Scatter Search Particle Filter to Solve the Dynamic Travelling Salesman Problem

  • Juan José Pantrigo
  • Abraham Duarte
  • Ángel Sánchez
  • Raúl Cabido
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3448)

Abstract

This paper presents the Scatter Search Particle Filter (SSPF) algorithm and its application to the Dynamic Travelling Salesman Problem (DTSP). SSPF combines sequential estimation and combinatorial optimization methods to improve the execution time in dynamic optimization problems. It allows obtaining new high quality solutions in subsequent iterations using solutions found in previous time steps. The hybrid SSPF approach increases the performance of general Scatter Search (SS) metaheuristic in dynamic optimization problems. We have applied the SSPF algorithm to different DTSP instances. Experimental results have shown that SSPF performance is significantly better than classical DTSP approaches, where new solutions of derived problems are obtained without taking advantage of previous solutions corresponding to similar problems. Our proposal reduces execution time appreciably without affecting the quality of the estimated solution.

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References

  1. 1.
    Randall, M.: Constructive Meta-heuristics for Dynamic Optimization Problems. Technical Report. School of Information Technology. Bond University (2002)Google Scholar
  2. 2.
    Sadeh, N., Kott, A.: Models and Techniques for Dynamic Demand-Responsive Transportation Planning. Tech. Rept. TR-96-09, Carnegie Mellon University (1996)Google Scholar
  3. 3.
    Dror, M., Powell, W.: Stochastic and Dynamic Models in Transportation. Operations Research 41, 11–14 (1993)CrossRefGoogle Scholar
  4. 4.
    Beasley, J., Krishnamoorthy, M., Sharaiha, Y., Abramson, D.: The displacement Problem and Dynamically Scheduling Aircraft Landings. Working paper (2002), Available online at http://graph.ms.ic.ac.uk/jeb/displace.pdf
  5. 5.
    Beasley, J., Sonander, J., Havelock, P.: Scheduling Aircraft Landings at London Heathrow using a Population Heuristic. Journal of the Operational Research Society 52, 483–493 (2001)MATHCrossRefGoogle Scholar
  6. 6.
    Glover, F., Kochenberger, G.A.: Handbook of metaheuristics. Kluwer, Dordrecht (2002)Google Scholar
  7. 7.
    Dorigo, M., Gambardella, L.M.: Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Trans. on Evolutionary Computation 1(1), 53–66 (1997)CrossRefGoogle Scholar
  8. 8.
    Zhang-Can, H., Xiao-Lin, H., Si-Duo, C.: Dynamic traveling salesman problem based on evolutionary computation. In: Proc. of Evolutionary Computation Conf. 2, pp. 1283–1288 (2001)Google Scholar
  9. 9.
    Carpenter, J., Clifford, P., Fearnhead, P.: Building robust simulation based filters for evolving data sets. Tech. Rep., Dept. Statist., Univ. Oxford, Oxford, U.K (1999)Google Scholar
  10. 10.
    Arulampalam, M., et al.: A Tutorial on Particle Filter for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. On Signal Processing 50(2), 174–188 (2002)CrossRefGoogle Scholar
  11. 11.
    Blum, C., Roli, A.: Metaheuristics in Combinatorial Optimization: Overview and Conceptual Comparison. ACM Computing Surveys 35(3), 268–308 (2003)CrossRefGoogle Scholar
  12. 12.
    Eyckelhof, C.J., Snoek, M.: Ant Systems for A Dynamic DSP: Ants Caught in a Traffic Jam. In: Proc. of ANTS 2002 Conference (2002)Google Scholar
  13. 13.
    Karp, R.M.: Reducibility among Combinatorial Problems. In: Miller, R., Thatcher, J. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)Google Scholar
  14. 14.
    Reinelt, G.: TSPLIB. University of Heidelberg (1996), Available online at http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/
  15. 15.
    Guntsh, M., Middendorf, M.: Applying Population based ACO to Dynamic Optimization Problems. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms 2002. LNCS, vol. 2463, pp. 111–122. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Guntsh, M., Middendorf, M., Schmeck, H.: An Ant Colony Optimization Approach to Dynamic TSP. In: Proc. GECCO 2001 Conference, pp. 860–867. Morgan Kaufmann Publishers, San Francisco (2000)Google Scholar
  17. 17.
    Guntsh, M., Middendorf, M.: Pheromone Modification Strategies for Ant Algorithms applied to Dynamic TSP. In: Boers, E.J.W., Gottlieb, J., Lanzi, P.L., Smith, R.E., Cagnoni, S., Hart, E., Raidl, G.R., Tijink, H. (eds.) EvoIASP 2001, EvoWorkshops 2001, EvoFlight 2001, EvoSTIM 2001, EvoCOP 2001, and EvoLearn 2001. LNCS, vol. 2037, pp. 213–222. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Pantrigo, J.J., Sánchez, A., Gianikellis, K., Duarte, A.: Path Relinking Particle Filter for Human Body Pose Estimation. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 653–661. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Glover, F.: A Template for Scatter Search and Path Relinking. In: Hao, J.-K., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds.) AE 1997. LNCS, vol. 1363, pp. 1–53. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  20. 20.
    Laguna, M., Marti, R.: Scatter Search methodology and implementations in C. Kluwer Academic Publisher, Dordrecht (2003)Google Scholar
  21. 21.
    Vizeacoumar, F.: TSP Implementation. Project report Combinatorial Optimization CMPUT – 670Google Scholar
  22. 22.
    Campos, V., Laguna, M., Martí, R.: Scatter Search for the Linear Ordering Problem. New Ideas in Optimization. McGraw-Hill, New York (1999)Google Scholar
  23. 23.
    Michalewitz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Juan José Pantrigo
    • 1
  • Abraham Duarte
    • 1
  • Ángel Sánchez
    • 1
  • Raúl Cabido
    • 1
  1. 1.Universidad Rey Juan CarlosMóstolesSpain

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