Skip to main content
SpringerLink
Log in

Parallel local search

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

We present a survey of parallel local search algorithms in which we review the concepts that can be used to incorporate parallelism into local search. For this purpose we distinguish between single-walk and multiple-walk parallel local search and between asynchronous and synchronous parallelism. Within the class of single-walk algorithms we differentiate between multiple-step and single-step parallelism. To describe parallel local search we introduce the concepts of hyper neighborhood structures and distributed neighborhood structures. Furthermore, we present templates that capture most of the parallel local search algorithms proposed in the literature. Finally, we discuss some complexity issues related to parallel local search.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aarts, E.H.L., De Bont, F.M.I., Habers, J.H.A., and Van Laarhoven, P.J.M. (1986). Parallel implementations of the statistical cooling algorithms,Integration, 4, 209–238.

    Google Scholar 

  • Aarts, E.H.L., and Korst, J. (1989).Simulated Annealing and Bolztmann Machines. New York: Wiley.

    Google Scholar 

  • Aarts, E.H.L., and Lenstra, J.K. (Eds.). (1995).Local Search in Combinatorial Optimization. New York: Wiley.

    Google Scholar 

  • Abramson, D. (1991). Constructing school timetables using simulated annealing: Sequential and parallel algorithms.Management Science, 37, 98–113.

    Google Scholar 

  • Allwright, J.R.A., and Carpenter, D.B. (1989). A distributed implementation of simulated annealing for the traveling salesman problem.Parallel Computing, 10, 335–338.

    Article  MathSciNet  MATH  Google Scholar 

  • Azencott, R. (Ed.). (1992).Simulated Annealing: Parallelization Techniques. New York: Wiley.

    MATH  Google Scholar 

  • Bachem, A., and Wottawa. (1992).Parallelization of Heuristics for Large Traveling Salesman Problems (in German). Report no. 92. 119, Universität zu Köln, Germany.

    Google Scholar 

  • Barbosa, V.C., and Boeres, M.C.S. (1990). An Occam-based evaluation of a parallel version of simulated annealing.Microprocessing and Microprogramming, 30, 85–92.

    Article  Google Scholar 

  • Barbosa, V.C., and Gafni, E. (1989). A distributed implementation of simulated annealing.Journal of Parallel and Distributed Computing, 6, 411–434.

    Article  Google Scholar 

  • Battiti, R., and Tecchiolli, G. (1992). Parallel biased search for combinatorial optimization: Genetic algorithms and tabu.Microprocessors and Microsystems, 16, 351–367.

    Article  Google Scholar 

  • Brent, R.P. (1974). The parallel evaluation of general arithmetic expressions.Journal ACM, 21, 201–206.

    Article  MATH  MathSciNet  Google Scholar 

  • Casotto, A., Romeo, F., and Sangiovanni-Vincentelli, A. (1987). A parallel simulated annealing algorithm for the placement of macro-cells.IEEE Transactions on Computer-Aided Design, 6, 838–847.

    Article  Google Scholar 

  • Chakrapani, J., and Skorin-Kapov, J. (1993a). Connection machine implementation of a tabu search algorithm for the traveling salesman problem.Journal of Computing and Information Technology, 1, 29–36.

    Google Scholar 

  • Chakrapani, J., and Skorin-Kapov, J. (1993b). Massively parallel tabu search for the quadratic assignment problem.Annals of Operations Research, 41, 327–342.

    Article  MATH  Google Scholar 

  • Crainic, T.G., Toulouse, M., and Gendreau, M. (1993a).Parallel Asynchronous Tabu Search for Multicommodity Location-Allocation with Balancing Requirements. Publication 935, Centre de recherche sur les transports, Université de Montréal.

  • Crainic, T.G., Toulouse, M., and Gendreau, M. (1993b).Towards a Taxonomy of Parallel Tabu Search Algorithms. Publication 933, Centre de recherche sur les transports, Université de Montréal.

  • Crainic, T.G., Toulouse, M., and Gendreau, M. (1995). Synchronous tabu search parallelization strategies for multicommodity location-allocation with balancing requirements.OR Spektrum 17.

  • Darema, F., Kirkpatrick, S., and Norton, V.A. (1987). Parallel algorithms for chip placement by simulated annealing.IBM Journal of Research and Development, 31, 391–402.

    Article  Google Scholar 

  • Diekmann, R., Lüling, R., and Simon, J. (1993). Problem independent distributed simulated annealing and its applications. In R.V.V. Vidal (Ed.),Applied Simulated Annealing (pp. 18–44). LNEMS 396. Berlin: Springer-Verlag.

    Google Scholar 

  • Dodd, N. (1990). Slow annealing versus multiple fast annealing runs: An empirical investigation.Parallel Computing, 16, 269–272.

    Article  MATH  Google Scholar 

  • Eikelder, H.M.M. Ten, Verhoeven, M.G.A., Vossen, T.W.M., and Aarts, E.H.L. (1995). A probabilistic analysis of local search. In I.H. Osman and J.P. Kelly (Eds.),Metaheuristics: The State of the Art 1995. Boston: Kluwer.

    Google Scholar 

  • Felten, E., Karlin, S., and Otto, S.W. (1985). The traveling salesman problem on a hypercubic MIMD machine.Proceedings of the International Conference on Parallel Processing (pp. 6–10). New York.

  • Ferreira, A.G., and Zerovnik, J. (1993). Bounding the probability of success of stochastic methods for global optimization.Computers and Mathematics with Applications, 25, 1–8.

    Article  MathSciNet  MATH  Google Scholar 

  • Fiechter, C.N. (1994). A parallel tabu search algorithm for large travelling salesman problems.Discrete Applied Mathematics, 51, 243–267.

    Article  MATH  MathSciNet  Google Scholar 

  • Fox, B.L. (1993). Integrating and accelerating tabu search, simulated annealing, and genetic algorithms.Annals of Operations Research, 41, 47–67.

    Article  MATH  Google Scholar 

  • Garcia, B.L., Potvin, J.Y., and Rousseau, J.M. (1994). A parallel implementation of the tabu search heuristic for vehicle routing problems with time window constraints.Computer Operations Research, 21, 1025–1033.

    Article  MATH  Google Scholar 

  • Garey, M.R., and Johnson, D.S. (1979).Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: Freeman.

    MATH  Google Scholar 

  • Glover, F. (1989). Tabus search: Part I.ORSA Journal on Computing, 1, 190–206.

    MATH  MathSciNet  Google Scholar 

  • Glover, F., Taillard, E., and De Werra, D. (1993). A user's guide to tabu search.Annals of Operations Research, 41, 3–28.

    Article  MATH  Google Scholar 

  • Goloberg, D.E. (1989).Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Greening, D.R. (1990). Parallel simulated annealing techniques.Physica D, 42, 293–306.

    Article  Google Scholar 

  • Jog, P., and Van Gucht, D. (1987). Parallelisation of probabilistic sequential search algorithms.Proceedings of the Second International Conference on Genetic Algorithms (pp. 170–176). San Mateo: Morgan Kaufmann.

    Google Scholar 

  • Johnson, D.S. (1990). Local optimization and the traveling salesman problem.Proceedings of the Seventeenth Colloquium on Automata, Languages, and Programming (pp. 446–461). LNCS 447. Berlin: Springer.

    Google Scholar 

  • Johnson, D.S., Papadimitriou, C.H., and Yannakakis, M. (1988). How easy is local search?Journal of Computer and System Sciences, 37, 79–100.

    Article  MathSciNet  MATH  Google Scholar 

  • Jones, M.H., and Banerjee, P. (1987). An improved simulated annelaing algorithm for standard cell placement.Proceedings of the International Conference on Computer Design (pp. 83–86). Washington, D.C.

  • Kernighan, B.W., and Lin, S. (1970). An efficient heuristic procedure for partitioning graphs.Bell systems Technical Journal, 49, 291–307.

    Google Scholar 

  • Kindervater, G.A.P., Lenstra, J.K., and Savelsbergh, M.W.P. (1993). Sequential and parallel local search for the time constrained traveling salesman problem.Discrete Applied Mathematics, 42, 211–225.

    Article  MathSciNet  MATH  Google Scholar 

  • Kirkpatrick, S., Gelatt, Jr., C.D., and Vecchi, M.P. (1983). Optimization by simulated annealing.Science, 220, 671–680.

    MathSciNet  Google Scholar 

  • Kirkpatrick, S., and Toulouse, G. (1985). Configuration space analysis of travelling salesman problems.Journal Physique, 46, 1277–1292.

    MathSciNet  Google Scholar 

  • Kravitz, S.A., and Rutenbar, R.A. (1987). Placement by simulated annealing on a multiprocessor.IEEE Transactions on Computer Aided Design, 6, 534–549.

    Article  Google Scholar 

  • Kruskal, C.P., Rudolph, L., and Snir, M. (1990). A complexity theory of efficient parallel algorithms.Theoretical Computer Science, 71, 95–132.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, Y., and Pardalos, P.M. (1992). Parallel algorithms for the quadratic assignment problem. In P.M. Pardalos (Ed.),Advances in Optimization and Parallel Computing (pp. 177–189). Amsterdam: Elsevier Science Publishers.

    Google Scholar 

  • Lin, S. (1965). Computer solutions of the traveling salesman problem.Bell System Technical Journal, 44, 2245–2269.

    MATH  MathSciNet  Google Scholar 

  • Lin, S., and Kernichan, B.W. (1973). An effective heuristic algorithm for the traveling salesman problem.Operations Research, 21, 498–516.

    Article  MathSciNet  MATH  Google Scholar 

  • Lueker, G. (1975).Two NP-Complete Problems in Nonnegative Integer Programming. Manuscript, Princeton University.

  • Mahfoud, S.W., and Goldberg, D.E. (1995). Parallel recombinative simulated annealing: A genetic algorithm.Parallel Computing, 21, 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  • Malek, M., Guruswamy, M., and Pandya, M. (1989). Serial and parallel simulated annealing and tabu search for the traveling salesman problem.annals of Operations Research, 21, 59–84.

    Article  MathSciNet  MATH  Google Scholar 

  • Martin, O, Otto, S.W., and Felten, E.W. (1991). Large-steps Markov chains for the travelling salesman problem.Complex Systems, 5, 299–326.

    MathSciNet  MATH  Google Scholar 

  • Michalewicz, Z. (1992).Genetic Algorithms+Data Structures=Evolution Programs. Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Moscato, P. (1993). An introduction to population approaches for optimization and hierarchical objective functions: A discussion on the role of tabu search.Annals of Operations Research, 41, 85–122.

    Article  MATH  Google Scholar 

  • Mühlenbein, H. (1992). Parallel genetic algorithms in combinatorial optimization. In O. Balci (Ed.),Computer Science and Operations Research. London: Pergamon Press.

    Google Scholar 

  • Mühlenbein, H., Gorges-Schleuter, M., and Krämer, O. (1988). Evolution algorithms in combinatorial optimization.Parallel Computing, 7, 65–85.

    Article  MATH  Google Scholar 

  • Osborne, L.J., and Gillett, B.E. (1991). A comparison of two simulated annealing algorithms applied to the directed Steiner problem on networks.ORSA Journal on Computing, 3, 213–225.

    MATH  Google Scholar 

  • Papadimitriou, C.H., and Steiglitz, K. (1982).Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Parberry, I. (1987).Parallel Complexity Theory. London: Pitman.

    MATH  Google Scholar 

  • Ravikumar, C.P. (1992). Parallel techniques for solving large scale travelling salesperson problems.Microprocessors and Microsystems, 16, 149–158.

    Article  Google Scholar 

  • Reeves, C.R. (Ed.). (1993).Modern Heuristic Techniques for Combinatorial Problems. London: Blackwell.

    MATH  Google Scholar 

  • Romeo, F., and Sangiovanni-Vicentelli, A. (1991). a theoretical framework for simulated annealing.Algorithmica, 6, 302–345.

    Article  MathSciNet  MATH  Google Scholar 

  • Rose, J.S., Snelgrove, W.M., and Vranesic, Z.G. (1988). Parallel standard cell placement algorithms with quality equivalent to simulated annealing.IEEE Transactions on Computer-Aided Design, 7, 387–396.

    Article  Google Scholar 

  • Roussel-Ragot, P., and Dreyfus, G. (1990). A problem independent parallel implementation for simulated annealing: Models and experiments.IEEE Transactions on Computer-Aided Design, 9, 827–835.

    Article  Google Scholar 

  • Savage, J.E., and Wloka, M.G. (1991). Parallelism in graph-partioning.Journal of Parallel and Distributed Computing, 13, 257–272.

    Article  MathSciNet  Google Scholar 

  • Sechen, C. (1988).VLSI Placement and Global Routing Using Simulated Annealing. Boston: Kluwer.

    Google Scholar 

  • Shahookar, K., and Mazunder, P. (1991). VLSI cell-placement techniques.ACM Computing Surveys, 23, 143–220.

    Article  Google Scholar 

  • Taillard, E. (1990). Some efficient heuristic methods for the flow shop sequencing problem.European Journal of Operations Research, 47, 65–74.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Taillard, E. (1993). Parallel iterative search methods for vehicle routing problems.Networks, 23, 661–673.

    MATH  Google Scholar 

  • Taillard, E. (1994). Parallel taboo search techniques for the job shop scheduling problem.ORSA Journal on Computing, 6, 108–117.

    MATH  Google Scholar 

  • Vaessens, R.J.M., Aarts, E.H.L., and Lenstra, J.K. (1992). A local search template.Parallel Problem Solving from Nature, 2, 65–74.

    Google Scholar 

  • Verhoeven, M.G.A., Aarts, E.H.L., and Swinkels, P.C.J. (1995). A parallel 2-opt algorithm for the traveling salesman problem.Future Generation Computer Systems, 11, 175–182.

    Article  Google Scholar 

  • Verhoeven, M.G.A., Aarts, E.H.L., Van de Sluis, E., and Vaessens, R.J.M. (1992). Parallel local search and the travelling salesman problem (extended abstract).Proceedings of Parallel Problem Solving from Nature, 2, 543–552.

    Google Scholar 

  • Verhoeven, M.G.A., Swinkels, P.C.J., and Aarts, E.H.L. (1995). Parallel local search and the traveling salesman problem. Working document.

  • Voss, S. (1993). Tabu search: Applications and Prospects. In D.Z. Du and P.M. Pardalos (Eds.),Network Optimization Problems (pp. 333–353). City: World Scientific.

  • Yannakakis, M. (1990). The analysis of local search problems and their heuristics.Proceedings of the Seventh Symposium on Theoretical Aspects of Computer Science (pp. 298–311). LNCS 415. Berlin: Springer-Verlag.

    Google Scholar 

  • Yannakakis, M. (1995). Computational complexity of local search. In E.H.L. Aarts and J.K. Lenstra (Eds.),Local Search in Combinatorial Optimization. Berlin: Springer-Verlag.

    Google Scholar 

  • Yeong, C.S., and Kim, M.H. (1991). Fast parallel simulated annealing for traveling salesman problem on SIMD machines with linear interconnections.Parallel Computing, 17, 221–228.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, Netherlands

    M. G. A. Verhoeven

  2. Philips Research Laboratories, Endhoven University of Technology, P.O. Box 80000, 5600 JA, Eindhoven, Netherlands

    E. H. L. Aarts

Authors
  1. M. G. A. Verhoeven
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. H. L. Aarts
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Verhoeven, M.G.A., Aarts, E.H.L. Parallel local search. J Heuristics 1, 43–65 (1995). https://doi.org/10.1007/BF02430365

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02430365

Key Words

Search

Navigation