Skip to main content

Advertisement

Log in

Hybrid optimizer for the travelling salesman problem

  • Research Paper
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  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 656–665

    Google Scholar 

  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 2–11

  3. Dorigo M, Birattari M, Stützle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39

    Article  Google Scholar 

  4. Choudhary AK, Sahana SK (2019) Multicast routing: conventional algorithms vs ant colony system. Int J Comput Eng Appl XII:1–6

    Google Scholar 

  5. Sahana SK, Jain A, Mahanti PK (2014) Ant colony optimization for train scheduling: an analysis. IJ Intell Syst Appl 6(2):29–36

    Google Scholar 

  6. Bin Y, Zhong-Zhen B, Yao (2009) An improved ant colony optimization for vehicle routing problem. Eur J Oper Res 196:171–176

    Article  MATH  Google Scholar 

  7. Srivastava S, Sahana SK (2016) Nested hybrid evolutionary model for traffic signal optimization. Appl Intell 46(1):1–11

    Google Scholar 

  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):901–908

    Article  Google Scholar 

  9. Bersini H, Oury C, Dorigo M (1995) Hybridization of genetic algorithms. Université Libre de Bruxelles, Belgium, technical report no. IRIDIA/95-22

  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 341–350

  11. Karp RM (1982) Dynamic programming meets the principle of inclusion and exclusion. Oper Res Lett 1(2):49–51

    Article  MathSciNet  MATH  Google Scholar 

  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):81–86

    Article  MathSciNet  MATH  Google Scholar 

  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 369–443

    Google Scholar 

  14. Rosenkrantz DJ, Stearns RE, Lewis PM (1977) An analysis of several heuristics for the traveling salesman problem. SIAM J Comput 6(5):563–581

    Article  MathSciNet  MATH  Google Scholar 

  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 388

  16. Applegate D, Cook W, Rohe A (2003) Chained Lin-Kernighan for large traveling salesman problems. INFORMS J Comput 15:82–92

    Article  MathSciNet  MATH  Google Scholar 

  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 616–621

  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):339–355

    Article  Google Scholar 

  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 81–88

  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 978–981

  21. Sahana SK, Jain A (2011) An improved modular hybrid ant colony approach for solving travelling salesman problem. GSTF J Comput 1(2):123–127

    Article  Google Scholar 

  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 1–6

  23. Dong G, Guo WW, Tickle K (2012) Solving the traveling salesman problem using cooperative genetic ant systems. Expert Syst Appl 39(5):5006–5011

    Article  Google Scholar 

  24. Maity S, Roy A, Maiti M (2017) An intelligent hybrid algorithm for 4- dimensional TSP. J Ind Inf Integr 5:39–50

    Google Scholar 

  25. Khanra A, Maiti MK, Maiti M (2015) Profit maximization of TSP through a hybrid algorithm. Comput Ind Eng 88:229–236

    Article  Google Scholar 

  26. Mohsen AM (2016) Annealing ant colony optimization with mutation operator for solving TSP. Comput Intell Neurosci 2016:1–13 (Article ID 8932896)

    Article  Google Scholar 

  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, Berlin

    Google Scholar 

  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 2068–2072

  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):43–48

    Google Scholar 

  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):1–6

    Google Scholar 

  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 123–134

  32. Fogel D (1993) Applying evolutionary programming to selected traveling salesman problems. Cybern Syst Int J 24:27–36

    Article  MathSciNet  Google Scholar 

  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 133–140

    Google Scholar 

  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 23:1752–1767

    Article  Google Scholar 

  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 224–230

    Google Scholar 

  36. Eilon S, Watson-Gandy CDT, Christofides N (1969) Distribution management: mathematical modeling and practical analysis. Oper Res Q 20:37–53

    Article  Google Scholar 

  37. Angeniol B, Vaubois GDLC, Texier JYL (1988) Self-organizing feature maps and the traveling salesman problem. Neural Netw 4(1):289–293

    Article  Google Scholar 

  38. Somhom S, Modares A, Enkawa T (1997) A self-organizing model for the traveling salesman problem. J Oper Res Soc 48(4–6):919–928

    Article  MATH  Google Scholar 

  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 3760–3766

  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):1454–1468

    Article  MathSciNet  Google Scholar 

  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 38:14439–14450

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sudip Kumar Sahana.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sahana, S.K. Hybrid optimizer for the travelling salesman problem. Evol. Intel. 12, 179–188 (2019). https://doi.org/10.1007/s12065-019-00208-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-019-00208-7

Keywords

Navigation