The Traveling Salesman Problem (TSP) is an important problem in computer science which consists in finding a path linking a set of cities so that each of then can be visited once, before the traveler comes back to the starting point. This is highly relevant because several real world problems can be mapped to it. A special case of TSP is the one in which the cities (the points to be visited) are not static as the cities, but mobile, changing their positions as the time passes. This variation is known as Moving Target TSP (MT-TSP). Emerging systems for crowd monitoring and control based on unmanned aerial vehicles (UAVs) can be mapped to this variation of the TSP problem, as a number of persons (targets) in the crowd can be assigned to be monitored by a given number of UAVs, which by their turn divide the targets among them. These target persons have to be visited from time to time, in a similar way to the cities in the traditional TSP. Aiming at finding a suitable solution for this type of crowd monitoring application, and considering the fact that exact solutions are too complex to perform in a reasonable time, this work explores and compares different heuristic methods for the intended solution. The performed experiments showed that the Genetic Algorithms present the best performance in finding acceptable solutions for the problem in restricted time and processing power situations, performing better compared to Ant Colony Optimization and Simulated Annealing Algorithms. (C) 2019 Published by Elsevier Ltd.