Intelligent Service Robotics

, Volume 11, Issue 4, pp 355–369 | Cite as

An analytical hierarchy process-based approach to solve the multi-objective multiple traveling salesman problem

  • Sahar TriguiEmail author
  • Omar Cheikhrouhou
  • Anis Koubaa
  • Anis Zarrad
  • Habib Youssef
Original Research Paper


We consider the problem of assigning a team of autonomous robots to target locations in the context of a disaster management scenario while optimizing several objectives. This problem can be cast as a multiple traveling salesman problem, where several robots must visit designated locations. This paper provides an analytical hierarchy process (AHP)-based approach to this problem, while minimizing three objectives: the total traveled distance, the maximum tour, and the deviation rate. The AHP-based approach involves three phases. In the first phase, we use the AHP process to define a specific weight for each objective. The second phase consists in allocating the available targets, wherein we define and use three approaches: market-based, robot and task mean allocation-based, and balanced-based. Finally, the third phase involves the improvement in the solutions generated in the second phase. To validate the efficiency of the AHP-based approach, we used MATLAB to conduct an extensive comparative simulation study with other algorithms reported in the literature. The performance comparison of the three approaches shows a gap between the market-based approach and the other two approaches of up to 30%. Further, the results show that the AHP-based approach provides a better balance between the objectives, as compared to other state-of-the-art approaches. In particular, we observed an improvement in the total traveled distance when using the AHP-based approach in comparison with the distance traveled when using a clustering-based approach.


Assignment MTSP Multiple depots Multi-objective problem AHP 



The authors would like to thank the Center of Excellence and the Robotics and Internet-of-Things Unit at Prince Sultan University, Saudi Arabia, for their support of this work. The work is also supported by Gaitech Robotics.


  1. 1.
    Alexis K, Darivianakis G, Burri M, Siegwart R (2016) Aerial robotic contact-based inspection: planning and control. Auton Robots 40(4):631–655. CrossRefGoogle Scholar
  2. 2.
    Bektas T (2006) The multiple traveling salesman problem: an overview of formulations and solution procedures. Omega 34(3):209–219MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bolaños R, Echeverry M, Escobar J (2015) A multiobjective non-dominated sorting genetic algorithm (NSGA-II) for the multiple traveling salesman problem. Dec Sci Lett 4(4):559–568CrossRefGoogle Scholar
  4. 4.
    Brown EC, Ragsdale CT, Carter AE (2007) A grouping genetic algorithm for the multiple traveling salesperson problem. Int J Inf Technol Dec Mak 6(02):333–347CrossRefGoogle Scholar
  5. 5.
    Carter AE, Ragsdale CT (2006) A new approach to solving the multiple traveling salesperson problem using genetic algorithms. Eur J Oper Res 175(1):246–257. MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chaari I, Koubaa A, Bennaceur H, Trigui S, Al-Shalfan K (2012) Smartpath: a hybrid ACO-GA algorithm for robot path planning. In: 2012 IEEE congress on evolutionary computation, pp 1–8.
  7. 7.
    Chaari I, Koubaa A, Trigui S, Bennaceur H, Ammar A, Al-Shalfan K (2014) Smartpath: an efficient hybrid aco-ga algorithm for solving the global path planning problem of mobile robots. Int J Adv Robot Syst 11(7):94. CrossRefGoogle Scholar
  8. 8.
    Chan ZS, Collins L, Kasabov N (2006) An efficient greedy k-means algorithm for global gene trajectory clustering. Expert Syst Appl 30(1):137–141. CrossRefGoogle Scholar
  9. 9.
    Cheikhrouhou O, Koubaa A, Bennaceur H (2014) 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.
  10. 10.
    Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18CrossRefGoogle Scholar
  11. 11.
    Elango M, Nachiappan S, Tiwari MK (2011) Balancing task allocation in multi-robot systems using k-means clustering and auction based mechanisms. Expert Syst Appl 38(6):6486–6491. CrossRefGoogle Scholar
  12. 12.
    Falkenauer E (1992) The grouping genetic algorithms widening the scope of the GAs, jorbel. Belg J Oper Res Stat Comput Sci 33:79–102zbMATHGoogle Scholar
  13. 13.
    Ghafurian S, Javadian N (2011) An ant colony algorithm for solving fixed destination multi-depot multiple traveling salesmen problems. Appl Soft Comput 11(1):1256–1262. CrossRefGoogle Scholar
  14. 14.
    Gutin G, Punnen AP (2006) The traveling salesman problem and its variations, vol 12. Springer, New YorkzbMATHGoogle Scholar
  15. 15.
    Heap B, Pagnucco M (2012) Repeated sequential auctions with dynamic task clusters. In: Proceedings of the twenty-sixth AAAI conference on artificial intelligence, AAAI’12. AAAI Press, pp 1997–2002.
  16. 16.
    Helsgaun K (2012) LKH. Accessed 2012
  17. 17.
    Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Ann ArborzbMATHGoogle Scholar
  18. 18.
    Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering DepartmentGoogle Scholar
  19. 19.
    Ke L, Zhang Q, Battiti R (2013) MOEA/D-ACO: a multiobjective evolutionary algorithm using decomposition and antcolony. IEEE Trans Cybern 43(6):1845–1859. CrossRefGoogle Scholar
  20. 20.
    Király A, Abonyi J (2011) Optimization of multiple traveling salesmen problem by a novel representation based genetic algorithm. Springer, Berlin, pp 241–269. CrossRefGoogle Scholar
  21. 21.
    Kirk J (2011) Traveling-salesman-problem-genetic-algorithm. Accessed 11 July 2011
  22. 22.
    Kivelevitch E (2011) Mdmtspv\_ga-multiple depot multiple traveling salesmen problem solved by genetic algorithm. Accessed 15 June 2011
  23. 23.
    Kivelevitch E, Cohen K, Kumar M (2013) A market-based solution to the multiple traveling salesmen problem. J Intell Robot Syst 72(1):21–40. CrossRefGoogle Scholar
  24. 24.
    Koubâa A, Trigui S, Châari I (2012) Indoor surveillance application using wireless robots and sensor networks: coordination and path planning. In: Mobile ad hoc robots and wireless robotic systems: design and implementation, pp 19–57Google Scholar
  25. 25.
    Li J, Sun Q, Zhou M, Dai X (2013) A new multiple traveling salesman problem and its genetic algorithm-based solution. In: 2013 IEEE international conference on systems, man, and cybernetics, pp 627–632.
  26. 26.
    Liu W, Li S, Zhao F, Zheng A (2009) An ant colony optimization algorithm for the multiple traveling salesmen problem. In: 2009 4th IEEE conference on industrial electronics and applications, pp 1533–1537.
  27. 27.
    Lust T, Teghem J (2010) The multiobjective traveling salesman problem: a survey and a new approach. Springer, Berlin, pp 119–141. CrossRefzbMATHGoogle Scholar
  28. 28.
    Mehrabian A, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inform 1(4):355–366. CrossRefGoogle Scholar
  29. 29.
    Miettinen K (1999) Nonlinear multiobjective optimization. Springer, New YorkzbMATHGoogle Scholar
  30. 30.
    Peng W, Zhang Q, Li H (2009) Comparison between MOEA/D and NSGA-II on the multi-objective travelling salesman problem. Springer, Berlin, pp 309–324. CrossRefzbMATHGoogle Scholar
  31. 31.
    Punnen AP (2007) The traveling salesman problem: applications, formulations and variations. Springer, Boston, pp 1–28. CrossRefzbMATHGoogle Scholar
  32. 32.
    Saaty R (1987) The analytic hierarchy process: what it is and how it is used. Math Model 9(3–5):161–176. MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Shim VA, Tan KC, Cheong CY (2012) A hybrid estimation of distribution algorithm with decomposition for solving the multiobjective multiple traveling salesman problem. IEEE Trans Syst Man Cybern Part C (Appl Rev) 42(5):682–691. CrossRefGoogle Scholar
  34. 34.
    Shim VA, Tan KC, Tan KK (2012) A hybrid estimation of distribution algorithm for solving the multi-objective multiple traveling salesman problem. In: 2012 IEEE congress on evolutionary computation, pp 1–8.
  35. 35.
    Shuai Y, Bradley S, Shoudong H, Dikai L (2013) A new crossover approach for solving the multiple travelling salesmen problem using genetic algorithms. Eur J Oper Res 228:72–82MathSciNetCrossRefGoogle Scholar
  36. 36.
    Singh A, Baghel AS (2009) A new grouping genetic algorithm approach to the multiple traveling salesperson problem. Soft Comput 13(1):95–101. CrossRefGoogle Scholar
  37. 37.
    Singh H, Kaur R (2013) Resolving multiple traveling salesman problem using genetic algorithms. Int J Comput Sci Eng 3(2):209–212Google Scholar
  38. 38.
    Singh S, Lodhi EA (2014) Comparison study of multiple traveling salesmen problem using genetic algorithm. Int J Comput Sci Netw Secur (IJCSNS) 14(7):107–110Google Scholar
  39. 39.
    Trigui S, Cheikhrouhou O, Koubaa A, Baroudi U, Youssef H (2016) FL-MTSP: a fuzzy logic approach to solve the multi-objective multiple traveling salesman problem for multi-robot systems. Soft Comput. CrossRefGoogle Scholar
  40. 40.
    Trigui S, Koubaa A, Cheikhrouhou O, Qureshi B, Youssef H (2016) A clustering market-based approach for multi-robot emergency response applications. In: 2016 International conference on autonomous robot systems and competitions (ICARSC), pp 137–143.
  41. 41.
    Venkatesh P, Singh A (2015) Two metaheuristic approaches for the multiple traveling salesperson problem. Appl Soft Comput 26:74–89. CrossRefGoogle Scholar
  42. 42.
    Viguria A, Howard AM (2009) An integrated approach for achieving multirobot task formations. IEEE/ASME Trans Mechatron 14(2):176–186. CrossRefGoogle Scholar
  43. 43.
    Wang X, Liu D, Hou M (2013) A novel method for multiple depot and open paths, multiple traveling salesmen problem. In: 2013 IEEE 11th international symposium on applied machine intelligence and informatics (SAMI), pp 187–192.
  44. 44.
    Xu Z, Li Y, Feng X (2008) Constrained multi-objective task assignment for UUVs using multiple ant colonies system. In: 2008 ISECS international colloquium on computing, communication, control, and management, vol 1, pp 462–466.
  45. 45.
    Yong W (2015) Hybrid max–min ant system with four vertices and three lines inequality for traveling salesman problem. Soft Comput 19(3):585–596. CrossRefGoogle Scholar
  46. 46.
    Yousefikhoshbakht M, Didehvar F, Rahmati F (2013) Modification of the ant colony optimization for solving the multiple traveling salesman problem. Rom Acad Sect Inf Sci Technol 16(1):65–80Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ENSIUniversity of ManoubaManoubaTunisia
  2. 2.Cooperative Intelligent Networked Systems (COINS) Research GroupRiyadhSaudi Arabia
  3. 3.Taif UniversityTaifSaudi Arabia
  4. 4.Computer and Embedded Systems LabUniversity of SfaxSfaxTunisia
  5. 5.Prince Sultan UniversityRiyadhSaudi Arabia
  6. 6.CISTER/INESC-TEC, ISEPPolytechnic Institute of PortoPortoPortugal
  7. 7.School of Computer ScienceUniversity of BirminghamBirminghamUK
  8. 8.PRINCE Research LabUniversity of SousseSousseTunisia

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