In urban areas with many commercial facilities, patrolling by police officers or security guards is essential for crime prevention, in addition to the use of surveillance cameras. To address the challenge of planning effective patrol routes, Tohyama and Tomisawa introduced the Police Officer Patrolling Problem (POPP), an arc routing problem that allows for visual monitoring from intersections and is proven to be NP-complete. Building on this work, we propose the Generalized POPP (GPOPP), a more realistic bi-objective combinatorial optimization model. This model simultaneously minimizes the total patrol route length and maximizes the coverage of surveillance areas. The contributions of this paper are threefold: (1) we formulate the GPOPP by incorporating practical constraints, such as mandatory patrolling of high-security roads and visibility-based coverage from intersections; (2) we develop a novel hybrid heuristic method that combines a multi-objective evolutionary algorithm (MoEA-HSS) with an improved Jaya algorithm to solve the GPOPP effectively; and (3) we conduct comprehensive computational experiments using benchmark instances to evaluate the effectiveness and competitiveness of the proposed method. These contributions demonstrate the practicality and efficiency of our approach for addressing realistic urban patrolling problems.
Kudo et al. (2025) studied this question.