Advertisement

Combinatorial Optimization: Comparison of Heuristic Algorithms in Travelling Salesman Problem

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

Abstract

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.

Notes

Compliance with ethical standard

Conflict of interest

The authors declare that they have no conflict of interest.

References

  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. http://blogs.mathworks.com/community/2010/12/13/citing-file-exchange-submissions/
  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

Personalised recommendations