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Proper patrol route planning increases the effectiveness of police patrolling and improves public security. In this paper we present a new approach for the real-time patrol route planning in a dynamic environment. We first build a mathematic framework, and then propose a fast algorithm developed from the Cross Entropy method to meet the real-time computation requirement needed for many applications. In addition, as the randomness is an important factor for practices, the entropy concept is used for designing the randomized patrol routes schedule strategy. Numerical studies demonstrate that the approach has fast convergence property and is efficient in dynamic patrol environment.