Evolutionary Intelligence

, Volume 12, Issue 2, pp 179–188 | Cite as

Hybrid optimizer for the travelling salesman problem

  • Sudip Kumar SahanaEmail author
Research Paper


In this paper, a hybrid model which combines genetic algorithm and heuristics like remove-sharp and local-opt with ant colony system (ACS) has been implemented to speed-up convergence as well as positive feedback and optimizes the search space to generate an efficient solution for complex problems. This model is validated with well-known travelling salesman problem (TSP). Finally, performance and complexity analysis show that proposed nested hybrid ACS has faster convergence rate than other standard existing algorithms such as exact and approximation algorithms to reach the optimal solution. The standard TSP problems from the TSP library are also tested and found satisfactory.


Ant colony optimization (ACO) Travelling salesman problem (TSP) Genetic algorithm (GA) Heuristics Hybrid approach Pheromone 



  1. 1.
    Dorigo M, Gambardella LM (1996) A study of some properties of ant-Q. In: Voigt HM, Ebeling W, Rechenberg I, Schwefel HS (eds) Proceedings of PPSN IV—fourth international conference on parallel problem solving from nature. Springer, Berlin, pp 656–665Google Scholar
  2. 2.
    Arora S (1996) Polynomial time approximation schemes for Euclidean TSP and other geometric problems. In: 37th annual symposium on foundations of computer science (Burlington, VT, 1996), IEEE Computer Society Press, Los Alamitos, pp 2–11Google Scholar
  3. 3.
    Dorigo M, Birattari M, Stützle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39CrossRefGoogle Scholar
  4. 4.
    Choudhary AK, Sahana SK (2019) Multicast routing: conventional algorithms vs ant colony system. Int J Comput Eng Appl XII:1–6Google Scholar
  5. 5.
    Sahana SK, Jain A, Mahanti PK (2014) Ant colony optimization for train scheduling: an analysis. IJ Intell Syst Appl 6(2):29–36Google Scholar
  6. 6.
    Bin Y, Zhong-Zhen B, Yao (2009) An improved ant colony optimization for vehicle routing problem. Eur J Oper Res 196:171–176CrossRefzbMATHGoogle Scholar
  7. 7.
    Srivastava S, Sahana SK (2016) Nested hybrid evolutionary model for traffic signal optimization. Appl Intell 46(1):1–11Google Scholar
  8. 8.
    Kumar S, Rao CSP (2009) Application of ant colony, genetic algorithm and data mining-based techniques for scheduling. J Robot Comput Integr Manuf 25(6):901–908CrossRefGoogle Scholar
  9. 9.
    Bersini H, Oury C, Dorigo M (1995) Hybridization of genetic algorithms. Université Libre de Bruxelles, Belgium, technical report no. IRIDIA/95-22Google Scholar
  10. 10.
    Johnson DS, McGeoch LA, Rothberg EE (1996) Asymptotic experimental analysis for the Held–Karp traveling salesman bound. In: Proceedings of the annual ACM-SIAM symposium on discrete algorithms, pp 341–350Google Scholar
  11. 11.
    Karp RM (1982) Dynamic programming meets the principle of inclusion and exclusion. Oper Res Lett 1(2):49–51MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Gutin G, Zverovich A (2002) Traveling salesman should not be greedy: domination analysis of greedy-type heuristics for the TSP. Discrete Appl Math 117(1–3):81–86MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Johnson DS, McGeoch LA (2002) Experimental analysis of heuristics for the STSP. In: Gutin G, Punnen AP (eds) The traveling salesman problem and its variations. Kluwer Academic Publishers, Norwell, pp 369–443Google Scholar
  14. 14.
    Rosenkrantz DJ, Stearns RE, Lewis PM (1977) An analysis of several heuristics for the traveling salesman problem. SIAM J Comput 6(5):563–581MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Christofides N (1976) Worst case analysis of a new heuristic for the traveling salesman problem. Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA, technical report 388Google Scholar
  16. 16.
    Applegate D, Cook W, Rohe A (2003) Chained Lin-Kernighan for large traveling salesman problems. INFORMS J Comput 15:82–92MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Freisleben B, Merz P (1996) Genetic local search algorithm for solving symmetric and asymmetric traveling salesman problems. In: Proceedings of the IEEE conference on evolutionary computation. IEEE Press, Nagoya, pp 616–621Google Scholar
  18. 18.
    Jayalakshmi G, Rajaram SSathiamoorty,R (2001) A hybrid genetic algorithm—a new approach to solve travelling salesman problem. Int J Comput Eng Sci 2(2):339–355CrossRefGoogle Scholar
  19. 19.
    Takahashi R (2009) A hybrid method of genetic algorithms and ant colony optimization to solve the traveling salesman problem. In: Inter-national conference on machine learning and applications, pp 81–88Google Scholar
  20. 20.
    Sahana SK, Jain A (2010) A modular hybrid ant colony approach for travelling salesman approach. In: Annual international conference on infocomm technologies in competitive strategies (ICT 2010), Singapore, pp 978–981Google Scholar
  21. 21.
    Sahana SK, Jain A (2011) An improved modular hybrid ant colony approach for solving travelling salesman problem. GSTF J Comput 1(2):123–127CrossRefGoogle Scholar
  22. 22.
    Tseng S, Tsai C, Chiang M, Yang C (2010) A fast ant colony optimization for travelling salesman problem. In: IEEE congress on evolutionary computation (CEC), Barcelona, pp 1–6Google Scholar
  23. 23.
    Dong G, Guo WW, Tickle K (2012) Solving the traveling salesman problem using cooperative genetic ant systems. Expert Syst Appl 39(5):5006–5011CrossRefGoogle Scholar
  24. 24.
    Maity S, Roy A, Maiti M (2017) An intelligent hybrid algorithm for 4- dimensional TSP. J Ind Inf Integr 5:39–50Google Scholar
  25. 25.
    Khanra A, Maiti MK, Maiti M (2015) Profit maximization of TSP through a hybrid algorithm. Comput Ind Eng 88:229–236CrossRefGoogle Scholar
  26. 26.
    Mohsen AM (2016) Annealing ant colony optimization with mutation operator for solving TSP. Comput Intell Neurosci 2016:1–13 (Article ID 8932896) CrossRefGoogle Scholar
  27. 27.
    Dong G, Guo WW (2010) A Cooperative ant colony system and genetic algorithm for TSPs. In: Tan Y, Shi Y, Tan KC (eds) Advances in swarm intelligence. ICSI 2010. Lecture notes in computer science, vol 6145. Springer, BerlinGoogle Scholar
  28. 28.
    Gong D, Ruan X (2004) A hybrid approach of GA and ACO for TSP. In: Fifth world congress on intelligent control automation (IEEE cat. no. 04EX788), vol 3, no 2004, pp 2068–2072Google Scholar
  29. 29.
    Sahana SK, Mohammad ALF, Mahanti PK (2016) Application of modified ant colony optimization (MACO) for multicast routing problem. IJ Intell Syst Appl 8(4):43–48Google Scholar
  30. 30.
    Srivastava S, Sahana SK, Pant D, Mahanti PK (2015) Hybrid microscopic discrete evolutionary model for traffic signal optimization. J Next Gen Inf Technol 6(2):1–6Google Scholar
  31. 31.
    Kumari P, Sahana SK (2019) An efficient swarm-based multicast routing technique—review. In: Behera H, Nayak J, Naik B, Abraham A (eds) Computational intelligence in data mining. Advances in intelligent systems and computing, vol 711, pp 123–134Google Scholar
  32. 32.
    Fogel D (1993) Applying evolutionary programming to selected traveling salesman problems. Cybern Syst Int J 24:27–36MathSciNetCrossRefGoogle Scholar
  33. 33.
    Whitley D, Starkweather D, Fuquay D (1989) Scheduling problems and travelling salesman: the genetic edge recombination operator. In: Schaffer JD (ed) Proceedings of the third international conference on genetic algorithms. Morgan Kaufmann, San Mateo, pp 133–140Google Scholar
  34. 34.
    Lin FT, Kao CY, Hsu CC (1993) Applying the genetic approach to simulated annealing in solving some NP-hard problems. IEEE Trans Syst Man Cybern 23:1752–1767CrossRefGoogle Scholar
  35. 35.
    Oliver I, Smith D, Holland JR (1987) A study of permutation crossover operators on the travelling salesman problem. In: Grefenstette JJ (ed) Proceedings of the second international conference on genetic algorithms. Lawrence Erlbaum, Hillsdale, pp 224–230Google Scholar
  36. 36.
    Eilon S, Watson-Gandy CDT, Christofides N (1969) Distribution management: mathematical modeling and practical analysis. Oper Res Q 20:37–53CrossRefGoogle Scholar
  37. 37.
    Angeniol B, Vaubois GDLC, Texier JYL (1988) Self-organizing feature maps and the traveling salesman problem. Neural Netw 4(1):289–293CrossRefGoogle Scholar
  38. 38.
    Somhom S, Modares A, Enkawa T (1997) A self-organizing model for the traveling salesman problem. J Oper Res Soc 48(4–6):919–928CrossRefzbMATHGoogle Scholar
  39. 39.
    Pasti R, Castro LND (2006) A neuro-immune network for solving the travelling salesman problem. In: Proceedings of 2006 international joint conference on neural networks, Vancouver, BC, Canada, pp 3760–3766Google Scholar
  40. 40.
    Masutti TAS, Castro LND (2009) A self-organizing neural network using ideas from the immune system to solve the traveling salesman problem. Inf Sci 179(10):1454–1468MathSciNetCrossRefGoogle Scholar
  41. 41.
    Chen S, Chien C (2011) Solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. Expert Syst Appl 38:14439–14450CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Birla Institute of Technology, MesraRanchiIndia

Personalised recommendations