Analysing the Police Patrol Routing Problem: A Review

Police patrol is a complex process. While on patrol, police officers must balance many intersecting responsibilities. Most notably, police must proactively patrol and prevent offenders from committing crimes but must also reactively respond to real-time incidents. Efficient patrol strategies are crucial to manage scarce police resources and minimize emergency response times. The objective of this review paper is to discuss solution methods that can be used to solve the so-called police patrol routing problem (PPRP). The starting point of the review is the existing literature on the dynamic vehicle routing problem (DVRP). A keyword search resulted in 30 articles that focus on the DVRP with a link to police. Although the articles refer to policing, there is no specific focus on the PPRP; hence, there is a knowledge gap. A diversity of approaches is put forward ranging from more convenient solution methods such as a (hybrid) Genetic Algorithm (GA), linear programming and routing policies, to more complex Markov Decision Processes and Online Stochastic Combinatorial Optimization. Given the objectives, characteristics, advantages and limitations, the (hybrid) GA, routing policies and local search seem the most valuable solution methods for solving the PPRP.

Genetic Algorithm for Optimizing Routing Design and Fleet Allocation of Freeway Service Overlapping Patrol

The freeway service patrol problem involves patrol routing design and fleet allocation on freeways that would help transportation agency decision-makers when developing a freeway service patrols program and/or altering existing route coverage and fleet allocation. Based on the actual patrol process, our model presents an overlapping patrol model and addresses patrol routing design and fleet allocation in a single integrated model. The objective is to minimize the overall average incident response time. Two strategies—overlapping patrol and non-overlapping patrol—are compared in our paper. Matrix encoding is applied in the genetic algorithm (GA), and to maintain population diversity and avoid premature convergence, a niche strategy is incorporated into the traditional genetic algorithm. Meanwhile, an elitist strategy is employed to speed up the convergence. Using numerical experiments conducted based on data from the Sioux Falls network, we clearly show that: overlapping patrol strategy is superior to non-overlapping patrol strategy; the GA outperforms the simulated annealing (SA) algorithm; and the computational efficiency can be improved when LINGO software is used to solve the problem of fleet allocation.