Improvements to the Linear Optimization Models of Patrol Scheduling for Mobile Targets

Abstract

Recent work in the field of security for the generation of patrol schedules has provided many solutions to real-world situations by using Stackelberg models and solving them with linear programming software. More specifically, some approaches have addressed the difficulties of defining patrol schedules for moving targets such as ferries to minimize their vulnerabilities to terrorist threats. However, one important aspect of these types of problems that hasn’t been explored yet concerns the concept of time-windows. In this work, we show the relevance of considering time-windows when generating solutions such as to attend to a broader class of problems and generate sound solutions. We propose some improvements to the model for the generation of patrol schedules for attacks on mobile targets with adjustable time durations while keeping the constraints linear to take advantage of linear programming solvers. To address the scalability issues raised by this new model, we propose a general column-generation approach composed of a master and slave problem, which can also be used on the original problem of patrol generation without time-windows. Finally, we discuss and propose a new two-phase equilibrium refinement approach to improve the robustness of the solutions found.

J.-F. Landry–This work was funded by MITACS, Menya Solutions inc. and the Natural Sciences and Engineering Research Council of Canada (NSERC).