The effective design of patrol strategies is a difficult and complex problem, especially in medium and large areas. The objective is to plan, in a coordinated manner, the optimal routes for a set of patrols in a given area, in order to achieve maximum coverage of the area, while also trying to minimize the number of patrols. In this paper, we propose a multi-agent reinforcement learning (MARL) model, based on a decentralized partially observable Markov decision process, to plan unpredictable patrol routes within an urban environment represented as an undirected graph. The model attempts to maximize a target function that characterizes the environment within a given time frame. Our model has been tested to optimize police patrol routes in three medium-sized districts of the city of Malaga. The aim was to maximize surveillance coverage of the most crime-prone areas, based on actual crime data in the city. To address this problem, several MARL algorithms have been studied, and among these the Value Decomposition Proximal Policy Optimization (VDPPO) algorithm exhibited the best performance. We also introduce a novel metric, the coverage index, for the evaluation of the coverage performance of the routes generated by our model. This metric is inspired by the predictive accuracy index (PAI), which is commonly used in criminology to detect hotspots. Using this metric, we have evaluated the model under various scenarios in which the number of agents (or patrols), their starting positions, and the level of information they can observe in the environment have been modified. Results show that the coordinated routes generated by our model achieve a coverage of more than $90\%$ of the $3\%$ of graph nodes with the highest crime incidence, and $65\%$ for $20\%$ of these nodes; $3\%$ and $20\%$ represent the coverage standards for police resource allocation.

Crime is one of the greatest threats to urban security. Around 80 percent of the world's population lives in countries with high levels of criminality. Most of the crimes committed in the cities take place in their urban environments. This paper presents the development and validation of a digital shadow platform for modeling and simulating urban crime. This digital shadow has been constructed using data-driven agent-based modeling and simulation techniques, which are suitable for capturing dynamic interactions among individuals and with their environment. Our approach transforms and integrates well-known criminological theories and the expert knowledge of law enforcement agencies (LEA), policy makers, and other stakeholders under a theoretical model, which is in turn combined with real crime, spatial (cartographic) and socio-economic data into an urban model characterizing the daily behavior of citizens. The digital shadow has also been instantiated for the city of Malaga, for which we had over 300,000 complaints available. This instance has been calibrated with those complaints and other geographic and socio-economic information of the city. To the best of our knowledge, our digital shadow is the first for large urban areas that has been calibrated with a large dataset of real crime reports and with an accurate representation of the urban environment. The performance indicators of the model after being calibrated, in terms of the metrics widely used in predictive policing, suggest that our simulated crime generation matches the general pattern of crime in the city according to historical data. Our digital shadow platform could be an interesting tool for modeling and predicting criminal behavior in an urban environment on a daily basis and, thus, a useful tool for policy makers, criminologists, sociologists, LEAs, etc. to study and prevent urban crime.