Combinatorial Optimization: Comparison of Heuristic Algorithms in Travelling Salesman Problem

  • A. Hanif HalimEmail author
  • I. Ismail
Original Paper


The Travelling Salesman Problem (TSP) is an NP-hard problem with high number of possible solutions. The complexity increases with the factorial of n nodes in each specific problem. Meta-heuristic algorithms are an optimization algorithm that able to solve TSP problem towards a satisfactory solution. To date, there are many meta-heuristic algorithms introduced in literatures which consist of different philosophies of intensification and diversification. This paper focuses on 6 heuristic algorithms: Nearest Neighbor, Genetic Algorithm, Simulated Annealing, Tabu Search, Ant Colony Optimization and Tree Physiology Optimization. The study in this paper includes comparison of computation, accuracy and convergence.


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Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Luke S (2013) Essentials of metaheuristics, 2nd edn. Lulu, RaleighGoogle Scholar
  2. 2.
    Nagham Azmi AM, Ahamad TK (2008) The travelling salesman problem as a benchmark test for a social-based genetic algorithm. J Comput Sci 4:871–876Google Scholar
  3. 3.
    Bharati TP, Kalshetty YR (2016) A hybrid method to solve travelling salesman problem. IJIRCCE 4(8):15148–15152Google Scholar
  4. 4.
    Wang Z, Guo J, Zheng M, Wang Y (2015) Uncertain multiobjective travelling salesman problem. Eur J Oper Res 241:478–489zbMATHGoogle Scholar
  5. 5.
    Crama Y, van de Klundert J, Spieksma FCR (2002) Production planning problems in printed circuit board assembly. Discrete Appl Math 123:339–361MathSciNetzbMATHGoogle Scholar
  6. 6.
    Bertsimas DJ, Simchi-Levi D (1996) A new generation of vehicle routing research: robust algorithms, addressing uncertainty. Oper Res 44(2):286–304zbMATHGoogle Scholar
  7. 7.
    Tsung-Sheng C, Yat-Wah W, Wei TO (2009) A stochastic dynamic travelling salesman problem with hard time windows. Eur J Oper Res 198:749–759zbMATHGoogle Scholar
  8. 8.
    Hromkovič J (2013) Algorithmics for hard problems: introduction to combinatorial optimization, randomization, approximation, and heuristics, chapter 2, 2nd edn. Springer, BerlinGoogle Scholar
  9. 9.
    Tanasanee P (2014) Clustering evolutionary computation for solving travelling salesman problem. Int J Adv Comput Sci Inf Technol 3(3):243–262Google Scholar
  10. 10.
    Yang X-S (2010) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver Press, FromeGoogle Scholar
  11. 11.
    de Smith MJ, Goodchild MF, Longley PA (2015) Geospatial Analysis: a comprehensive guide to principles, techniques and software tools. Winchelsea Press, Leicester. ISBN 978-1905886-69-9Google Scholar
  12. 12.
    Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549MathSciNetzbMATHGoogle Scholar
  13. 13.
    Held M et al (1984) Aspects of the travelling salesman problem. IBM J Res Dev 28(4):476–486zbMATHGoogle Scholar
  14. 14.
    Yang X-S (2015) Introduction to Computational Mathematics. World Scientific Publishing, SingaporezbMATHGoogle Scholar
  15. 15.
    Eppstein D (2007) The travelling salesman problem for cubic graphs. JGAA 11:61–81zbMATHGoogle Scholar
  16. 16.
    Hahsler M, Hornik K (2007) TSP—infrastructure for the travelling salesman problem. JSTATSOFT 23(2):1–21Google Scholar
  17. 17.
    Kizilateş G, Nuriyeva F (2013) On the nearest neighbor algorithms for the travelling salesman problem. In: Advances in computational science, engineering and information technology. Advances in intelligent systems and computing, vol 225. pp 111–118Google Scholar
  18. 18.
    Chauhan C, Gupta R, Pathak K (2012) Survey of methods of solving TSP along with its implementation using dynamic programming approach. Int J Comput Appl 52(4):12–19Google Scholar
  19. 19.
    Wiak S, Krawczyk A, Dolezel I (2008) Intelligent computer techniques in applied electromagnetics. Springer, Berlin, p 190Google Scholar
  20. 20.
    Arora K, Arora M (2016) Better result for solving TSP: GA versus ACO. Int J Adv Res Comput Sci Softw Eng 6(3):219–224MathSciNetGoogle Scholar
  21. 21.
    Ansari AQ, Ibraheem, Katiyar S (2015) Comparison and analysis of solving travelling salesman problem using GA, ACO and hybrid of ACO with GA and CS. In: IEEE workshop on computational intelligence: theories, applications and future directionsGoogle Scholar
  22. 22.
    Sze SN, Tiong WK (2007) A comparison between heuristic and meta-heuristic methods for solving the multiple travelling salesman problem. World Acad Sci Eng Technol Int J Math Comput Phys Electr Comput Eng 1(1):13–16Google Scholar
  23. 23.
    Laporte G (1992) The travelling salesman problem: an overview of exact and approximate algorithms. Eur J Oper Res 59:231–247MathSciNetzbMATHGoogle Scholar
  24. 24.
    Jean-Yves P (1996) Genetic algorithms for the travelling salesman problem. Ann Oper Res 63:339–370zbMATHGoogle Scholar
  25. 25.
    Rani K, Kumar V (2014) Solving travelling salesman problem using genetic algorithm based on heuristic crossover and mutation operator. IJRET 2(2):27–34Google Scholar
  26. 26.
    Abdoun O, Jaafar A, Chakir T (2012) Analyzing the performance of mutation operators to solve the travelling salesman problem. Neural Evolut Comput Int J Emerg Sci 2(1):61–77zbMATHGoogle Scholar
  27. 27.
    Kirk J (2014) Travelling salesman problem-genetic algorithm.
  28. 28.
    Alsalibi BA, Jelodar MB, Venkat I (2013) A comparative study between the nearest neighbor and genetic algorithms: a revisit to the travelling salesman problem. IJCSEE 1(1):34–38Google Scholar
  29. 29.
    Zhan S, Lin J, Zhang Z, Zhong Y (2016) List-based simulated annealing algorithm for travelling salesman problem. Comput Intell Neurosci 2016:1–12Google Scholar
  30. 30.
    Hasegawa M (2011) Verification and rectification of physical analogy of simulated annealing for the solution of traveling salesman problem. Phys Rev E 83:036708MathSciNetGoogle Scholar
  31. 31.
    Tian P, Yang Z (1993) An improved simulated annealing algorithm with genetic characteristics and the travelling salesman problem. J Inf Optim Sci 14(3):241–255zbMATHGoogle Scholar
  32. 32.
    Basu S (2012) Tabu search implementation on travelling salesman problem and its variations: a literature survey. Am J Oper Res 2:163–173Google Scholar
  33. 33.
    Dorigo M (1997) Ant colonies for the travelling salesman problem. BioSystems 43:73–81Google Scholar
  34. 34.
    Hanif Halim A, Ismail I (2013) Nonlinear plant modeling using neuro-fuzzy system with Tree Physiology Optimization. In: IEEE student conference on research and development (SCOReD)Google Scholar
  35. 35.
    Fajar A, Herman NS, Abu NA, Shahib S (2011) Hierarchical approach in clustering to euclidean travelling salesman problem. In: ECWAC 2011 Part 1, CCIS 143, Springer, pp 192–198Google Scholar
  36. 36.
    Fischer T, Merz P (2007) Reducing the size of trevelling salesman problem instances by fixing edges. In: EvoCOP seventh European conference on evolutionary computation in combinatorial optimisation, vol 4446. Springer, pp 72–83Google Scholar
  37. 37.
    Zacharisen M, Dam M (1996) Tabu search on the geometric travelling salesman problem. In: Osman IH, Kelly JP (eds) Metaheuristics. Theory and applications. Kluwer, BostonGoogle Scholar
  38. 38.
    Miča O (2015) Comparison metaheuristic methods by solving travelling salesman problem. In: The international scientific conference INPROFORUM, pp 161–165Google Scholar
  39. 39.
    Mamun-Ur-Rashid Khan Md, Asadijjaman Md (2016) A tabu search approximation for finding the shortest distance using travelling salesman problem. IOSR J Math 12(5):80–84Google Scholar
  40. 40.
    Laguna M, Barnes JW, Glover FW (1991) Tabu search methods for a single machine scheduling problem. J Intell Manuf 2:63–74Google Scholar
  41. 41.
    Civicioglu P, Besdok E (2013) A conceptual comparison of the cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artif Intell Rev 39(4):315–346Google Scholar
  42. 42.
    Hanif Halim A, Ismail I (2017) Comparative study of meta-heuristics optimization algorithm using benchmark function. Int J Electr Comput Eng 7(2):1103–1109Google Scholar
  43. 43.
    Hanif Halim A, Ismail I (2016) Online PID controller tuning using tree physiology optimization. In: International conference on intelligent and advanced systems (ICIAS), pp 1–5Google Scholar

Copyright information

© CIMNE, Barcelona, Spain 2017

Authors and Affiliations

  1. 1.Electrical and Electronic Engineering DepartmentUniversiti Teknologi PETRONASTronohMalaysia

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