Improving Law Enforcement Daily Deployment Through Machine Learning-Informed Optimization under Uncertainty

Abstract

Urban law enforcement agencies are under great pressure to respond to emergency incidents effectively while operating within restricted budgets. Minutes saved on emergency response times can save lives and catch criminals, and a responsive police force can deter crime and bring peace of mind to citizens. To efficiently minimize the response times of a law enforcement agency operating in a dense urban environment with limited manpower, we consider in this paper the problem of optimizing the spatial and temporal deployment of law enforcement agents to predefined patrol regions in a real-world scenario informed by machine learning. To this end, we develop a mixed integer linear optimization formulation (MIP) to minimize the risk of failing response time targets. Given the stochasticity of the environment in terms of incident numbers, location, timing, and duration, we use Sample Average Approximation (SAA) to find a robust deployment plan. To overcome the sparsity of real data, samples are provided by an incident generator that learns the spatio-temporal distribution and demand parameters of incidents from a real world historical dataset and generates sets of training incidents accordingly. To improve runtime performance across multiple samples, we implement a heuristic based on Iterated Local Search (ILS), as the solution is intended to create deployment plans quickly on a daily basis. Experimental results demonstrate that ILS performs well against the integer model while offering substantial gains in execution time.

OFFICERS: Operational Framework for Intelligent Crime-and-Emergency Response Scheduling

“…Incident prediction is a vital prerequisite to effective deployment planning, as the knowledge of where emergencies occur will inform the positioning of response agents. Examples of prediction approaches used in the past include statistical aggregation of historical demands (Malleson and Andresen 2015), spatial hotspot identification with temporal regression (Butt et al 2021), risk terrain modeling (Caplan, Kennedy, and Miller 2011), continuous time modelling of burglary (Mukhopadhyay et al 2016), Gaussian Process incident generation for discrete space-time intervals (Chase et al 2019), deep learning (Chase et al 2021), (Wang et al 2017), and network analytics (Dash, Safro, and Srinivasamurthy 2018). Where many of these methods fall short is in capturing the spatio-temporal dependencies in crime data, where incidents appearing in one location or time period implies they will not also appear in the immediately adjacent locations or periods.…”

GRAND-VISION: An Intelligent System for Optimized Deployment Scheduling of Law Enforcement Agents

“…The previous generation method in (Chase et al 2019) applied separate models to predict the additional parameters of service time, agent demand, start time (in minutes), and priority, given the patrol region and start hour of an incident predicted by the GP. However, by using a Generative Adversarial neural Network (GAN), we can output all variables at once.…”

“…This paper builds upon the work in (Chase et al 2019), but improves it in a number of significant ways. The contributions of this paper are as follows.…”