A Hybrid Diploid Genetic Based Algorithm for Solving the Generalized Traveling Salesman Problem | SpringerLink
Skip to main content
Springer Nature Link
Log in

A Hybrid Diploid Genetic Based Algorithm for Solving the Generalized Traveling Salesman Problem

  • Conference paper
  • First Online:
Hybrid Artificial Intelligent Systems (HAIS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10334))

Included in the following conference series:

Abstract

In this paper, we are addressing the generalized traveling salesman problem, denoted by GTSP, which is a variant of the classical traveling salesman problem (TSP). The GTSP is characterized by the fact that the vertices of the graph are partitioned into a given number of clusters and we are looking for the minimum cost tour that visits exactly one vertex from each cluster. The goal of this paper is to present a novel method for solving the GTSP, namely a hybrid diploid genetic based algorithm. The preliminary computational results on an often set of benchmark instances show that our proposed approach provides competitive solutions compared to the existing state-of-the-arts methods for solving the GTSP.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bhattacharya, B., Ćustić, A., Rafiey, A., Rafiey, A., Sokol, V.: Approximation algorithms for generalized MST and TSP in grid clusters. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, D.-Z. (eds.) COCOA 2015. LNCS, vol. 9486, pp. 110–125. Springer, Cham (2015). doi:10.1007/978-3-319-26626-8_9

    Chapter  Google Scholar 

  2. Chisman, J.A.: The clustered traveling salesman problem. Comput. Oper. Res. 2(2), 115–119 (1975)

    Article  Google Scholar 

  3. Feremans, C., Labbe, M., Laporte, G.: Generalized network design problems. Eur. J. Oper. Res. 148(1), 1–13 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fischetti, M., Salazar-Gonzales, J.J., Toth, P.: The symmetric generalized traveling salesman polytope. Networks 26(2), 113–123 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fischetti, M., Salazar-Gonzales, J.J., Toth, P.: A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Oper. Res. 45(3), 378–394 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Goldberg, D.E., Smith, R.E.: Nonstationary function optimization using genetic algorithms with dominance and diploidy. In: Proceedings of the Second International Conference on Genetic Algorithms and their application, pp. 59–68 (1987)

    Google Scholar 

  7. Gutin, G., Karapetyan, D.: A memetic algorithm for the generalized traveling salesman problem. Natural Comput. 9(1), 47–60 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Helsgaun, K.: Solving the equality generalized traveling salesman problem using the LinKernighanHelsgaun Algorithm. Math. Prog. Comp. 7(3), 269–287 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  9. Henry-Labordere, A.L.: The record balancing problem: a dynamic programming solution of a generalized travelling salesman problem. RIRO B-2, 43–49 (1969)

    Google Scholar 

  10. Karapetyan, D., Gutin, G.: Efficient local search algorithms for known and new neighborhoods for the generalized traveling salesman problem. Eur. J. Oper. Res. 219(2), 234–251 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  11. Laporte, G., Nobert, Y.: Generalized travelling salesman problem through n sets of nodes: an integer programming approach. Infor. 21, 61–75 (1983)

    MATH  Google Scholar 

  12. Laporte, G., Asef-Vaziri, A., Sriskandarajah, C.: Some applications of the generalized travelling salesman problem. J. Oper. Res. Soc. 47(12), 1461–1467 (1996)

    Article  MATH  Google Scholar 

  13. Matei, O., Pop, P.C.: An efficient genetic algorithm for solving the generalized traveling salesman problem. In: Proceedings of 6th IEEE International Conference on Intelligent Computer Communication and Processing, pp. 87–92 (2010)

    Google Scholar 

  14. Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press (1998)

    Google Scholar 

  15. Pintea, C.-M., Chira, C., Dumitrescu, D., Pop, P.C.: A sensitive metaheuristic for solving a large optimization problem. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 551–559. Springer, Heidelberg (2008). doi:10.1007/978-3-540-77566-9_48

    Chapter  Google Scholar 

  16. Pintea, C.-M., Pop, P.C., Chira, C.: Reinforcing ant colony system for the generalized traveling salesman problem. In: Proceedings of BIC-TA 2006, pp. 245–252 (2006)

    Google Scholar 

  17. Pintea, C.-M., Chira, C., Dumitrescu, D., Pop, P.C.: Sensitive ants in solving the generalized vehicle routing problem. Int. J. Comput. Commun. Control 6(4), 734–741 (2011)

    Article  Google Scholar 

  18. Pintea, C.-M., Pop, P.C., Chira, C.: The Generalized Traveling Salesman Problem solved with Ant Algorithms (2013). arXiv:1310.2350

  19. Pop, P.C.: New integer programming formulations of the generalized traveling salesman problem. Am. J. Appl. Sci. 4(11), 932–937 (2007)

    Article  Google Scholar 

  20. Pop, P.C.: Generalized Network Design Problems, Modelling and Optimization. De Gruyter, Germany (2012)

    Book  MATH  Google Scholar 

  21. Pop, P.C., Iordache, S.: A hybrid heuristic approach for solving the generalized traveling saleasman problem. In: Proceedings of GECCO 2011, pp. 481–488 (2011)

    Google Scholar 

  22. Pop, P.C., Matei, O., Sabo, C.: A new approach for solving the generalized traveling salesman problem. In: Blesa, M.J., Blum, C., Raidl, G., Roli, A., Sampels, M. (eds.) HM 2010. LNCS, vol. 6373, pp. 62–72. Springer, Heidelberg (2010). doi:10.1007/978-3-642-16054-7_5

    Chapter  Google Scholar 

  23. Reihaneh, M., Karapetyan, D.: An efficient hybrid ant colony system for the generalized traveling salesman problem. Algorithmic Oper. Res. 7, 21–28 (2012)

    MATH  MathSciNet  Google Scholar 

  24. Renaud, J., Boctor, F.F.: An efficient composite heuristic for the symmetric generalized traveling salesman problem. Eur. J. Oper. Res. 108(3), 571–584 (1998)

    Article  MATH  Google Scholar 

  25. Reinelt, G.: TSPLIB - A traveling salesman problem library. ORSA J. Comput. 3, 376–384 (1991). http://www.crpc.rice.edu/softlib/tsplib/

  26. Silberholz, J., Golden, B.: The Generalized Traveling Salesman Problem: a new genetic algorithm approach. In: Baker, E.K., Joseph, A., Mehrotra, A., Trick, M.A. (eds.) Extending the Horizons: Advances in Computing, Optimization and Decision Technologies. Operations Research/Computer Science Interfaces Series, vol. 37, pp. 165–181. Springer, New York (2007)

    Google Scholar 

  27. Slavik, P.: On the approximation of the generalized traveling salesman problem. Working paper, University of Buffalo (1997)

    Google Scholar 

  28. Snyder, L.V., Daskin, M.S.: A random-key genetic algorithm for the generalized traveling salesman problem. Eur. J. Oper. Res. 174, 38–53 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Srivastava, S.S., Kumar, S., Garg, R.C., Sen, P.: Generalized travelling salesman problem through n sets of nodes. CORS J. 7, 97–101 (1969)

    MATH  MathSciNet  Google Scholar 

  30. Tasgetiren, M.F., Suganthan, P.N., Pan, Q.-K.: A discrete particle swarm optimization algorithm for the generalized traveling salesman problem. In Proceedings of GECCO, pp. 158–167 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Baia Mare, Romania

    Petrica Pop, Matei Oliviu & Cosmin Sabo

Authors
  1. Petrica Pop
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matei Oliviu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cosmin Sabo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Petrica Pop .

Editor information

Editors and Affiliations

  1. University of La Rioja , Logroño, La Rioja, Spain

    Francisco Javier Martínez de Pisón

  2. University of La Rioja , Logroño, La Rioja, Spain

    Rubén Urraca

  3. University of A Coruña , Ferrol, La Coruña, Spain

    Héctor Quintián

  4. University of Salamanca, Salamanca, Spain

    Emilio Corchado

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Pop, P., Oliviu, M., Sabo, C. (2017). A Hybrid Diploid Genetic Based Algorithm for Solving the Generalized Traveling Salesman Problem. In: Martínez de Pisón, F., Urraca, R., Quintián, H., Corchado, E. (eds) Hybrid Artificial Intelligent Systems. HAIS 2017. Lecture Notes in Computer Science(), vol 10334. Springer, Cham. https://doi.org/10.1007/978-3-319-59650-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59650-1_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59649-5

  • Online ISBN: 978-3-319-59650-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation