Unmanned Combat Aerial Vehicles are defense systems based on artificial intelligence which is intensively used by many countries to provide national security on military operations. By means of these systems, moving or non-moving threat factors in the operation field could be destroyed under harsh and challenging geographical conditions without requiring a pilot with the help of a control center. In fleet operations, the necessity of destroying moving targets successfully under constraints of the endurance, munition capacity, time window and fuel cost of unmanned combat aerial vehicles brings out the moving customer-vehicle routing problem. In this study, Heterogeneous Fleet-Moving Customer Vehicle Routing Problem with Time Windows under constraint of vehicle capacity (endurance) has been aimed to be solved considering the minimum operation time and cost. In order to solve the problem, heuristic algorithms (CARA, RASA) were developed and metaheuristic algorithms (Genetic Algorithm, NSGA-II and Simulated Annealing) were used. The effectiveness of the proposed algorithms was tested on 30 different experimental sets with the number of pursuers ranging from 5-10 and the number of targets ranging from 10-35. Taguchi method was used to determine the appropriate parameter set for the algorithms. As a result of the analysis, it has been found that Genetic Algorithm produces much better results than other algorithms.