Soft Computing

, Volume 21, Issue 24, pp 7351–7362 | Cite as

FL-MTSP: a fuzzy logic approach to solve the multi-objective multiple traveling salesman problem for multi-robot systems

  • Sahar Trigui
  • Omar Cheikhrouhou
  • Anis Koubaa
  • Uthman Baroudi
  • Habib Youssef
Methodologies and Application

Abstract

This paper considers the problem of assigning target locations to be visited by mobile robots. We formulate the problem as a multiple-depot multiple traveling salesman problem (MD-MTSP), an NP-Hard problem instance of the MTSP. In contrast to most previous works, we seek to optimize multiple performance criteria, namely the maximum traveled distance and the total traveled distance, simultaneously. To address this problem, we propose, FL-MTSP, a new fuzzy logic approach that combines both metrics into a single fuzzy metric, reducing the problem to a single-objective optimization problem. Extensive simulations show that the proposed fuzzy logic approach outperforms an existing centralized Genetic Algorithm (MDMTSP_GA) in terms of providing a good trade-off of the two performance metrics of interest. In addition, the execution time of FL-MTSP was shown to be always faster than that of the MDMTSP_GA approach, with a ratio of 89 %.

Keywords

MD-MTSP Fuzzy logic Optimization problem Multi-objective 

References

  1. Bérubé JF, Gendreau M, Potvin JY (2009) An exact \(\varepsilon \)-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits. Eur J Oper Res 194:39–50CrossRefMATHMathSciNetGoogle Scholar
  2. Bolaños R, Echeverry M, Escobar J (2015) A multiobjective non-dominated sorting genetic algorithm (NSGA-II) for the multiple traveling salesman problem. Decis Sci Lett 4:559–568CrossRefGoogle Scholar
  3. Brown EC, Ragsdale CT, Carter AE (2007) A grouping genetic algorithm for the multiple traveling salesperson problem. Int J Inf Technol Decis Mak 6:333347CrossRefMATHGoogle Scholar
  4. Carter AE, Ragsdale CT (2006) A new approach to solving the multiple traveling salesperson problem using genetic algorithms. Eur J Oper Res 175:245–257CrossRefMATHMathSciNetGoogle Scholar
  5. Cheikhrouhou O, Koubâa A, Bennaceur H (2014) Move and improve: a distributed multi-robot coordination approach for multiple depots multiple travelling salesmen problem. In: IEEE international conference on autonomous robot systems and competitions (ICARSC) 2014, IEEE, p 28–35Google Scholar
  6. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  7. Fazli P, Davoodi A, Pasquier P, Mackworth AK (2010) Complete and robust cooperative robot area coverage with limited range. In: 2010 IEEE/RSJ international conference on intelligent robots and systems (IROS), p 5577–5582Google Scholar
  8. Ke L, Zhang Q, Battiti R (2013) MOEA/D-ACO: a multiobjective evolutionary algorithm using decomposition and antcolony. IEEE Trans Cybern 43:1845–1859CrossRefGoogle Scholar
  9. Khamis AM, Elmogy AM, Karray FO (2011) Complex task allocation in mobile surveillance systems. J Intell Robot Syst 64:33–55CrossRefGoogle Scholar
  10. Kivelevitch E (2011) MDMTSPV_GA—multiple depot multiple traveling salesmen problem solved by genetic algorithm. http://www.mathworks.com/matlabcentral/fileexchange/31814-mdmtspv-ga-multiple-depot-multiple-traveling-salesmen-problem-solved-by-genetic-algorithm
  11. Kivelevitch E, Cohen K, Kumar M (2013) A market-based solution to the multiple traveling salesmen problem. J Intell Robot Syst 72:21–40CrossRefGoogle Scholar
  12. 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: Design and Implementation, pp 19–57Google Scholar
  13. Liu W, Li S, Zhao F, Zheng A (2009) An ant colony optimization algorithm for the multiple traveling salesmen problem. In: 4th IEEE conference on industrial electronics and applications, 2009. ICIEA 2009, p 1533–1537Google Scholar
  14. Mamdani EH, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Man Mach Stud 7:1–13CrossRefMATHGoogle Scholar
  15. Marler RT, Arora JS (2010) The weighted sum method for multi-objective optimization: new insights. Struct Multidiscip Optim 41:853–862CrossRefMATHMathSciNetGoogle Scholar
  16. Mavrotas G (2009) Effective implementation of the \(\varepsilon \)-constraint method in multi-objective mathematical programming problems. Appl Math Comput 213:455–465MATHMathSciNetGoogle Scholar
  17. Nikolić I (2007) Total time minimizing transportation problem. Yugosl J Oper Res 17(1):125–133CrossRefMATHMathSciNetGoogle Scholar
  18. Pippin C, Christensen H, Weiss L (2013) Performance based task assignment in multi-robot patrolling. In: Proceedings of the 28th annual ACM symposium on applied computing, p 70–76Google Scholar
  19. Sariel S, Erdogan N, Balch T (2007) An integrated approach to solving the real-world multiple traveling robot problem. In: 5th international conference on electrical and electronics engineeringGoogle Scholar
  20. Seshadri A (2006) A fast elitist multiobjective genetic algorithm: NSGA-II. MATLAB Central 182Google Scholar
  21. Shim VA, Tan KC, Tan KK (2012b) A hybrid estimation of distribution algorithm for solving the multi-objective multiple traveling salesman problem. In: 2012 IEEE congress on evolutionary computation (CEC), p 1–8Google Scholar
  22. Shim VA, Tan KC, Cheong CY (2012a) A hybrid estimation of distribution algorithm with decomposition for solving the multiobjective multiple traveling salesman problem. IEEE Trans Syst Man Cybern C Appl Rev 42:682–691CrossRefGoogle Scholar
  23. Singh A, Baghel AS (2009) A new grouping genetic algorithm approach to the multiple traveling salesperson problem. Soft Comput 13:95–101CrossRefGoogle Scholar
  24. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 1:116–132CrossRefMATHGoogle Scholar
  25. Trigui S, Koubâa A, Cheikhrouhou O, Youssef H, Bennaceur H, Sriti MF, Javed Y (2014) A distributed market-based algorithm for the multi-robot assignment problem. Proced Comput Sci 32:1108–1114CrossRefGoogle Scholar
  26. Trigui S, Koubâa A, Ben Jamâa M, Châari I, Al-Shalfan K (2012) Coordination in a multi-robot surveillance application using wireless sensor networks. In: 16th IEEE mediterranean electrotechnical conference (MELECON), IEEE, p 989–992Google Scholar
  27. Wang X, Liu D, Hou M (2013) A novel method for multiple depot and open paths, Multiple Traveling Salesmen Problem. In: 11th IEEE international symposium on applied machine intelligence and informatics (SAMI), IEEE, p 187–192Google Scholar
  28. Xu Z, Li Y, Feng X (2008) Constrained multi-objective task assignment for UUVs using multiple ant colonies system. In: ISECS international colloquium on computing, communication, control, and management, 2008. CCCM’08., vol 1, p 462–466Google Scholar
  29. Yousefikhoshbakht M, Didehvar F, Rahmati F (2013) Modification of the ant colony optimization for solving the multiple traveling salesman problem. Roman Acad Sect Inf Sci Technol 16:65–80Google Scholar
  30. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar
  31. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoningI. Inf Sci 8:199–249CrossRefMATHGoogle Scholar
  32. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Sahar Trigui
    • 1
    • 2
  • Omar Cheikhrouhou
    • 3
    • 4
  • Anis Koubaa
    • 5
    • 6
  • Uthman Baroudi
    • 7
  • Habib Youssef
    • 8
  1. 1.University of ManoubaManoubaTunisia
  2. 2.Cooperative Intelligent Networked Systems (COINS) Research GroupRiyadhSaudi Arabia
  3. 3.Taif UniversityTaifKingdom of Saudi Arabia
  4. 4.Computer and Embedded Systems LaboratoryUniversity of SfaxSfaxTunisia
  5. 5.Prince Sultan UniversityRiyadhSaudi Arabia
  6. 6.CISTER/INESC-TEC, ISEPPolytechnic Institute of PortoPortoPortugal
  7. 7.Wireless Sensors and Robotics Laboratory, Computer EngineeringKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  8. 8.PRINCE Research UnitUniversity of SousseSousseTunisia

Personalised recommendations