On Tightly Bounding the Dubins Traveling Salesman's Optimum

The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal solution to the problem. In addition, relaxing the motion constraints and solving the resulting Euclidean TSP (ETSP) provides the only lower bound available for the problem. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This article addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.

[1]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[2]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[3]  Xavier Goaoc,et al.  Bounded-Curvature Shortest Paths through a Sequence of Points Using Convex Optimization , 2013, SIAM J. Comput..

[4]  Richard J. Kenefic.  Finding Good Dubins Tours for UAVs Using Particle Swarm Optimization , 2008, J. Aerosp. Comput. Inf. Commun..

[5]  Mario Fernando Montenegro Campos,et al.  Data gathering tour optimization for Dubins' vehicles , 2012, 2012 IEEE Congress on Evolutionary Computation.

[6]  Mario Fernando Montenegro Campos,et al.  An Orientation Assignment Heuristic to the Dubins Traveling Salesman Problem , 2014, IBERAMIA.

[7]  Abraham P. Punnen,et al.  The traveling salesman problem and its variations , 2007 .

[8]  Ümit Özgüner,et al.  Motion planning for multitarget surveillance with mobile sensor agents , 2005, IEEE Transactions on Robotics.

[9]  James C. Bean,et al.  A Lagrangian Based Approach for the Asymmetric Generalized Traveling Salesman Problem , 1991, Oper. Res..

[10]  João Pedro Hespanha,et al.  Dubins Traveling Salesman Problem with Neighborhoods: A Graph-Based Approach , 2013, Algorithms.

[11]  Jean-Daniel Boissonnat,et al.  Shortest paths of bounded curvature in the plane , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[12]  Tim Smithers,et al.  Research issues , 1994, Formal Design Methods for CAD.

[13]  Tal Shima,et al.  On the discretized Dubins Traveling Salesman Problem , 2017 .

[14]  Xiang Ma,et al.  Receding Horizon Planning for Dubins Traveling Salesman Problems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[15]  Eloy García,et al.  Shortest Paths of Bounded Curvature for the Dubins Interval Problem , 2015, ArXiv.

[16]  Dejan Milutinovic,et al.  On the Construction of Minimum-Time Tours for a Dubins Vehicle in the Presence of Uncertainties , 2015 .

[17]  Jean-Daniel Boissonnat,et al.  Accessibility region for a car that only moves forwards along optimal paths , 1993 .

[18]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study , 2007 .

[19]  Swaroop Darbha,et al.  Computation of a Lower Bound for a Vehicle Routing Problem With Motion Constraints , 2012 .

[20]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics) , 2007 .

[21]  P. B. Sujit,et al.  Route Planning for Angle Constrained Terrain Mapping Using an Unmanned Aerial Vehicle , 2013, J. Intell. Robotic Syst..

[22]  Mario Fernando Montenegro Campos,et al.  Efficient target visiting path planning for multiple vehicles with bounded curvature , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[23]  Emilio Frazzoli,et al.  On the Dubins Traveling Salesman Problem , 2012, IEEE Transactions on Automatic Control.

[24]  F. Bullo,et al.  On the point-to-point and traveling salesperson problems for Dubins' vehicle , 2005, Proceedings of the 2005, American Control Conference, 2005..

[25]  Emilio Frazzoli,et al.  Traveling Salesperson Problems for the Dubins Vehicle , 2008, IEEE Transactions on Automatic Control.

[26]  Swaroop Darbha,et al.  Lower Bounds for a Vehicle Routing Problem with Motion Constraints , 2015, Int. J. Robotics Autom..

[27]  Swaroop Darbha,et al.  Computation of lower bounds for a multiple depot, multiple vehicle routing problem with motion constraints , 2013, 52nd IEEE Conference on Decision and Control.

[28]  Mario Fernando Montenegro Campos,et al.  Nonholonomic path planning optimization for Dubins' vehicles , 2011, 2011 IEEE International Conference on Robotics and Automation.

[29]  Swaroop Darbha,et al.  Today's Traveling Salesman Problem , 2010, IEEE Robotics & Automation Magazine.

[30]  M. Pachter,et al.  Research issues in autonomous control of tactical UAVs , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[31]  Sebastián Urrutia,et al.  Discrete optimization methods to determine trajectories for Dubins' vehicles , 2010, Electron. Notes Discret. Math..

[32]  Raja Sengupta,et al.  A Resource Allocation Algorithm for Multivehicle Systems With Nonholonomic Constraints , 2007, IEEE Transactions on Automation Science and Engineering.

[33]  Eloy García,et al.  Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points , 2017, Journal of Intelligent & Robotic Systems.

[34]  Tal Shima,et al.  Motion planning algorithms for the Dubins Travelling Salesperson Problem , 2015, Autom..