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A parallel formulation for general branch-and-bound algorithms

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Parallel Algorithms for Irregularly Structured Problems (IRREGULAR 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 980))

Abstract

We consider in this paper the problem of searching for an (sub)optimal solution in a discrete solution space and we formulate the method called branch- and- bound. It is shown that the formulation is general to A *, state-space and LP- based branch- and- bound and branch- and-cut. It includes a parallel data structure that can express a large variety of parallel strategies used in parallel branch-and-bound. The general formulation can be used in designing libraries that make accessible the parallelism to the operations research community.

This work was partially supported by DRET, the project Stratagème of the French CNRS, and the Human Capital and Mobility project SCOOP — Solving Combinatorial Optimization Problems in Parallel — of the European Union.

Partially supported by a CNPq (Brazil) fellowship, grant 201421/92-5 (BC).

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References

  1. E. Beale. Branch and bound methods for mathematical programming systems. Annals of Discrete Mathematics, 5:201–219, 1979.

    MathSciNet  Google Scholar 

  2. R. Corrêa and A. Ferreira. A distributed implementation of asynchronous parallel branch-and-bound. In A. Ferreira and J. Rolim, editors, Solving Irregular Problems in Parallel: State of the Art. Kluwer Academic Publisher, Boston (USA), 1995.

    Google Scholar 

  3. R. Corrêa and A. Ferreira. On the effectiveness of synchronous branch-and-bound algorithms. Parallel Processing Letters, 1995. To appear.

    Google Scholar 

  4. R. Corrêa and A. Ferreira. Parallel best-first branch-and-bound in discrete optimization: a framework. Tec. Rep. 95-03, DIMACS, Rutgers Univ., March 1995.

    Google Scholar 

  5. R. Finkel and U. Manber. DIB — A distributed implementation of backtracking. ACM Transactions on Prog. Lang. and Syst., 9(2):235–256, April 1987.

    Article  Google Scholar 

  6. T. Ibaraki. The power of dominance relations in branch-and-bound algorithms. Journal of the ACM, 24(2):264–279, April 1977.

    Article  Google Scholar 

  7. T. Ibaraki. Branch-and-bound procedure and the state-space representation of combinatorial optimization problems. Inf. and Control, 36:1–27, 1978.

    Article  Google Scholar 

  8. V. Kumar, A. Grama, A. Gupta, and G. Karypis. Introduction to Parallel Computing: Design and Analysis of Algorithms. The Benjamin/Cummings Publishing Company, Inc., 1994.

    Google Scholar 

  9. V. Kumar and L. Kanal. A general branch-and-bound formulation for understanding and synthesizing And/Or tree search procedures. Artificial Intelligence, 21:179–198, 1983.

    Google Scholar 

  10. T. Lai and S. Sahni. Anomalies in parallel branch-and-bound algorithms. Communications of the ACM, 27:594–602, 1984.

    Article  Google Scholar 

  11. T. Lai and A. Sprague. Performance of parallel branch-and-bound algorithms. IEEE Transactions on Computers, C-34(10):962–964, October 1985.

    Google Scholar 

  12. G. Li and B. Wah. Coping with anomalies in parallel branch-and-bound algorithms. IEEE Transactions on Computers, C-35(6):568–573, June 1986.

    Google Scholar 

  13. G. McKeown, V. Rayward-Smith, and H. Turpin. Branch-and-bound as a higherorder function. Annals of Operations Research, 33:379–402, 1991.

    Google Scholar 

  14. L. Mitten. Branch-and-bound methods: General formulation and properties. Operations Research, 18:24–34, 1970. Errata in Operations Research 19 (1971), 550.

    Google Scholar 

  15. D. Nau, V. Kumar, and L. Kanal. General branch and bound, and its relation to A* and AO*. Artificial Intelligence, (23):29–58, 1984.

    Article  Google Scholar 

  16. M. Padberg and G. Rinaldi. A branch and cut algorithm for the solution of largescale symmetric traveling salesman problem. SIAM Review, 33:60–100, 1991.

    Article  Google Scholar 

  17. J. Pearl. Heuristics — Intelligent Search Strategies for Computer Problem Solving. Reading, MA: Addison-Wesley, 1984.

    Google Scholar 

  18. B. Wah and Y. Eva. MANIP — A multicomputer architecture for solving combinatorial extremum-search problems. IEEE T. on Comp., C-33(5):377–390, 1984.

    Google Scholar 

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Authors and Affiliations

  1. LMC - IMAG, 46, av. Félix Viallet, 38031, Grenoble Cedex, France

    Ricardo Corrêa

Authors
  1. Ricardo Corrêa
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Afonso Ferreira José Rolim

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© 1995 Springer-Verlag Berlin Heidelberg

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Corrêa, R. (1995). A parallel formulation for general branch-and-bound algorithms. In: Ferreira, A., Rolim, J. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1995. Lecture Notes in Computer Science, vol 980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60321-2_31

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  • DOI: https://doi.org/10.1007/3-540-60321-2_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60321-4

  • Online ISBN: 978-3-540-44915-7

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