Skip to main content
SpringerLink
Log in

Fixed Set Search Applied to the Traveling Salesman Problem

  • Conference paper
  • First Online:
Hybrid Metaheuristics (HM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11299))

Included in the following conference series:

Abstract

In this paper we present a new population based metaheuristic called the fixed set search (FSS). The proposed approach represents a method of adding a learning mechanism to the greedy randomized adaptive search procedure (GRASP). The basic concept of FSS is to avoid focusing on specific high quality solutions but on parts or elements that such solutions have. This is done through fixing a set of elements that exist in such solutions and dedicating computational effort to finding near optimal solutions for the underlying subproblem. The simplicity of implementing the proposed method is illustrated on the traveling salesman problem. Our computational experiments show that the FSS manages to find significantly better solutions than the GRASP it is based on, the dynamic convexized method and the ant colony optimization combined with a local search.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part I: background and development. Nat. Comput. 6(4), 467–484 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Nat. Comput. 7(1), 109–124 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bentley, J.J.: Fast algorithms for geometric traveling salesman problems. ORSA J. Comput. 4(4), 387–411 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Blum, C., Pinacho, P., López-Ibáñez, M., Lozano, J.A.: Construct, merge, solve & adapt a new general algorithm for combinatorial optimization. Comput. Oper. Res. 68, 75–88 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Blum, C., Puchinger, J., Raidl, G.R., Roli, A.: Hybrid metaheuristics in combinatorial optimization: a survey. Appl. Soft Comput. 11(6), 4135–4151 (2011)

    Article  MATH  Google Scholar 

  6. Caserta, M., Voß, S.: Metaheuristics: intelligent problem solving. In: Maniezzo, V., Stützle, T., Voß, S. (eds.) Matheuristics: Hybridizing Metaheuristics and Mathematical Programming, vol. 10, pp. 1–38. Springer, Boston (2010). https://doi.org/10.1007/978-1-4419-1306-7_1

    Chapter  Google Scholar 

  7. Concorde: Concorde TSP solver (2015). http://www.math.uwaterloo.ca/tsp/concorde/index.html

  8. Croes, G.A.: A method for solving traveling-salesman problems. Oper. Res. 6(6), 791–812 (1958)

    Article  MathSciNet  Google Scholar 

  9. De Boer, P.T., Kroese, D.P., Mannor, S., Rubinstein, R.Y.: A tutorial on the cross-entropy method. Ann. Oper. Res. 134(1), 19–67 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dorigo, M., Blum, C.: Ant colony optimization theory: a survey. Theor. Comput. Sci. 344(2–3), 243–278 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Englert, M., Röglin, H., Vöcking, B.: Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP. Algorithmica 68(1), 190–264 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Feo, T.A., Resende, M.G.: Greedy randomized adaptive search procedures. J. Global Optim. 6(2), 109–133 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  13. Festa, P., Resende, M.G.C.: Hybridizations of GRASP with path-relinking. In: Talbi, E.G. (ed.) Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 434, pp. 135–155. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-30671-6_5

    Chapter  Google Scholar 

  14. Fister, I., Yang, X.S., Fister, D., Fister, I.: Cuckoo search: a brief literature review. In: Yang, X.S. (ed.) Cuckoo Search and Firefly Algorithm: Theory and Applications, vol. 516, pp. 49–62. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-02141-6_3

    Chapter  MATH  Google Scholar 

  15. Glover, F.: Tabu search-part I. ORSA J. Comput. 1(3), 190–206 (1989)

    Article  MATH  Google Scholar 

  16. Glover, F.: Tabu search-part II. ORSA J. Comput. 2(1), 4–32 (1990)

    Article  MATH  Google Scholar 

  17. Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130(3), 449–467 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hart, J., Shogan, A.: Semi-greedy heuristics: an empirical study. Oper. Res. Lett. 6, 107–114 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  19. Jovanovic, R., Bousselham, A., Voß, S.: Partitioning of supply/demand graphs with capacity limitations: an ant colony approach. J. Comb. Optim. 35(1), 224–249 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  20. Jovanovic, R., Tuba, M.: An ant colony optimization algorithm with improved pheromone correction strategy for the minimum weight vertex cover problem. Appl. Soft Comput. 11(8), 5360–5366 (2011)

    Article  Google Scholar 

  21. Jovanovic, R., Tuba, M., Voß, S.: An ant colony optimization algorithm for partitioning graphs with supply and demand. Appl. Soft Comp. 41, 317–330 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated annealing. In: van Laarhoven, P.J.M., Aarts, E.H.L., et al. (eds.) Simulated Annealing: Theory and Applications, vol. 37, pp. 7–15. Springer, Dordrecht (1987). https://doi.org/10.1007/978-94-015-7744-1_2

    Chapter  MATH  Google Scholar 

  24. Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Tech. J. 44(10), 2245–2269 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  25. Marinakis, Y., Marinaki, M., Dounias, G.: Honey bees mating optimization algorithm for the Euclidean traveling salesman problem. Inf. Sci. 181(20), 4684–4698 (2011)

    Article  MathSciNet  Google Scholar 

  26. Marinakis, Y., Migdalas, A., Pardalos, P.M.: Expanding neighborhood GRASP for the traveling salesman problem. Comput. Optim. Appl. 32(3), 231–257 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  28. Neri, F., Tirronen, V.: Recent advances in differential evolution: a survey and experimental analysis. Artif. Intell. Rev. 33(1–2), 61–106 (2010)

    Article  Google Scholar 

  29. Reinelt, G.: TSPLIB—a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)

    Article  MATH  Google Scholar 

  30. Sondergeld, L., Voß, S.: Cooperative intelligent search using adaptive memory techniques. In: Voß, S., Martello, S., Osman, I., Roucairol, C. (eds.) Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pp. 297–312. Springer, Boston (1999). https://doi.org/10.1007/978-1-4615-5775-3_21

    Chapter  MATH  Google Scholar 

  31. Sörensen, K.: Metaheuristics - the metaphor exposed. Int. Trans. Oper. Res. 22(1), 3–18 (2015). https://doi.org/10.1111/itor.12001

    Article  MathSciNet  MATH  Google Scholar 

  32. Stützle, T., Hoos, H.: Max-min ant system and local search for the traveling salesman problem, pp. 309–314. IEEE (1997)

    Google Scholar 

  33. Taillard, E., Voß, S.: POPMUSIC - a partial optimization metaheuristic under special intensification conditions. In: Ribeiro, C., Hansen, P. (eds.) Essays and Surveys in Metaheuristics. Operations Research/Computer Science Interfaces Series, vol. 15, pp. 613–629. Kluwer, Boston (2002). https://doi.org/10.1007/978-1-4615-1507-4_27

    Chapter  Google Scholar 

  34. Tsai, C.F., Tsai, C.W., Tseng, C.C.: A new hybrid heuristic approach for solving large traveling salesman problem. Inf. Sci. 166(1), 67–81 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  35. Voß, S., Gutenschwager, K.: A chunking based genetic algorithm for the Steiner tree problem in graphs. In: Pardalos, P., Du, D.Z. (eds.) Network Design: Connectivity and Facilities Location. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 40, pp. 335–355. AMS, Princeton (1998)

    Chapter  Google Scholar 

  36. Woodruff, D.: Proposals for chunking and tabu search. Eur. J. Oper. Res. 106, 585–598 (1998)

    Article  MATH  Google Scholar 

  37. Zhu, M., Chen, J.: Computational comparison of GRASP and DCTSP methods for the Traveling Salesman Problem, pp. 1044–1048 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Qatar Environment and Energy Research Institute (QEERI), Hamad Bin Khalifa University, PO Box 5825, Doha, Qatar

    Raka Jovanovic

  2. Department of Technical Sciences, State University of Novi Pazar, Vuka Karadzica bb, 36300, Novi Pazar, Serbia

    Milan Tuba

  3. Institute of Information Systems, University of Hamburg, Von-Melle-Park 5, 20146, Hamburg, Germany

    Stefan Voß

  4. Escuela de Ingenieria Industrial, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Stefan Voß

Authors
  1. Raka Jovanovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Milan Tuba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stefan Voß
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raka Jovanovic .

Editor information

Editors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Maria J. Blesa Aguilera

  2. Spanish National Research Council, Bellaterra, Spain

    Christian Blum

  3. Universidade Federal de Ouro Preto, Ouro Preto, Brazil

    Haroldo Gambini Santos

  4. University of Concepción, Concepción, Chile

    Pedro Pinacho-Davidson

  5. Universidad de Concepción, Concepción, Chile

    Julio Godoy del Campo

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jovanovic, R., Tuba, M., Voß, S. (2019). Fixed Set Search Applied to the Traveling Salesman Problem. In: Blesa Aguilera, M., Blum, C., Gambini Santos, H., Pinacho-Davidson, P., Godoy del Campo, J. (eds) Hybrid Metaheuristics. HM 2019. Lecture Notes in Computer Science(), vol 11299. Springer, Cham. https://doi.org/10.1007/978-3-030-05983-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-05983-5_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05982-8

  • Online ISBN: 978-3-030-05983-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation