Simulation optimization of police patrol district design using an adjusted simulated annealing approach

In this study, a simulated annealing approach is developed to find optimal police patrol district design using a discreteevent simulation to evaluate the performances of districting plans, such as average response time and workload variation among districts. Similar to the solution neighborhood definition in an existing simulated annealing approach, the new solution (districting plan) in each iteration is developed by making changes to the current solution. Instead of changing the assignment of only one atom (atomic geographical unit), the new approach makes relatively big changes to a current districting plan through a cutting and merging process of current districts. A case study on Charlottesville, VA is conducted. Experimental results show that the new approach uses fewer iterations to reach optima so it is wellsuited for discrete-event simulation. It evaluates districting plans in a more detailed way but uses longer computational times than Police Car Allocation Model (PCAM). In addition, the new approach is more robust for the adjacency pattern where atoms have relatively fewer adjacent neighbors. The adjusted simulated annealing approach is also compared with a response surface method of optimizing district design. Experimental result shows that the simulated annealing approach provides better solution. It is also an automatic method and thus better for practical application.