Skip to main content
SpringerLink
Log in

A swarm intelligence approach for the colored traveling salesman problem

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper addresses the recently introduced colored traveling salesman problem (CTSP), which is a variant of the multiple traveling salesman problem (MTSP). In the MTSP, given a set of cities, there are multiple salesman to visit these cities though each city must be visited exactly once by one salesman only. On the other hand in case of the CTSP, every salesman have their exclusive cities to visit and a group of shared cities that are shared among different salesmen but should be visited exactly once by one salesman only. In this paper, an artificial bee colony (ABC) algorithm based approach is proposed for the CTSP and its superiority over other state-of-the-art approaches is demonstrated experimentally in terms of both quality of solution and computational time on the benchmark instances available in the literature. In addition, the encoding scheme that we have used to represent a CTSP solution within the ABC algorithm is theoretically analyzed and it is shown that our encoding scheme yields a solution space that is considerably smaller than the scheme used by the state-of-the-art approaches for the CTSP.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. scis.uohyd.ac.in/~alokcs/ctsp_new.zip

References

  1. Akay B, Karaboga D (2012) A modified artificial bee colony algorithm for real-parameter optimization. Inform Sci 192:120–142

    Article  Google Scholar 

  2. Arora S, Singh S (2017) An effective hybrid butterfly optimization algorithm with artificial bee colony for numerical optimization. Int J Interact Multimed Artif Intell 4:14–21

    Google Scholar 

  3. Bai W, Eke I, Lee K Y (2017) An improved artificial bee colony optimization algorithm based on orthogonal learning for optimal power flow problem. Control Eng Pract 61:163–172

    Article  Google Scholar 

  4. Banda J, Singh A (2017) A hybrid artificial bee colony algorithm for the cooperative maximum covering location problem. Int J Mach Learn Cybern 8:691–697

    Article  Google Scholar 

  5. Basturk B, Karaboga D (2006) An artificial bee colony (ABC) algorithm for numeric function optimization. In: Proceedings of the IEEE Swarm Intelligence Symposium. IEEE, Indianapolis, pp 12–14

  6. Braekers K, Ramaekers K, Van Nieuwenhuyse I (2016) The vehicle routing problem: state of the art classification and review. Comput Indus Eng 99:300–313

    Article  Google Scholar 

  7. Bräysy O, Gendreau M (2005a) Vehicle routing problem with time windows, part i: route construction and local search algorithms. Transport Sci 39(1):104–118

    Article  Google Scholar 

  8. Bräysy O, Gendreau M (2005b) Vehicle routing problem with time windows, part ii: metaheuristics. Transport Sci 39(1):119–139

    Article  Google Scholar 

  9. Candan G, Yazgan H R (2015) Genetic algorithm parameter optimisation using taguchi method for a flexible manufacturing system scheduling problem. Int J Prod Res 53(3):897–915

    Article  Google Scholar 

  10. Carter A E, Ragsdale C T (2006) A new approach to solving the multiple traveling salesperson problem using genetic algorithms. Eur J Oper Res 175:245–257

    Article  MathSciNet  Google Scholar 

  11. Eksioglu B, Vural A V, Reisman A (2009) The vehicle routing problem: a taxonomic review. Comput Indus Eng 57(4):1472–1483

    Article  Google Scholar 

  12. El-Sherbeny N A (2010) Vehicle routing with time windows: an overview of exact, heuristic and metaheuristic methods. J King Saud Univ-Sci 22(3):123–131

    Article  Google Scholar 

  13. Gao W, Liu S (2011) Improved artificial bee colony algorithm for global optimization. Inf Process Lett 111:871–882

    Article  MathSciNet  Google Scholar 

  14. Gao W, Liu S, Huang L (2012) A global best artificial bee colony algorithm for global optimization. J Comput Appl Math 236:2741–2753

    Article  MathSciNet  Google Scholar 

  15. Gendreau M, Tarantilis C D (2010) Solving large-scale vehicle routing problems with time windows: the state-of-the-art. Technical Report CIRRELT-2010-04, CIRRELT University of Montreal, Montreal

  16. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report TR06 Computer Engineering Department, Erciyes University, Turkey

  17. Karaboga D, Akay B (2011) A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl Soft Comput 11:3021–3031

    Article  Google Scholar 

  18. Karaboga D, Basturk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. In: Lecture notes in artificial intelligence, vol 4529. Springer, Berlin, pp 789–798

  19. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numeric function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471

    Article  Google Scholar 

  20. Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8:687–697

    Article  Google Scholar 

  21. Karaboga D, Gorkemli B (2011) A combinatorial artificial bee colony algorithm for traveling salesman problem. In: 2011 International symposium on innovations in intelligent systems and applications (INISTA). IEEE, pp 50–53

  22. Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42(1):21–57

    Article  Google Scholar 

  23. Li J, Qiru S, Zhou M, Dai X (2013) A new multiple traveling salesman problem and its genetic algorithm-based solution. In: Proceedings of the 2013 IEEE international conference on systems man and cybernetics. Manchester, pp 1–6

  24. Li J, Sun Q, Zhou M, Yu X, Dai X (2014) Colored traveling salesman problem and solution. IFAC Proc 47(3):9575–9580

    Article  Google Scholar 

  25. Li J, Dai X, Liu H, Zhou M (2015) A decomposition approach to colored traveling salesman problems. In 2015 IEEE International conference on automation science and engineering (CASE). IEEE, pp 51–56

  26. Li J, Zhou M, Dai X, Sun Q, Yu X (2015) A colored traveling salesman problem model for planning dual-bridge waterjet cutting paths. IEEE Trans Indus Inf (Under Review)

  27. Li J, Zhou M, Sun Q, Dai X, Yu X (2015) Colored traveling salesman problem. IEEE Trans Cybern 45(11):2390–2401

    Article  Google Scholar 

  28. Li J, Meng X, Dai X (2017) Collision-free scheduling of multi-bridge machining systems: a colored traveling salesman problem-based approach. IEEE/CAA Journal of Automatica Sinica, 1–9. https://doi.org/10.1109/JAS.2017.7510415

    Article  MathSciNet  Google Scholar 

  29. Li J, Meng X, Zhou M, Dai X (2017) A two-stage approach to path planning and collision avoidance of multibridge machining systems. IEEE Trans Syst Man Cybern Syst 47:1039–1049

    Article  Google Scholar 

  30. Li L, Cheng Y, Tan L, Niu B (2011) A discrete artificial bee colony algorithm for TSP problem. In: Bio-Inspired computing and applications - 7th international conference on intelligent computing, ICIC 2011, Zhengzhou, China, August 11-14. 2011, Revised Selected Papers, pp 566–573

  31. Li W H, Li W J, Yang Y, Liao H Q, Li J L, Zheng X P (2011) Artificial bee colony algorithm for traveling salesman problem. In: Advanced materials research, vol 314.Trans Tech Publ, pp 2191–2196

    Article  Google Scholar 

  32. Malmborg C (1996) A genetic algorithm for service level based vehicle scheduling. Eur J Oper Res 93:121–134

    Article  Google Scholar 

  33. Pan Q K, Tasgetiren M, Suganthan P, Chua T (2011) A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem. Inform Sci 181:2455–2468

    Article  MathSciNet  Google Scholar 

  34. Park Y B (2001) A hybrid genetic algorithm for the vehicle scheduling problem with due times and time deadlines. Int J Prod Econ 73:175–188

    Article  Google Scholar 

  35. Potvin J Y (1996) Genetic algorithms for the traveling salesman problem. Ann Oper Res 63:339–370

    Article  Google Scholar 

  36. Ross S (2010) A first course in probability, 8th edn. Pearson Education, Upper Saddle River

    MATH  Google Scholar 

  37. Singh A (2009) An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem. Appl Soft Comput 9:625–631

    Article  Google Scholar 

  38. Singh A, Baghel A S (2009) A new grouping genetic algorithm approach to the multiple traveling salesperson problem. Soft Comput 13:95–101

    Article  Google Scholar 

  39. Singh A, Banda J (2017) Hybrid artificial bee colony algorithm based approaches for two ring loading problems. Appl Intell 47:1157–1168

    Article  Google Scholar 

  40. Sundar S, Singh A (2010a) A swarm intelligence approach to the quadratic minimum spanning tree problem. Inform Sci 180:3182–3191

    Article  MathSciNet  Google Scholar 

  41. Sundar S, Singh A (2010b) A swarm intelligence approach to the quadratic multiple knapsack problem Lecture notes in computer science, vol 6443. Springer, Berlin, pp 626–633

    Chapter  Google Scholar 

  42. Sundar S, Singh A (2012) A swarm intelligence approach to the early/tardy scheduling problem. Swarm Evol Comput 4:25–32

    Article  Google Scholar 

  43. Tang L, Liu J, Rong A, Yang Z (2000) A multiple traveling salesman problem model for hot rolling scheduling in shangai baoshan iron and steel complex. Eur J Oper Res 124:1267–1282

    MATH  Google Scholar 

  44. Zhang X, Bai Q, Yun X (2011) A new hybrid artificial bee colony algorithm for the traveling salesman problem. In: 2011 IEEE 3rd International Conference on communication software and networks (ICCSN). IEEE, pp 155–159

Download references

Acknowledgments

The authors would like to place on record their sincere thanks to Prof. MengChu Zhou and Prof. Jun Li for providing their test problems and answering our queries regarding their approaches. Authors are also grateful to four anonymous reviewers for their valuable comments and suggestions which helped in improving the quality of this manuscript. The first author acknowledges the financial support received from Council of Scientific & Industrial Research (CSIR), Government of India in the form of a senior research fellowship.

Author information

Authors and Affiliations

  1. School of Computer and Information Sciences, University of Hyderabad, Hyderabad, 500 046, India

    Venkatesh Pandiri & Alok Singh

Authors
  1. Venkatesh Pandiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alok Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alok Singh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pandiri, V., Singh, A. A swarm intelligence approach for the colored traveling salesman problem. Appl Intell 48, 4412–4428 (2018). https://doi.org/10.1007/s10489-018-1216-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-018-1216-0

Keywords

Search

Navigation