Tunnelling Crossover Networks for the Asymmetric TSP

  • Nadarajen Veerapen
  • Gabriela Ochoa
  • Renato Tinós
  • Darrell Whitley
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9921)

Abstract

Local optima networks are a compact representation of fitness landscapes that can be used for analysis and visualisation. This paper provides the first analysis of the Asymmetric Travelling Salesman Problem using local optima networks. These are generated by sampling the search space by recording the progress of an existing evolutionary algorithm based on the Generalised Asymmetric Partition Crossover. They are compared to networks sampled through the Chained Lin-Kernighan heuristic across 25 instances. Structural differences and similarities are identified, as well as examples where crossover smooths the landscape.

References

  1. 1.
    Applegate, D., Bixby, R., Chvátal, V., Cook, W.: Concorde TSP solver (2003). http://www.math.uwaterloo.ca/tsp/concorde.html
  2. 2.
    Applegate, D., Cook, W., Rohe, A.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS J. Comput. 15, 82–92 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Chicano, F., Whitley, D., Sutton, A.M.: Efficient identification of improving moves in a ball for pseudo-boolean problems. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2014), pp. 437–444. ACM (2014)Google Scholar
  4. 4.
    Doye, J.P.K.: The network topology of a potential energy landscape: a static scale-free network. Phys. Rev. Lett. 88, 238701 (2002)CrossRefGoogle Scholar
  5. 5.
    Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. Eur. J. Oper. Res. 126(1), 106–130 (2000)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Iclanzan, D., Daolio, F., Tomassini, M.: Data-driven local optima network characterization of QAPLIB instances. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2014), pp. 453–460. ACM (2014)Google Scholar
  7. 7.
    Jonker, R., Volgenant, T.: Transforming asymmetric into symmetric traveling salesman problems. Oper. Res. Lett. 2(4), 161–163 (1983)CrossRefMATHGoogle Scholar
  8. 8.
    Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21, 498–516 (1973)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ochoa, G., Chicano, F., Tinós, R., Whitley, D.: Tunnelling crossover networks. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2015), pp. 449–456. ACM (2015)Google Scholar
  10. 10.
    Ochoa, G., Tomassini, M., Verel, S., Darabos, C.: A study of NK landscapes’ basins and local optima networks. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2008), pp. 555–562. ACM (2008)Google Scholar
  11. 11.
    Ochoa, G., Veerapen, N.: Additional dimensions to the study of funnels in combinatorial landscapes. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2016). ACM (2016, to appear)Google Scholar
  12. 12.
    Ochoa, G., Veerapen, N., Whitley, D., Burke, E.K.: The multi-funnel structure of TSP fitness landscapes: a visual exploration. In: Bonnevay, S., Legrand, P., Monmarché, N., Lutton, E., Schoenauer, M. (eds.) EA 2015. LNCS, vol. 9554, pp. 1–13. Springer, Heidelberg (2016). doi:10.1007/978-3-319-31471-6_1 CrossRefGoogle Scholar
  13. 13.
    Ochoa, G., Veerapen, N.: Deconstructing the big valley search space hypothesis. In: Chicano, F., Hu, B., García-Sánchez, P. (eds.) EvoCOP 2016. LNCS, vol. 9595, pp. 58–73. Springer, Heidelberg (2016). doi:10.1007/978-3-319-30698-8_5 CrossRefGoogle Scholar
  14. 14.
    Reinelt, G.: TSPLIB - a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Tinós, R., Whitley, D., Ochoa, G.: Generalized asymmetric partition crossover (GAPX) for the asymmetric TSP. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2014), pp. 501–508. ACM (2014)Google Scholar
  16. 16.
    Tinós, R., Whitley, L.D., Chicano, F.: Partition crossover for pseudo-boolean optimization. In: Proceedings of the 2015 ACM Conference on Foundations of Genetic Algorithms XIII, Aberystwyth, United Kingdom, 17–20 January 2015, pp. 137–149 (2015)Google Scholar
  17. 17.
    Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Trans. Evol. Comput. 15(6), 783–797 (2011)CrossRefGoogle Scholar
  18. 18.
    Vérel, S., Daolio, F., Ochoa, G., Tomassini, M.: Local optima networks with escape edges. In: Hao, J.-K., Legrand, P., Collet, P., Monmarché, N., Lutton, E., Schoenauer, M. (eds.) EA 2011. LNCS, vol. 7401, pp. 49–60. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  19. 19.
    Whitley, D., Hains, D., Howe, A.: Tunneling between optima: partition crossover for the traveling salesman problem. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2009), pp. 915–922. ACM (2009)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Nadarajen Veerapen
    • 1
  • Gabriela Ochoa
    • 1
  • Renato Tinós
    • 2
  • Darrell Whitley
    • 3
  1. 1.Division of Computing Science and MathematicsUniversity of StirlingStirlingUK
  2. 2.Department of Computing and MathematicsUniversity of São PauloSão PauloBrazil
  3. 3.Department of Computer ScienceColorado State UniversityFort CollinsUSA

Personalised recommendations