Journal of Intelligent & Robotic Systems

, Volume 85, Issue 2, pp 307–330 | Cite as

Move and Improve: a Market-Based Mechanism for the Multiple Depot Multiple Travelling Salesmen Problem

  • Anis Koubâa
  • Omar Cheikhrouhou
  • Hachemi Bennaceur
  • Mohamed-Foued Sriti
  • Yasir Javed
  • Adel Ammar


Consider the problem of having a team of cooperative and autonomous robots to repeatedly visit a set of target locations and return back to their initial locations. This problem is known as multi-robot patrolling and can be cast to the multiple depot multiple traveling salesman problem (MD-MTSP), which applies to several mobile robots applications. As an NP-Hard problem, centralized approaches using meta-heuristic search are typically used to solve it, but such approaches are computation-intensive and cannot effectively deal with the dynamic nature of the system. This paper provides a distributed solution based on a market-based approach, called Move-and-Improve. It involves the cooperation of the robots to incrementally allocate targets and remove possible overlap. The concept is simple: in each step, a robot moves and attempts to improve its solution while communicating with its neighbors. Our approach consists of four main phases: (1) initial target allocation, (2) tour construction, (3) negotiation of conflicting targets, (4) solution improvement. To validate the efficiency of the Move-and-Improve distributed algorithm, we first conducted extensive simulations using Webots and evaluated its performance in terms of total traveled distance, maximum tour length, and ratio of overlapped targets, under different settings. We also demonstrated through MATLAB simulations the benefits of using our decentralized approach as compared to a centralized Genetic Algorithm approach to solve the MD-MTSP problem. Finally, we implemented Move-and-Improve using ROS and deployed it on real robots.


Cooperative mobile robots Robot operating system ROS Multiple depot multiple traveling salesman problem Webots 


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  1. 1.
    Farinelli, A., Iocchi, L., Nardi, D.: Multirobot systems: a classification focused on coordination. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34, 2015–2028 (2004)CrossRefGoogle Scholar
  2. 2.
    Yasuda, T. (ed.). InTechOpen, Multi-robot systems, trends and development (2011)Google Scholar
  3. 3.
    Maza, I, Ollero, A.: Multiple uav cooperative searching operation using polygon area decomposition and efficient coverage algorithms. In: Alami, R., Chatila, R., Asama, H. (eds.) Distributed Autonomous Robotic Systems 6, pp 221–230. Springer, Japan (2007)Google Scholar
  4. 4.
    Guo, W., Zhu, Z., Hou, Y.: Bayesian network based cooperative area coverage searching for uavs. In: Sambath, S., Zhu, E. (eds.) Frontiers in Computer Education vol. 133 of Advances in Intelligent and Soft Computing, pp 611–618. Springer Berlin Heidelberg (2012)Google Scholar
  5. 5.
    Pennisi, A., Previtali, F., Ficarola, F., Bloisi, D., Iocchi, L., Vitaletti, A.: Distributed sensor network for multi-robot surveillance, Procedia Computer Science, vol. 32, no. 0, pp. 1095–1100, 2014. The 5th International Conference on Ambient Systems, Networks and Technologies (ANT-2014), the 4th International Conference on Sustainable Energy Information Technology (SEIT-2014)Google Scholar
  6. 6.
    Ghaffarkhah, A., Mostofi, Y.: Path planning for networked robotic surveillance. IEEE Trans. Signal Process. 60, 3560–3575 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Anisi, D., Ogren, P., Hu, X.: Cooperative minimum time surveillance with multiple ground vehicles. IEEE Trans. Autom. Control 55, 2679–2691 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Sharma, R., Beard, R., Taylor, C., Quebe, S.: Graph-based observability analysis of bearing-only cooperative localization. IEEE Trans. Robot. 28, 522–529 (2012)CrossRefGoogle Scholar
  9. 9.
    Luo, R.: Cooperative global localization in multi-robot system. In: Yasuda, T. (ed.) Multi-Robot Systems, Trends and Development. InTechOpen (2011)Google Scholar
  10. 10.
    Arturo, G., Monica, B., Miguel, J., Oscar, R., David, U.: Cooperative simultaneous localisation and mapping using independent rao-blackwellised filters. IET Comput. Vis. 6, 407–414 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gouveia, B., Portugal, D., Silva, D., Marques, L.: Computation sharing in distributed robotic systems: a case study on slam. IEEE Trans. Autom. Sci. Eng. 12, 410–422 (2015)CrossRefGoogle Scholar
  12. 12.
    Chen, H., Sun, D., Yang, J., Chen, J.: Localization for multirobot formations in indoor environment. IEEE/ASME Trans. Mechatron. 15, 561–574 (2010)CrossRefGoogle Scholar
  13. 13.
    Francesco Conte, A.R., Cristofaro, A., Martinelli, A.: Cooperative localization and slam based on the extended information filter. In: Yasuda, T. (ed.) Multi-Robot Systems, Trends and Development. InTech Open (2011)Google Scholar
  14. 14.
    Hajjdiab, H., Laganiere, R.: Multi-robot slam: a vision-based approach. In: Yasuda, T. (ed.) Multi-Robot Systems, Trends and Development. InTech Open (2011)Google Scholar
  15. 15.
    Portugal, D., Rocha, R.: A survey on multi-robot patrolling algorithms. In: Camarinha-Matos, L. (ed.) Technological Innovation for Sustainability vol. 349 of IFIP Advances in Information and Communication Technology, pp 139–146. Springer Berlin Heidelberg (2011)Google Scholar
  16. 16.
    Portugal, D., Rocha, R.: Cooperative multi-robot patrol in an indoor infrastructure. In: Spagnolo, P., Mazzeo, P.L., Distante, C. (eds.) Human Behavior Understanding in Networked Sensing, pp 339–358. Springer International Publishing (2014)Google Scholar
  17. 17.
    Chevaleyre, Y.: Theoretical analysis of the multi-agent patrolling problem. In: Proceedings. IEEE/WIC/ACM International Conference on Intelligent Agent Technology, 2004. (IAT 2004), pp 302–308 (2004)Google Scholar
  18. 18.
    Pasqualetti, F., Durham, J., Bullo, F.: Cooperative patrolling via weighted tours: Performance analysis and distributed algorithms. IEEE Trans. Robot. 28, 1181–1188 (2012)CrossRefGoogle Scholar
  19. 19.
    Pasqualetti, F., Franchi, A., Bullo, F.: On cooperative patrolling: optimal trajectories, complexity analysis, and approximation algorithms. IEEE Trans. Robot. 28, 592–606 (2012)CrossRefGoogle Scholar
  20. 20.
    Fazli, P., Davoodi, A., Mackworth, A.K.: Multi-robot repeated area coverage. Auton. Robot. 34, 251–276 (2013)CrossRefGoogle Scholar
  21. 21.
    Jung, D., Cheng, G., Zelinsky, A.: Robot cleaning: an application of distributed planning and real-time vision. In: Zelinsky, A. (ed.) Field and Service Robotics, pp 187–194. Springer, London (1998)Google Scholar
  22. 22.
    Luo, C., Yang, S.X.: A real-time cooperative sweeping strategy for multiple cleaning robots. In: Proceedings of the 2002 IEEE International Symposium on Intelligent Control, 2002, pp 660–665 (2002)Google Scholar
  23. 23.
    Kong, C.S., Peng, N.A., Rekleitis, I.: Distributed coverage with multi-robot system. In: Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006, pp 2423–2429 (2006)Google Scholar
  24. 24.
    Ahmadi, M., Stone, P.: A multi-robot system for continuous area sweeping tasks. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 2006, pp 1724–1729 (2006)Google Scholar
  25. 25.
    Koubaa, A., Khelil, A. (eds.): Cooperative Robots and Sensor Networks, 1st edn. Springer (2013)Google Scholar
  26. 26.
    Koubaaa, A., Khelil, A.: Cooperative Robots and Sensor Networks, 2nd edn. Springer (2014)Google Scholar
  27. 27.
    Shih, C.-Y., Capitan, J., Marron, P., Viguria, A., Alarcon, F., Schwarzbach, M., Laiacker, M., Kondak, K., Martinezde Dios, J., Ollero, A.: On the cooperation between mobile robots and wireless sensor networks. In: Koubaa, A., Khelil, A. (eds.) Cooperative Robots and Sensor Networks 2014 vol. 554 of Studies in Computational Intelligence, pp 67–86. Springer, Berlin Heidelberg (2014)Google Scholar
  28. 28.
    Planet project: platform for the deployment and operation of heterogeneous networked cooperating objects. (2014)
  29. 29.
    Di Francesco, M., Das, S.K., Anastasi, G.: Data collection in wireless sensor networks with mobile elements: a survey. ACM Trans. Sensor Netw. (TOSN) 8(1), 7 (2011)Google Scholar
  30. 30.
    Trigui, S., Cheikhrouhou, O., Koubaa, A., Youssef, H.: Distributed market-based algorithm for multi-robot assignment problem. In: The International Workshop on Cooperative Robots and Sensor Networks, pp 2–5 (2014)Google Scholar
  31. 31.
    De San Bernabe, A., Martinez-de Dios, J., Regoli, C., Ollero, A.: Wireless sensor network connectivity and redundancy repairing with mobile robots. In: Koubaa, A., Khelil, A. (eds.) Cooperative Robots and Sensor Networks 2014 vol. 554 of Studies in Computational Intelligence, pp 185–204. Springer, Berlin Heidelberg (2014)Google Scholar
  32. 32.
    Li, J., Li, K., Wei, Z.: Improving sensing coverage of wireless sensor networks by employing mobile robots. In: IEEE International Conference on Robotics and Biomimetics, 2007. ROBIO 2007, pp 899–903 (2007)Google Scholar
  33. 33.
    Tafa, Z.: Towards improving barrier coverage using mobile robots. In: 2012 Mediterranean Conference on Embedded Computing (MECO), pp 166–169 (2012)Google Scholar
  34. 34.
    Kivelevitch, E., Cohen, K., Kumar, M.: Comparing the robustness of market-based task assignment to genetic algorithm. In: Proceedings of the 2012 AIAA Infotech@ Aerospace Conference. AIAA, AIAA-2012-2451 (2012)Google Scholar
  35. 35.
    Michael, R.G., David, S.J.: Computers and Intractability: a Guide to the Theory of np-Completeness. WH Freeman & Co., San Francisco (1979)zbMATHGoogle Scholar
  36. 36.
    Carter, A., Ragsdale, C.: Scheduling pre-printed newspaper advertising inserts using genetic algorithms. Omega 30, 415–421 (2002)CrossRefGoogle Scholar
  37. 37.
    Svestka, J., Huckfeldt, V.: Computational experience with an m-salesman traveling salesman algorithm. Manag. Sci. 19(7), 790–799 (1973)CrossRefzbMATHGoogle Scholar
  38. 38.
    Gilbert, R., Hofstra, K.C.: A new multiperiod multiple traveling salesman problem with heuristic and application to a scheduling problemGoogle Scholar
  39. 39.
    Brummit, B., Stentz, A.: Dynamic mission planning for multiple mobile robots. In: Proceedings of the IEEE International Conference on Robotics and Automation. IEEE (1996)Google Scholar
  40. 40.
    Brummit, B., Stentz, A.: Grammps: a generalized mission planner for multiple mobile robots. In: Proceedings of the IEEE International Conference on Robotics and Automation. IEEE (1998)Google Scholar
  41. 41.
    Yu, Z., Jinhai, L., Guochang, G., Rubo, Z., H. Y.: An implementation of evolutionary computation for path planning of cooperative mobile robots. In: Proceedings of the Fourth World Congress on Intelligent Control and Automation, pp 798–802 (2002)Google Scholar
  42. 42.
    Saleh, H., Chelouah, R.: The design of the global navigation satellite system surveying networks using genetic algorithms. Eng. Appl. Artif. Intel. 17, 111–122 (2004)CrossRefGoogle Scholar
  43. 43.
    Oberlin, P., Rathinam, S., Darbha, S.: A transformation for a multiple depot, multiple traveling salesman problem. In: Proceedings of the 2009 Conference on American Control Conference, ACC’09, pp 2636–2641. IEEE Press, NJ, USA (2009)Google Scholar
  44. 44.
    Gerkey, B.P., Matarić, M.J.: A formal analysis and taxonomy of task allocation in multi-robot systems. Int. J. Robot. Res. 23(9), 939–954 (2004)CrossRefGoogle Scholar
  45. 45.
    Vidal, T., Crainic, T.G., Gendreau, M., Lahrichi, N., Rei, W.: A hybrid genetic algorithm for multidepot and periodic vehicle routing problems. Oper. Res. 60, 611–624 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Maischberger, M., Cordeau, J.-F. In: Pahl, J., Reiners, T., Vob, S. (eds.) Network Optimization vol. 6701 of Lecture Notes in Computer Science, pp 395–400. Springer, Berlin Heidelberg (2011)Google Scholar
  47. 47.
    Escobar, J.W., Linfati, R., Toth, P., Baldoquin, M.G.: A hybrid granular tabu search algorithm for the multi-depot vehicle routing problem. J. Heuristics 20, 483–509 (2014)CrossRefGoogle Scholar
  48. 48.
    Kulkarni, A.J., Tai, K.: Probability collectives: a multi-agent approach for solving combinatorial optimization problems. Appl. Soft Comput. 10(3), 759–771 (2010)CrossRefGoogle Scholar
  49. 49.
    Batalin, M.A., Sukhatme, G.S.: Spreading out: a local approach to multi-robot coverage. In: Distributed Autonomous Robotic Systems 5, pp 373–382. Springer (2002)Google Scholar
  50. 50.
    Zheng, X., Jain, S., Koenig, S., Kempe, D.: Multirobot forest coverage. In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005. (IROS 2005), pp 3852–3857. IEEE (2005)Google Scholar
  51. 51.
    Lagoudakis, M.G., Markakis, E., Kempe, D., Keskinocak, P., Kleywegt, A.J., Koenig, S., Tovey, C.A., Meyerson, A., Jain, S.: Auction-based multi-robot routing. In: Robotics: Science and Systems, vol. 5 (2005)Google Scholar
  52. 52.
    Sariel, S., Erdogan, N., Balch, T.: An integrated approach to solving the real-world multiple traveling robot problem. In: 5th International Conference on Electrical and Electronics Engineering (2007).
  53. 53.
    Botelho, S.C., Alami, R.: M+: a scheme for multirobot cooperation through negotiated task allocation and achievement. In: 1999 IEEE International Conference on Robotics and Automation, 1999. Proceedings, vol. 2, pp 1234–1239. IEEE (1999)Google Scholar
  54. 54.
    Choi, H.-L., Brunet, L., How, J.P.: Consensus-based decentralized auctions for robust task allocation. IEEE Trans. Robot. 25(4), 912–926 (2009)CrossRefGoogle Scholar
  55. 55.
    Karmani, R.K., Latvala, T., Agha, G.: On scaling multi-agent task reallocation using market-based approach. In: First International Conference on Self-Adaptive and Self-Organizing Systems, 2007. SASO’07, pp 173–182. IEEE (2007)Google Scholar
  56. 56.
    Kivelevitch, E., Cohen, K., Kumar, M.: A market-based solution to the multiple traveling salesmen problem. J. Intell. Robot. Syst., 1–20 (2013)Google Scholar
  57. 57.
    Cui, R., Guo, J., Gao, B.: Game theory-based negotiation for multiple robots task allocation. Robotica 31(06), 923–934 (2013)CrossRefGoogle Scholar
  58. 58.
    Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  59. 59.
    Braun, H.: On solving travelling salesman problems by genetic algorithms. In: Parallel Problem Solving from Nature, pp 129–133. Springer (1991)Google Scholar
  60. 60.
    Webots: the mobile robotics simulation software. (2016)
  61. 61.
  62. 62.
    Webots simulation scenarios. (2016)
  63. 63.
    iroboapp project. (2016)
  64. 64.
    Cheikhrouhou, O., Koubaa, A., Bennaceur, H.: Move and improve: a distributed multi-robot coordination approach for multiple depots multiple travelling salesmen problem. In: 2014 IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC), pp 28–35 (2014)Google Scholar
  65. 65.
    The multi-robot simulator (mrtasim). (2016)
  66. 66.
    Hohl, L., Tellez, R., Michel, O., Ijspeert, A.J.: Aibo and webots: simulation, wireless remote control and controller transfer. Robot. Auton. Syst 54(6), 472–485 (2006)CrossRefGoogle Scholar
  67. 67.
    Kivelevitch, E.: Multiple depots multiple traveling salesmen problem (M-TSP) with variable number of salesmen using genetic algorithm (GA). In: Matlab Central File Exchange (2016)Google Scholar
  68. 68.
    Kirk, J.: Multiple variable traveling salesmen problem - genetic algorithm (GA). In: Matlab Central File Exchange (2016)Google Scholar
  69. 69.
    MRS: The multi-robot simulator. (2016)
  70. 70.
    Koubaaa, A., Sriti, M.-F., Bennaceur, H., Ammar, A., Javed, Y., Alajlan, M., Al-Elaiwi, N., Tounsi, M., Shakshuki, E.: Coros: a multi-agent software architecture for cooperative and autonomous service robots. Coop. Robot. Sens. Netw. 2015 1(1), 7 (2015)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Anis Koubâa
    • 1
    • 2
  • Omar Cheikhrouhou
    • 3
    • 4
  • Hachemi Bennaceur
    • 5
  • Mohamed-Foued Sriti
    • 5
  • Yasir Javed
    • 1
  • Adel Ammar
    • 5
  1. 1.Prince Sultan UniversityRiyadhSaudi Arabia
  2. 2.CISTER/INESC-TEC, ISEPPolytechnic Institute of PortoPortoPortugal
  3. 3.Taif UniversityTaifSaudi Arabia
  4. 4.ISIMAUniversity of MonastirMonastirTunisia
  5. 5.College of Computer and Information SciencesAl Imam Mohammad Ibn Saud Islamic University (IMSIU)RiyadhKingdom of Saudi Arabia

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