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Mathematical Problems in Engineering
Volume 2016, Article ID 3690474, 13 pages
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.


In the current economic climate, law enforcement agencies are facing resource shortages. The effective and efficient use of scarce resources is therefore of the utmost importance to provide a high standard public safety service. Optimization models specifically tailored to the necessity of police agencies can help to ameliorate their use. The Multicriteria Police Districting Problem (MC-PDP) on a graph concerns the definition of sound patrolling sectors in a police district. The objective of this problem is to partition a graph into convex and continuous subsets, while ensuring efficiency and workload balance among the subsets. The model was originally formulated in collaboration with the Spanish National Police Corps. We propose for its solution three local search algorithms: a Simple Hill Climbing, a Steepest Descent Hill Climbing, and a Tabu Search. To improve their diversification capabilities, all the algorithms implement a multistart procedure, initialized by randomized greedy solutions. The algorithms are empirically tested on a case study on the Central District of Madrid. Our experiments show that the solutions identified by the novel Tabu Search outperform the other algorithms. Finally, research guidelines for future developments on the MC-PDP are given.