A transformation for a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem

Abstract

Unmanned aerial vehicles (UAVs) are being increasingly used for surveillance missions in civil and military applications. These vehicles can be heterogeneous in the sense that they can differ either in their motion constraints or sensing/attack capabilities. Given a surveillance mission that require a group of heterogeneous UAVs to visit a set of targets, this paper addresses a resource allocation problem of finding the optimal sequence of targets for each vehicle such that 1) each target is visited at least once by some vehicle, and 2) the total cost travelled by all the vehicles is minimized. This problem can be posed as a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP). This paper presents a transformation of a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available for the single salesman problem can be used to solve the HMDMTSP. To show the effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results show that good quality solutions can be obtained for the HMDMTSP relatively fast.