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Optimization Letters

, Volume 5, Issue 3, pp 467–478 | Cite as

Restart strategies for GRASP with path-relinking heuristics

  • Mauricio G. C. Resende
  • Celso C. Ribeiro
Original Paper

Abstract

GRASP with path-relinking is a hybrid metaheuristic, or stochastic local search (Monte Carlo) method, for combinatorial optimization. A restart strategy in GRASP with path-relinking heuristics is a set of iterations {i 1, i 2, …} on which the heuristic is restarted from scratch using a new seed for the random number generator. Restart strategies have been shown to speed up stochastic local search algorithms. In this paper, we propose a new restart strategy for GRASP with path-relinking heuristics. We illustrate the speedup obtained with our restart strategy on GRASP with path-relinking heuristics for the maximum cut problem, the maximum weighted satisfiability problem, and the private virtual circuit routing problem.

Keywords

GRASP Path-relinking Restart strategy Experimental algorithmics 

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References

  1. 1.
    D’Apuzzo M., Migdalas A., Pardalos P., Toraldo G.: Parallel computing in global optimization. In: Kontoghiorghes, E. (eds) Handbook of Parallel Computing and Statistics, Chapman & Hall/CRC, London (2006)Google Scholar
  2. 2.
    Duarte, A., Martí, R., Resende, M., Silva, R.: GRASP with path relinking heuristics for the antibandwidth problem. Networks (2010). doi: 10.1002/net.20418
  3. 3.
    Feo T., Resende M.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Feo T., Resende M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Festa, P., Pardalos, P., Pitsoulis, L., Resende, M.: GRASP with path-relinking for the weighted MAXSAT problem. ACM J. Exp. Algorithmics 11, 1–16 (2006) (article 2.4)Google Scholar
  6. 6.
    Festa P., Pardalos P., Resende M., Ribeiro C.: Randomized heuristics for the MAX-CUT problem. Optim. Methods Softw. 7, 1033–1058 (2002)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Festa P., Resende M.: GRASP: an annotated bibliography. In: Ribeiro, C., Hansen, P. (eds) Essays and Surveys on Metaheuristics, pp. 325–367. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  8. 8.
    Festa P., Resende M.: An annotated bibliography of GRASP—Part I: Algorithms. Int. Trans. Oper. Res. 16, 1–24 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Festa P., Resende M.: An annotated bibliography of GRASP—Part II: Applications. Int. Trans. Oper. Res. 16, 131–172 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gendreau, M., Potvin , J.Y. (eds): Handbook of Metaheuristics. Springer Science+Business Media, Boston (2010)zbMATHGoogle Scholar
  11. 11.
    Glover F.: Tabu search and adaptive memory programing—advances, applications and challenges. In: Barr, R., Helgason, R., Kennington, J. (eds) Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer, Dordrecht (1996)Google Scholar
  12. 12.
    Glover F., Kochenberger G.: Handbook of Metaheuristics. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  13. 13.
    Glover F., Laguna M., Martí R.: Fundamentals of scatter search and path relinking. Control Cybern. 39, 653–684 (2000)Google Scholar
  14. 14.
    Kautz, H., Horvitz, E., Ruan, Y., Gomes, C., Selman, B.: Dynamic restart policies. In: Proceedings of the Eighteenth National Conference on Artificial Intelligence, Edmonton, Canada, pp. 674–681. AAAI Press, Menlo Park (2002)Google Scholar
  15. 15.
    Laguna M., Martí R.: GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J. Comput. 11, 44–52 (1999)zbMATHCrossRefGoogle Scholar
  16. 16.
    Luby M., Sinclair A., Zuckerman D.: Optimal speedup of Las Vegas algorithms. Inform. Process. Lett. 47, 173–180 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Mateus, G., Resende, M., Silva, R.: GRASP with path-relinking for the generalized quadratic assignment problem. J. Heuristics 1–39 (2010). doi: 10.1007/s10732-010-9144-0
  18. 18.
    Nowicki E., Smutnicki C.: An advanced tabu search algorithm for the job shop problem. J. Sched. 8(2), 145–159 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Palubeckis G.: Multistart tabu search strategies for the unconstrained binary quadratic optimization problem. Ann. Oper. Res. 131(1), 259–282 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Pitsoulis L., Resende M.: Greedy randomized adaptive search procedures. In: Pardalos, P., Resende, M. (eds) Handbook of Applied Optimization, pp. 168–183. Oxford University Press, New York (2002)Google Scholar
  21. 21.
    Resende M., Ribeiro C.: Greedy randomized adaptive search procedures. In: Glover, F., Kochenberger, G. (eds) Handbook of Metaheuristics, pp. 219–249. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  22. 22.
    Resende M., Ribeiro C.: A GRASP with path-relinking for private virtual circuit routing. Networks 41(1), 104–114 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Resende M., Ribeiro C.: GRASP with path-relinking: recent advances and application. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds) Metaheuristics: Progress as Real Problem Solvers, pp. 29–63. Springer, Berlin (2005)CrossRefGoogle Scholar
  24. 24.
    Resende M., Ribeiro C.: Greedy randomized adaptive search procedures: advances and applications. In: Gendreau, M., Potvin, J.Y. (eds) Handbook of Metaheuristics. 2nd edn., pp. 281–317. Springer Science+Business Media, Boston (2010)Google Scholar
  25. 25.
    Resende M., Ribeiro C., Martí R., Glover F.: Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau, M., Potvin, J.Y. (eds) Handbook of Metaheuristics. 2nd edn., pp. 87–107. Springer Science+Business Media, Boston (2010)CrossRefGoogle Scholar
  26. 26.
    Ribeiro, C.C., Resende, M.G.C.: Path-relinking intensification methods for stochastic local search algorithms. Tech. rep., AT&T Labs Research, Florham Park, NJ 07932 (2010). http://www.research.att.com/~mgcr/docs/spr.pdf
  27. 27.
    Sergienko I.V., Shilo V.P., Roshchin V.A.: Optimization parallelizing for discrete programming problems. Cybern. Syst. Anal. 40(2), 184–189 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Shylo O.V., Middelkoop T., Pardalos P.M.: Restart strategies in optimization: parallel and serial cases. Parallel Comput. 37, 60–68 (2011)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Shylo O.V., Prokopyev O.A., Rajgopal J.: On algorithm portfolios and restart strategies. Oper. Res. Lett. 39, 49–52 (2011)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.AT&T Labs ResearchFlorham ParkUSA
  2. 2.Universidade Federal FluminenseNiteróiBrazil

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