Non-prespecified Starting Depot Formulations for Minimum-Distance Trajectory Optimization in Patrolling Problem

Abstract

In this paper, two new formulations are presented for trajectory optimization in the patrolling problem. It is assumed that the starting depot is not prespecified; an assumption that distinguishes the present work from the existing literature. A number of viewpoints are assigned to be visited in a certain sequence to minimize the total travel distance. The problem turns out to be a variant of the well-known Traveling Salesmen Problem (TSP), namely the Single depot multiple Traveling Salesmen Problem (mTSP). Comparisons between the commonly-used prespecified starting depot approach and the proposed formulations are performed and the efficacy of the results is presented through simulations. It is noted that by using the new approach, the total travel distance can be improved by an average of about 20 % compared to the case where the starting depot is prespecified, and by about 40 % in the worst-case scenario (in terms of the starting depot).