Skip to main content

Advertisement

SpringerLink
Log in

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

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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)

    Article  Google Scholar 

  2. Yasuda, T. (ed.). InTechOpen, Multi-robot systems, trends and development (2011)

  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)

  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)

  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)

  6. Ghaffarkhah, A., Mostofi, Y.: Path planning for networked robotic surveillance. IEEE Trans. Signal Process. 60, 3560–3575 (2012)

    Article  MathSciNet  Google Scholar 

  7. Anisi, D., Ogren, P., Hu, X.: Cooperative minimum time surveillance with multiple ground vehicles. IEEE Trans. Autom. Control 55, 2679–2691 (2010)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  9. Luo, R.: Cooperative global localization in multi-robot system. In: Yasuda, T. (ed.) Multi-Robot Systems, Trends and Development. InTechOpen (2011)

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  12. Chen, H., Sun, D., Yang, J., Chen, J.: Localization for multirobot formations in indoor environment. IEEE/ASME Trans. Mechatron. 15, 561–574 (2010)

    Article  Google Scholar 

  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)

  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)

  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)

  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)

  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)

  18. Pasqualetti, F., Durham, J., Bullo, F.: Cooperative patrolling via weighted tours: Performance analysis and distributed algorithms. IEEE Trans. Robot. 28, 1181–1188 (2012)

    Article  Google Scholar 

  19. Pasqualetti, F., Franchi, A., Bullo, F.: On cooperative patrolling: optimal trajectories, complexity analysis, and approximation algorithms. IEEE Trans. Robot. 28, 592–606 (2012)

    Article  Google Scholar 

  20. Fazli, P., Davoodi, A., Mackworth, A.K.: Multi-robot repeated area coverage. Auton. Robot. 34, 251–276 (2013)

    Article  Google Scholar 

  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)

  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)

  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)

  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)

  25. Koubaa, A., Khelil, A. (eds.): Cooperative Robots and Sensor Networks, 1st edn. Springer (2013)

  26. Koubaaa, A., Khelil, A.: Cooperative Robots and Sensor Networks, 2nd edn. Springer (2014)

  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)

  28. Planet project: platform for the deployment and operation of heterogeneous networked cooperating objects. http://www.planet-ict.eu/ (2014)

  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. 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)

  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)

  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)

  33. Tafa, Z.: Towards improving barrier coverage using mobile robots. In: 2012 Mediterranean Conference on Embedded Computing (MECO), pp 166–169 (2012)

  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)

  35. Michael, R.G., David, S.J.: Computers and Intractability: a Guide to the Theory of np-Completeness. WH Freeman & Co., San Francisco (1979)

    MATH  Google Scholar 

  36. Carter, A., Ragsdale, C.: Scheduling pre-printed newspaper advertising inserts using genetic algorithms. Omega 30, 415–421 (2002)

    Article  Google Scholar 

  37. Svestka, J., Huckfeldt, V.: Computational experience with an m-salesman traveling salesman algorithm. Manag. Sci. 19(7), 790–799 (1973)

    Article  MATH  Google Scholar 

  38. Gilbert, R., Hofstra, K.C.: A new multiperiod multiple traveling salesman problem with heuristic and application to a scheduling problem

  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)

  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)

  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)

  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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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)

  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)

  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). http://www2.itu.edu.tr/sariel/publications.php

  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)

  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)

    Article  Google Scholar 

  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)

  56. Kivelevitch, E., Cohen, K., Kumar, M.: A market-based solution to the multiple traveling salesmen problem. J. Intell. Robot. Syst., 1–20 (2013)

  57. Cui, R., Guo, J., Gao, B.: Game theory-based negotiation for multiple robots task allocation. Robotica 31(06), 923–934 (2013)

    Article  Google Scholar 

  58. Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  59. Braun, H.: On solving travelling salesman problems by genetic algorithms. In: Parallel Problem Solving from Nature, pp 129–133. Springer (1991)

  60. Webots: the mobile robotics simulation software. http://www.cyberbotics.com/ (2016)

  61. Pioneer3AT Robots. http://www.mobilerobots.com/ResearchRobots/P3AT.aspx

  62. Webots simulation scenarios. http://www.iroboapp.org/index.php?title=Videos (2016)

  63. iroboapp project. http://www.iroboapp.org (2016)

  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)

  65. The multi-robot simulator (mrtasim). http://www.iroboapp.org/index.php?title=MRTAsim (2016)

  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)

    Article  Google Scholar 

  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)

  68. Kirk, J.: Multiple variable traveling salesmen problem - genetic algorithm (GA). In: Matlab Central File Exchange (2016)

  69. MRS: The multi-robot simulator. http://www.iroboapp.org/index.php?title=MRTAsim (2016)

  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 

Download references

Author information

Authors and Affiliations

  1. Prince Sultan University, Riyadh, Saudi Arabia

    Anis Koubâa & Yasir Javed

  2. CISTER/INESC-TEC, ISEP, Polytechnic Institute of Porto, Porto, Portugal

    Anis Koubâa

  3. Taif University, Taif, Saudi Arabia

    Omar Cheikhrouhou

  4. ISIMA, University of Monastir, Monastir, Tunisia

    Omar Cheikhrouhou

  5. College of Computer and Information Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Kingdom of Saudi Arabia

    Hachemi Bennaceur, Mohamed-Foued Sriti & Adel Ammar

Authors
  1. Anis Koubâa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Omar Cheikhrouhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hachemi Bennaceur
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohamed-Foued Sriti
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yasir Javed
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Adel Ammar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anis Koubâa.

Additional information

This paper is an extended version of the conference paper [1] published in the IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC 2014). This version presents a new introduction, an extended literature review, a new illustration of the algorithms, a completely new simulation study using Webots, and an experimental deployment on real robots.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koubâa, A., Cheikhrouhou, O., Bennaceur, H. et al. Move and Improve: a Market-Based Mechanism for the Multiple Depot Multiple Travelling Salesmen Problem. J Intell Robot Syst 85, 307–330 (2017). https://doi.org/10.1007/s10846-016-0400-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-016-0400-x

Keywords

Search

Navigation