Google Scholar · View at Scopus
  19. J. M. Chaiken and P. Dormont, “A patrol car allocation model: background,” Management Science, vol. 24, no. 12, pp. 1280–1290, 1978. View at Publisher · View at Google Scholar
  20. J. M. Chaiken and P. Dormont, “A patrol car allocation model: capabilities and algorithms,” Management Science, vol. 24, no. 12, pp. 1291–1300, 1978. View at Publisher · View at Google Scholar
  21. K. Curtin, F. Qui, K. Hayslett-McCall, and T. Bray, “Geographic information systems and crime analysis,” in Integrating GIS and Maximal Coverage Models to Determine Optimal Police Patrol Areas, pp. 214–235, Idea Group, 2005. View at Google Scholar
  22. K. M. Curtin, K. Hayslett-McCall, and F. Qiu, “Determining optimal police patrol areas with maximal covering and backup covering location models,” Networks and Spatial Economics, vol. 10, no. 1, pp. 125–145, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. Y. Zhang and D. E. Brown, “Police patrol districting method and simulation evaluation using agent-based model & GIS,” Security Informatics, vol. 2, article 7, 2013. View at Publisher · View at Google Scholar
  24. D. Artigas, M. C. Dourado, and J. L. Szwarcfiter, “Convex partitions of graphs,” Electronic Notes in Discrete Mathematics, vol. 29, pp. 147–151, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. D. Artigas, S. Dantas, M. C. Dourado, and J. L. Szwarcfiter, “Partitioning a graph into convex sets,” Discrete Mathematics, vol. 311, no. 17, pp. 1968–1977, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. L. N. Grippo, M. Matamala, M. D. Safe, and M. J. Stein, “Convex p-partitions of bipartite graphs,” Theoretical Computer Science, vol. 609, part 2, pp. 511–514, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  27. R. Glantz and H. Meyerhenke, “Finding all convex cuts of a plane graph in cubic time,” in Algorithms and Complexity, vol. 7878 of Lecture Notes in Computer Science, pp. 246–263, Springer, 2013. View at Publisher · View at Google Scholar
  28. J. Bozeman, L. Pyrik, and J. Theoret, “Nearly convex sets and the shape of legislative districts,” International Journal of Pure and Applied Mathematics, vol. 49, no. 3, pp. 341–347, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. C. P. Chambers and A. D. Miller, “A measure of bizarreness,” Quarterly Journal of Political Science, vol. 5, no. 1, pp. 27–44, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. J. K. Hodge, E. Marshall, and G. Patterson, “Gerrymandering and convexity,” The College Mathematics Journal, vol. 41, no. 4, pp. 312–324, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  31. R. W. Floyd, “Algorithm 97: shortest path,” Communications of the ACM, vol. 5, no. 6, artilce 345, 1962. View at Publisher · View at Google Scholar
  32. S. Warshall, “A theorem on boolean matrices,” Journal of the Association for Computing Machinery, vol. 9, pp. 11–12, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. S. Russell and P. Norvig, Artificial Intelligence: A Modern Approach, Pearson, 3rd edition, 2009.
  34. F. Glover, “Tabu search—part I,” ORSA Journal on Computing, vol. 1, no. 3, pp. 190–206, 1989. View at Google Scholar
  35. F. Glover, “Tabu search—part II,” ORSA Journal on Computing, vol. 2, no. 1, pp. 4–32, 1990. View at Publisher · View at Google Scholar
  36. İ. Muter, Ş. İlker Birbil, and K. Bülbül, “Simultaneous column-and-row generation for large-scale linear programs with column-dependent-rows,” Mathematical Programming, vol. 142, no. 1-2, pp. 47–82, 2013. View at Publisher · View at Google Scholar