Tamás Kalmár-Nagy, Giovanni Giardini


The purpose of this paper is to present a Multi-Agent planner for a team of autonomous agents. The approach is demonstrated by the Multi-Agent Planning Problem, which is a variant of the classical Multiple Traveling Salesmen Problem (MTSP): given a set of n goals/targets and a team of m agents, the optimal team strategy consists of finding m tours such that each target is visited only once and by only one agent, and the total cost of visiting all nodes is minimal. The proposed solution method is a Genetic Algorithm Inspired Steepest Descent (GAISD) method. To validate the approach, the method has been benchmarked against MTSPs and routing problems. Numerical experiments demonstrate the goodness of the approach.


  1. Ali, A. I. and Kennington, J. L. (1986). The asymmetric mtraveling salesman problem: a duality based branchand-bound algorithm. Discrete Applied Mathematics, 13(2-3):259-276.
  2. Balas, E. and Toth, P. (1985). Branch and bound methods. In Lawler, E. L., Lenstra, J., Rinnooy Kart, A. H. G., and Shmoys, D. B., editors, The Traveling Salesman Problem, chapter 10, pages 361-397. New York, John Wiley and Sons edition.
  3. Baumgartner, E. T. (2000). In-situ exploration of Mars using rover systems. In Proceedings of the AIAA Space 2000 Conference, number 2000-5062, Long Beach, CA, USA. AIAA.
  4. Bektas, T. (2006). The Multiple Traveling Salesman Problem: an overview of formulations and solution procedures. Omega (Oxford), 34(3):209-219.
  5. Bellmore, M. and Hong, S. (1974). Transformation of Multisalesman Problem to the standard Traveling Salesman Problem. Journal of the ACM, 21(3):500-504.
  6. Bentley, J. L. (1990). Experiments on Traveling Salesman heuristics. In Proceedings of the First Annual ACMSIAM Symposium on Discrete Algorithms, pages 91- 99, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics.
  7. Birk, A. and Carpin, S. (2006). Rescue robotics - A crucial milestone on the road to autonomous systems. Advanced Robotics, 20(5):595-605.
  8. Bondy, J. and Murty, U. (1976). Graph Theory with applications. Macmillan London.
  9. Brown, E. C., Ragsdale, C. T., and Carter, A. E. (2007). A grouping Genetic Algorithm for the Multiple Traveling Salesperson Problem. International Journal of Information Technology and Decision Making, 6(2):333-347.
  10. Carpin, S., Wang, J., Lewis, M., Birk, A., and Jacoff, A. (2006). High fidelity tools for rescue robotics: results and perspectives. RoboCup 2005: Robot Soccer World Cup IX, 4020:301-311.
  11. Carter, A. E. (2003). Design and application of Genetic Algorithms for the Multiple Traveling Salesperson Assignment Problem. PhD thesis, Department of Management Science and Information Technology, Virginia Polytechnic Institute and State University.
  12. Carter, A. E. and Ragsdale, C. T. (2002). Scheduling preprinted newspaper advertising inserts using genetic algorithms. Omega, 30(6):415-421.
  13. Carter, A. E. and Ragsdale, C. T. (2006). A new approach to solving the Multiple Travelling Salesperson Problem using Genetic Algorithms. European Journal Operational Research, 175(1):246-257.
  14. Diestel, R. (2005). Graph Theory. Springer.
  15. Gavish, B. and Srikanth, K. (1986). An optimal solution method for large-scale Multiple Traveling Salesmen Problems. Operations Research, 34(5):698-717.
  16. Giardini, G. and Kalmár-Nagy, T. (2007). Centralized and distributed path planning for Multi-Agent exploration. In AIAA 2007, Conference of Guidance, Navigation and Control.
  17. Goldberg, D. E. (1989). Genetic Algorithms in search, optimization, and machine learning. Addison-Wesley Professional, Boston, MA, USA.
  18. Gorenstein, S. (1970). Printing Press Scheduling for Multi-Edition Periodicals. Management Science, 16(6):B373-B383.
  19. Gutin, G. and Punnen, A. (2002). The Traveling Salesman Problem and its variations, volume 12 of Combinatorial Optimizations. Kluwer Academic Publishers, Norwell, MA, Springer edition.
  20. Hayati, S., Volpe, R., Backes, P., Balaram, J., Welch, R., Ivlev, R., Tharp, G., Peters, S., Ohm, T., Petras, R., and Laubach, S. (1997). The Rocky 7 rover: a Mars sciencecraft prototype. In IEEE International Conference on Robotics and Automation, volume 3, pages 2458-2464, Albuquerque.
  21. Hong, S. and Padberg, M. (1977). A note on the Symmetric Multiple Traveling Salesman Problem with fixed charges. Operations Research, 25(5):871-874.
  22. Jacoff, A., Messina, E., and Evans, J. (2002). Experiences in deploying test arenas for autonomous mobile robots. NIST Special Publication, pages 87-94.
  23. Johnson, D. S. and McGeoch, L. A. (1997). The Traveling Salesman Problem: a case study in local optimization. Local Search in Combinatorial Optimization, pages 215-310.
  24. Junjie, P. and Dingwei, W. (2006). An Ant Colony Optimization Algorithm for Multiple Travelling Salesman Problem. In Proceedings of the First International Conference on Innovative Computing, Information and Control, pages 210-213, Washington, DC, USA. IEEE Computer Society.
  25. Kara, I. and Bektas, T. (2006). Integer linear programming formulations of multiple salesman problems and its variations. European Journal of Operational Research, 174(3):1449-1458.
  26. Kulich, M., Kubalik, J., Klema, J., and Faigl, J. (2004). Rescue operation planning by soft computing techniques.
  27. In IEEE 4th International Conference on Intelligent Systems Design and Application, pages 103-109, Budapest, Hungary.
  28. Laporte, G., Nobert, Y., and Taillefer, S. (1987). A branchand-bound algorithm for the asymmetrical distanceconstrained vehicle routing problem. Mathematical Modelling, 9(12):857-868.
  29. Matayoshi, M., Nakamura, M., and Miyagi, H. (2004). A Genetic Algorithm with the improved 2-opt method. In IEEE International Conference on Systems, Man and Cybernetics, volume 4, pages 3652-3658.
  30. Mitrovic-Minic, S. and Krishnamutri, R. (2002). The Multiple Traveling Salesman Problem with Time Windows: bounds for the minimum number of vehicles. Technical Report TR 2002-11, FU CS School.
  31. Na, B. (2006). Heuristics for No-depot Multiple Traveling Salesmen Problem with Minmax Objective. Master's thesis, H. Milton School of Industrial and Engineering, Georgia Institute of Technology, Atlanta, GA.
  32. Orloff, C. S. (1974). Routing a fleet of m vehicles to/from a central facility. Networks, 4(2):147-162.
  33. Pereira, F., Tavares, J., Machado, P., and Costa, E. (2002). GVR: a new Genetic Representation for the Vehicle Routing Problem. Lecture Notes in Computer Science, pages 95-102.
  34. Reinelt, G. (1991). TSPLIB: a Traveling Salesman Problem Library. In ORSA Journal on Computing, volume 3, pages 376-384.
  35. Sariel, S. and Akin, H. (2005). RoboCup 2004: Robot Soccer World Cup VIII, volume 3276/2005, chapter A Novel Search Strategy for Autonomous Search and Rescue Robots, pages 459-466. Springer.
  36. Schrijver, A. (1986). Theory of linear and integer programming. John Wiley and Sons, Inc. New York, NY, USA.
  37. Sengoku, H. and Yoshihara, I. (1998). A fast TSP solver using GA on JAVA. In Third International Symposium on Artificial Life, and Robotics (AROB III'98), pages 283-288.
  38. Singh, A. and Baghel, A. S. (2009). A new grouping genetic algorithm approach to the Multiple Traveling Salesperson Problem. Soft Computing - A Fusion of Foundations, Methodologies and Applications, 13(1):95- 101.
  39. Sofge, D., Schultz, A., and Jong, K. D. (2002). Evolutionary computational approaches to Solving the Multiple Traveling Salesman Problem using a neighborhood attractor schema. Application of Evolutionary Computing, 2279(0302-9743):153-162.
  40. Stentz, A. T. and Brummit, B. (1996). Dynamic mission planning for multiple mobile robots. In Proceedings of the IEEE International Conference on Robotics and Automation.
  41. Stentz, A. T. and Brummit, B. (1998). GRAMMPS: A Generalized Mission Planner for Multiple Mobile Robots. In Proceedings of the IEEE International Conference on Robotics and Automation.
  42. Tang, L., Liu, J., Rong, A., and Yang, Z. (2000). A Multiple Traveling Salesman Problem model for hot rolling scheduling in Shanghai Baoshan Iron and Steel Complex. European Journal of Operational Research, 124(2):267-282.
  43. Tschoke, S., Luling, R., and Monien, B. (1995). Solving the Traveling Salesman Problem with a distributed branch-and-bound algorithm on a 1024 processor network. Proceedings of the 9th International Symposium on Parallel Processing, pages 182-189.
  44. (2008). Multiple Traveling Salesmen Problem - Genetic Algorithm.
  45. Yu, Z., Jinhai, L., Guochang, G., Rubo, Z., and Haiyan, Y. (2002). An implementation of evolutionary computation for path planning of cooperative mobile robots. In Proceedings of the Fourth World Congress on Intelligent Control and Simulation, volume 3, pages 1798- 1802.

Paper Citation

in Harvard Style

Kalmár-Nagy T. and Giardini G. (2011). THE MULTI-AGENT PLANNING PROBLEM . In Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-8425-40-9, pages 296-305. DOI: 10.5220/0003177502960305

in Bibtex Style

author={Tamás Kalmár-Nagy and Giovanni Giardini},
booktitle={Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

in EndNote Style

JO - Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
SN - 978-989-8425-40-9
AU - Kalmár-Nagy T.
AU - Giardini G.
PY - 2011
SP - 296
EP - 305
DO - 10.5220/0003177502960305