A Comparison of Local Search Methods for the Multi-Criteria Police Districting Problem on Graph

In the current economic climate, law enforcement agencies are facing resource shortages. The e ective and e cient use of scarce resources is therefore of the utmost importance to provide a high standard public safety service. Optimization models speci cally tailored to the necessity of police agencies can help to ameliorate their use. The Multi-Criteria Police Districting Problem (MC-PDP) concerns the de nition of sound patrolling sectors in a police district. The model was originally formulated in collaboration with the Spanish National Police Corps and was solved by means of a Steepest Descent Hill Climbing algorithm. One of the major limitations of the MC-PDP is that it requires the territory to be organized as a grid. In this work we formulate the MC-PDP for a generic graph, which results in a more applicable and usable model. Also, we propose for its solution three local search algorithms, including a Tabu Search. The algorithms are empirically tested on a case study on the Central District of Madrid. Our experiments show that the solutions identi ed by the novel Tabu Search outperforms those of the previously used algorithm. Finally, research guidelines for future developments on the MC-PDP are given.