Vehicle Routing Problem Instances: Application to Multi-UAV Mission Planning Mariam Faied, Ahmed Mostafa, and Anouck Girard * †‡ § For many decades, the Vehicle Routing Problem (VRP) and its different variants have been studied and found applications in the real world. This paper briefly surveys VRP instances with applications to multi-objective Unmanned Aerial Vehicle (UAV) operations. Focusing on multi-objective multi-UAV mission planning problems, we try to take advan- tage of the literature in the VRP and its variants. We show that each military multi-UAV mission has its corresponding VRP variant. We present a novel algorithm that relies on an enhanced tree search algorithm to solve complex multi-UAV mission planning problems with complex constraints. In simulation, we introduce examples for practical problem sizes in military UAV applications. I. Introduction The VRP is faced every day by thousands of distributors worldwide and has significant economic impor- tance. In recent years, many service suppliers and distributors have recognized the importance of designing efficient distribution strategies to improve the level of customer’s service. The VRP arises naturally 1 as a central problem in the fields of transportation, distribution and logistics. Some market sectors have reported that utilization of computerized methods for transportation often results in significant savings ranging from 5% to 20% in the total costs. 2 In the last decade, new insights and algorithms have been obtained for the classical determinstic VRP as well as for natural stochastic and dynamic variations of it. These new de- velopments are based on theoretical analysis, combined probabilistic and combinatorial modeling, and lead to new and effective algorithms and a deeper understanding of uncertainty issues in vehicle routing prob- lems. 3 The VRP is an NP-hard problem with many extensions such as the Vehicle Routing Problem with Time Windows (VRPTW) and the Multiple Depot Vehicle Routing Problem (MDVRP). These extensions easily lend themselves to Unmanned Aerial Vehicles (UAV) task assignment problems. Cosidering the VRP applications, military UAV missions have emerged in the literature in the last decade. 4–6 The UAV routing problem is comparable to the Vehicle Routing Problem (VRP). The VRP optimizes the routes that several vehicles should follow when delivering goods to a network of customers from a single place of origin, a depot. When assigning UAVs, the customers are analogous to targets and the depot is the launch and landing site. In, 7, 8 A VRPTW is developed to minimize both the total distance of the routes and the number of vehicles by minimizing the summation of all chosen routes between customers in a supply delivery scenario. Joint and overlapping tasks and limited time windows were imposed in. 9 In, 6 a MILP formulation for a wide area search munitions team of UAVs to search and destroy various targets was implemented. Each target required three distinct tasks to be executed in a specific order. In, 4 a vehicle routing algorithm was applied to an ISR type scenario using a small team of UAVs with specific emphasis on an urban environment. Because the UAV task assignment problem is NP-hard, the size of the problem and thus the computational effort increases exponentially. This issue is specifically investigated in. 6 With five UAVs, four targets, and three tasks per target the computation was terminated because of the excessive computation time. 6 A prob- lem formulation, therefore, must be created that is robust enough to examine a wide variety of scenarios * This work was supported by The Ministry of Higher Education in Egypt, AFRL and AFOSR under grant number FA 8650-07-2-3744. † M. Faied is with the Aerospace Engineering Departement, The University of Michigan, Ann Arbor, MI USA, and the Department of Electrical Engineering, Fayoum University, Fayoum, Egypt mfaieda@umich.edu ‡ A. Mostafa is with the Evara Group, Ann Arbor, MI 48103-2140 USA am.evara@gmail.com § A. Girard is with the Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2140 USA anouck@umich.edu 1 of 11 American Institute of Aeronautics and Astronautics AIAA Guidance, Navigation, and Control Conference 2 - 5 August 2010, Toronto, Ontario Canada AIAA 2010-8435 Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.