Skip to main content

Parallel GRASP heuristics

  • Chapter
  • First Online:
Optimization by GRASP

Abstract

Parallel computers and parallel algorithms have increasingly found their way into metaheuristics. Most parallel implementations of GRASP found in the literature consist in either partitioning the search space or the GRASP iterations and assigning each partition to a processor. GRASP is applied to each partition in parallel. These implementations can be categorized as multiple-walk independent-thread, with the communication among processors during GRASP iterations being limited to the detection of program termination and gathering the best solution found over all processors. Approaches for the parallelization of GRASP with path-relinking can be categorized as either multiple-walk independent-thread or multiple-walk cooperative-thread, with processors sharing and exchanging information about elite solutions visited during the GRASP iterations. This chapter is an introduction to parallel GRASP heuristics, covering multiple-walk independent-thread strategies, multiple-walk cooperative-thread strategies, and some applications of parallel GRASP and parallel GRASP with path-relinking.

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

Access this chapter

Institutional subscriptions

References

  • R.M. Aiex and M.G.C. Resende. Parallel strategies for GRASP with path-relinking. In T. Ibaraki, K. Nonobe, and M. Yagiura, editors, Metaheuristics: Progress as real problem solvers, pages 301–331. Springer, New York, 2005.

    Google Scholar 

  • R.M. Aiex, S. Binato, and M.G.C. Resende. Parallel GRASP with path-relinking for job shop scheduling. Parallel Computing, 29:393–430, 2003.

    Article  MathSciNet  Google Scholar 

  • R.M. Aiex, M.G.C. Resende, P.M. Pardalos, and G. Toraldo. GRASP with path relinking for three-index assignment. INFORMS Journal on Computing, 17: 224–247, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  • E. Alba. Parallel metaheuristics: A new class of algorithms. Wiley, New York, 2005.

    Book  MATH  Google Scholar 

  • A.C. Alvim and C.C. Ribeiro. Load balancing for the parallelization of the GRASP metaheuristic. In Proceedings of the X Brazilian Symposium on Computer Architecture, pages 279–282, Búzios, 1998.

    Google Scholar 

  • E. Balas and M.J. Saltzman. An algorithm for the three-index assignment problem. Operations Research, 39:150–161, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  • J.E. Beasley. OR-Library: Distributing test problems by electronic mail. Journal of the Operational Research Society, 41:1069–1072, 1990a.

    Google Scholar 

  • S. Binato, W.J. Hery, D. Loewenstern, and M.G.C. Resende. A GRASP for job shop scheduling. In C.C. Ribeiro and P. Hansen, editors, Essays and surveys in metaheuristics, pages 59–79. Kluwer Academic Publishers, Boston, 2002.

    Chapter  Google Scholar 

  • R.E. Burkard and K. Fröhlich. Some remarks on 3-dimensional assignment problems. Methods of Operations Research, 36:31–36, 1980.

    MATH  Google Scholar 

  • R.E. Burkard and R. Rudolf. Computational investigations on 3-dimensional axial assignment problems. Belgian Journal of Operational Research, Statistics and Computer Science, 32:85–98, 1993.

    MATH  Google Scholar 

  • R.E. Burkard, R. Rudolf, and G.J. Woeginger. Three-dimensional axial assignment problems with decomposable cost coefficients. Discrete Applied Mathematics, 65:123–139, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  • S.A. Canuto, M.G.C. Resende, and C.C. Ribeiro. Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks, 38:50–58, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  • Y. Crama and F.C.R. Spieksma. Approximation algorithms for three-dimensional assignment problems with triangle inequalities. European Journal of Operational Research, 60:273–279, 1992.

    Article  MATH  Google Scholar 

  • V.-D. Cung, S.L. Martins, C.C. Ribeiro, and C. Roucairol. Strategies for the parallel implementation of metaheuristics. In C.C. Ribeiro and P. Hansen, editors, Essays and surveys in metaheuristics, pages 263–308. Kluwer Academic Publishers, Boston, 2002.

    Chapter  MATH  Google Scholar 

  • G. Dahl and B. Johannessen. The 2-path network design problem. Networks, 43:190–199, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  • L.M.A. Drummond, L.S. Vianna, M.B. Silva, and L.S. Ochi. Distributed parallel metaheuristics based on GRASP and VNS for solving the traveling purchaser problem. In Proceedings of the Ninth International Conference on Parallel and Distributed Systems, pages 257–263, Chungli, 2002. IEEE.

    Google Scholar 

  • S. Duni Ekşog̃lu, P.M. Pardalos, and M.G.C. Resende. Parallel metaheuristics for combinatorial optimization. In R. Corrêa, I. Dutra, M. Fiallos, and F. Gomes, editors, Models for parallel and distributed computation – Theory, algorithmic techniques and applications, pages 179–206. Kluwer Academic Publishers, Boston, 2002.

    Google Scholar 

  • T.A. Feo, M.G.C. Resende, and S.H. Smith. A greedy randomized adaptive search procedure for maximum independent set. Operations Research, 42: 860–878, 1994.

    Article  MATH  Google Scholar 

  • A.M. Frieze. Complexity of a 3-dimensional assignment problem. European Journal of Operational Research, 13:161–164, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  • M.R. Garey and D.S. Johnson. Computers and intractability. Freeman, San Francisco, 1979.

    MATH  Google Scholar 

  • A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Mancheck, and V. Sunderam. PVM: Parallel virtual machine, A user’s guide and tutorial for networked parallel computing. Scientific and Engineering Computation. MIT Press, Cambridge, 1994.

    Book  MATH  Google Scholar 

  • P. Hansen and L. Kaufman. A primal-dual algorithm for the three-dimensional assignment problem. Cahiers du CERO, 15:327–336, 1973.

    MathSciNet  MATH  Google Scholar 

  • J.K. Lenstra and A.H.G. Rinnooy Kan. Computational complexity of discrete optimization problems. Annals of Discrete Mathematics, 4:121–140, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  • O. Leue. Methoden zur Lösung dreidimensionaler Zuordnungsprobleme. Angewandte Informatik, 14:154–162, 1972.

    MATH  Google Scholar 

  • Y. Li, P.M. Pardalos, and M.G.C. Resende. A greedy randomized adaptive search procedure for the quadratic assignment problem. In P.M. Pardalos and H. Wolkowicz, editors, Quadratic assignment and related problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 237–261. American Mathematical Society, Providence, 1994.

    Google Scholar 

  • S.L. Martins, C.C. Ribeiro, and M.C. Souza. A parallel GRASP for the Steiner problem in graphs. In A. Ferreira, J. Rolim, H. Simon, and S.-H. Teng, editors, Solving irregularly structured problems in parallel, volume 1457 of Lecture Notes in Computer Science, pages 285–297. Springer, Berlin, 1998.

    Google Scholar 

  • S.L. Martins, P.M. Pardalos, M.G.C. Resende, and C.C. Ribeiro. Greedy randomized adaptive search procedures for the Steiner problem in graphs. In P.M. Pardalos, S. Rajasejaran, and J. Rolim, editors, Randomization methods in algorithmic design, volume 43 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 133–145. American Mathematical Society, Providence, 1999.

    Google Scholar 

  • S.L. Martins, P.M. Pardalos, M.G.C. Resende, and C.C. Ribeiro. A parallel GRASP for the Steiner tree problem in graphs using a hybrid local search strategy. Journal of Global Optimization, 17:267–283, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  • S.L. Martins, C.C. Ribeiro, and I. Rosseti. Applications and parallel implementations of metaheuristics in network design and routing. In S. Manandhar, J. Austin, U. Desai, Y. Oyanagi, and A.K. Talukder, editors, Applied computing, volume 3285 of Lecture Notes in Computer Science, pages 205–213. Springer, Berlin, 2004.

    Google Scholar 

  • R.A. Murphey, P.M. Pardalos, and L.S. Pitsoulis. A parallel GRASP for the data association multidimensional assignment problem. In P.M. Pardalos, editor, Parallel processing of discrete problems, volume 106 of The IMA Volumes in Mathematics and Its Applications, pages 159–180. Springer, New York, 1998.

    Google Scholar 

  • P.M. Pardalos and L.S. Pitsoulis. Nonlinear assignment problems: Algorithms and applications. Kluwer Academic Publishers, Boston, 2000.

    Book  MATH  Google Scholar 

  • P.M. Pardalos, L.S. Pitsoulis, and M.G.C. Resende. A parallel GRASP implementation for the quadratic assignment problem. In A. Ferreira and J. Rolim, editors, Parallel algorithms for irregular problems: State of the art, pages 115–133. Kluwer Academic Publishers, Boston, 1995.

    Chapter  MATH  Google Scholar 

  • P.M. Pardalos, L.S. Pitsoulis, and M.G.C. Resende. A parallel GRASP for MAX-SAT problems. In J. Waśniewski, J. Dongarra, K. Madsen, and D. Olesen, editors, Applied parallel computing industrial computation and optimization, volume 1184 of Lecture Notes in Computer Science, pages 575–585. Springer, Berlin, 1996.

    Google Scholar 

  • W.P. Pierskalla. The tri-substitution method for the three-multidimensional assignment problem. Journal of the Canadian Operational Research Society, 5:71–81, 1967.

    MATH  Google Scholar 

  • W.P. Pierskalla. The multidimensional assignment problem. Operations Research, 16:422–431, 1968.

    Article  MATH  Google Scholar 

  • M.G.C. Resende, T.A. Feo, and S.H. Smith. Algorithm 787: Fortran subroutines for approximate solution of maximum independent set problems using GRASP. ACM Transactions on Mathematical Software, 24:386–394, 1998.

    Article  MATH  Google Scholar 

  • C.C. Ribeiro and I. Rosseti. A parallel GRASP heuristic for the 2-path network design problem. In B. Monien and R. Feldmann, editors, Euro-Par 2002 Parallel Processing, volume 2400 of Lecture Notes in Computer Science, pages 922–926. Springer, Berlin, 2002.

    Google Scholar 

  • C.C. Ribeiro and I. Rosseti. Efficient parallel cooperative implementations of GRASP heuristics. Parallel Computing, 33:21–35, 2007.

    Article  MathSciNet  Google Scholar 

  • B. Roy and B. Sussmann. Les problèmes d’ordonnancement avec contraintes disjonctives. Technical Report Note DS no. 9 bis, SEMA, Montrouge, 1964.

    Google Scholar 

  • M. Snir, S. Otto, S. Huss-Lederman, D. Walker, and J. Dongarra. MPI – The complete reference, Volume 1 – The MPI core. MIT Press, Cambridge, 1998.

    Google Scholar 

  • E.D. Taillard. Robust taboo search for the quadratic assignment problem. Parallel Computing, 17:443–455, 1991.

    Article  MathSciNet  Google Scholar 

  • E.-G. Talbi. Metaheuristics: From design to implementation. Wiley, New York, 2009.

    Book  MATH  Google Scholar 

  • M.G.A. Verhoeven and E.H.L. Aarts. Parallel local search. Journal of Heuristics, 1:43–66, 1995.

    Article  MATH  Google Scholar 

  • M. Vlach. Branch and bound method for the three index assignment problem. Ekonomicko-Mathematický Obzor, 3:181–191, 1967.

    MathSciNet  Google Scholar 

  • S. Voss. Heuristics for nonlinear assignment problems. In P.M. Pardalos and L.S. Pitsoulis, editors, Nonlinear assignment problems: Algorithms and applications, pages 175–215. Kluwer Academic Publishers, Boston, 2000.

    Chapter  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this chapter

Cite this chapter

Resende, M.G.C., Ribeiro, C.C. (2016). Parallel GRASP heuristics. In: Optimization by GRASP. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6530-4_10

Download citation

Publish with us

Policies and ethics