Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Hybrid Artificial Intelligent Systems (HAIS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14001))

Included in the following conference series:

  • 553 Accesses

Abstract

We study the clustered generalized traveling salesman pro-blem (CGTSP), which is an extension of the generalized traveling salesman problem (GTSP), which in turn generalizes the well-known traveling salesman problem (TSP). The investigated problem was motivated by several practical applications such as modern logistics, data clustering, internet networks, etc., and it is defined on a graph, whose set of vertices are split up into clusters, and the clusters are further partitioned into sub-clusters of vertices. The aim of the CGTSP is to look for a minimum length tour that visits exactly one vertex from each sub-cluster with the main constraint that all the sub-clusters belonging to each given cluster are visited contiguously. In this paper, we describe a hybrid algorithm for solving the CGTSP that integrates the Dijkstra’s shortest path algorithm and a TSP solver within a genetic algorithm. Finally, we present a new set of instances for CGTSP derived from the GTSP_LIB [8] and some preliminary computational results are stated on a set of 40 instances to asses the efficiency of our designed hybrid based genetic algorithm.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • 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

References

  1. Applegate, D., Bixby, R., Chvatal, V., Cook, W.: Concorde tsp solver. http://www.tsp.gatech.edu/concorde/index.html

  2. Baniasadi, P., Foumani, M., Smith-Miles, K., Ejov, V.: A transformation technique for the clustered generalized traveling salesman problem with applications to logistics. Eur. J. Oper. Res. 285(2), 444–457 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cosma, O., Pop, P.C., Pop Sitar, C.: A two-level based genetic algorithm for solving the soft-clustered vehicle routing problem. Carpathian J. Math. 38(1), 117–128 (2022)

    Article  MathSciNet  Google Scholar 

  4. Cosma, O., Pop, P.C., Zelina, I.: An effective genetic algorithm for solving the clustered shortest-path tree problem. IEEE Access 9, 15570–15591 (2021)

    Article  Google Scholar 

  5. Cosma, O., Pop, P.C., Zelina, I.: A novel genetic algorithm for solving the clustered shortest-path tree problem. Carpathian J. Math. 36(3), 401–414 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  6. Demange, M., Monnot, J., Pop, P.C., Ries, B.: On the complexity of the selective graph coloring problem in some special classes of graphs. Theor. Comput. Sci. 540–541, 82–102 (2014)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Fidanova, S., Pop, P.C.: An improved hybrid ant-local search for the partition graph coloring problem. J. Comput. Appl. Math. 293, 55–61 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. 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  MathSciNet  MATH  Google Scholar 

  10. Foumani, M., Moeini, A., Haythorpe, M., Smith-Miles, K.: A cross-entropy method for optimising robotic automated storage and retrieval systems. Int. J. Prod. Res. 56(19), 6450–6472 (2018)

    Article  Google Scholar 

  11. Ghiani, G., Improta, G.: An efficient transformation of the generalized vehicle routing problem. Eur. J. Oper. Res. 122, 11–17 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. The LEMON library. http: https://lemon.cs.elte.hu/trac/lemon

  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. Petrovan, A., Pop, P.C., Sabo, C., Zelina, I.: Novel two-level hybrid genetic algorithms based on different Cayley-type encodings for solving the clustered shortest-path tree problem. Expert Syst. Appl. 215, 119372 (2023)

    Article  Google Scholar 

  15. Pop, P.C.: The generalized minimum spanning tree problem: an overview of formulations, solution procedures and latest advances. Eur. J. Oper. Res. 283(1), 1–15 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  16. Pop, P.C., Matei, O., Sabo, C., Petrovan, A.: A two-level solution approach for solving the generalized minimum spanning tree problem. Eur. J. Oper. Res. 265(2), 478–487 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. Pop, P.C., Fuksz, L., Horvat Marc, A., Sabo, C.: A novel two-level optimization approach for clustered vehicle routing problem. Comput. Ind. Eng. 115, 304–318 (2018)

    Article  Google Scholar 

  18. Pop, P.C.: Generalized Network Design Problems. Modeling and Optimization. De Gruyter Series in Discrete Mathematics and Applications, Germany (2012)

    Google Scholar 

  19. 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). https://doi.org/10.1007/978-3-642-16054-7_5

    Chapter  Google Scholar 

  20. 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 

  21. Schmidt, J., Irnich, S.: New neighborhoods and an iterated local search algorithm for the generalized traveling salesman problem. EURO J. Comput. Optim. 10, 100029 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sepehri, M.M., Motlagh, S.M.H., Ignatius, J.: A model for optimal routing of dangerous substances in warehousing operations via K-nested GTSP. Int. J. Nonlinear Sci. Num. Simul. 11(9), 701–704 (2010)

    Article  Google Scholar 

  23. Smith, S.L., Imeson, F.: GLNS: an effective large neighborhood search heuristic for the generalized traveling salesman problem. Comput. Oper. Res. 87, 1–19 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the project COSO that received funding from Romania’s National Recovery and Resilience Plan PNRR-III-C9-2022-I8, under grant agreement 760070.

Author information

Authors and Affiliations

  1. Technical University of Cluj-Napoca, North University Center of Baia Mare, Dr. V. Babes 62A, 430083, Baia Mare, Romania

    Ovidiu Cosma, Petrică C. Pop & Laura Cosma

Authors
  1. Ovidiu Cosma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Petrică C. Pop
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Laura Cosma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Petrică C. Pop .

Editor information

Editors and Affiliations

  1. University of Deusto, Bilbao, Spain

    Pablo García Bringas

  2. University of Leon, León, Spain

    Hilde Pérez García

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

    Francisco Javier Martínez de Pisón

  4. Pablo de Olavide University, Seville, Spain

    Francisco Martínez Álvarez

  5. Pablo de Olavide University, Seville, Spain

    Alicia Troncoso Lora

  6. University of Burgos, Burgos, Spain

    Álvaro Herrero

  7. University of A Coruña, Ferrol - Coruña, Spain

    José Luis Calvo Rolle

  8. University of A Coruña, Ferrol - Coruña, Spain

    Héctor Quintián

  9. University of Salamanca, Salamanca, Spain

    Emilio Corchado

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cosma, O., Pop, P.C., Cosma, L. (2023). A Hybrid Based Genetic Algorithm for Solving the Clustered Generalized Traveling Salesman Problem. In: García Bringas, P., et al. Hybrid Artificial Intelligent Systems. HAIS 2023. Lecture Notes in Computer Science(), vol 14001. Springer, Cham. https://doi.org/10.1007/978-3-031-40725-3_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-40725-3_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40724-6

  • Online ISBN: 978-3-031-40725-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation