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Computational aspects of a branch and bound algorithm for quadratic zero-one programming

Rechnerische Aspekte eines “Branch and Bound”-Algorithmus zur quadratischen Null-Eins-Programmierung

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Abstract

In this paper we describe computational experience in solving unconstrained quadratic zero-one problems using a branch and bound algorithm. The algorithm incorporates dynamic preprocessing techniques for forcing variables and heuristics to obtain good starting points. Computational results and comparisons with previous studies on several hundred test problems with dimensions up to 200 demonstrate the efficiency of our algorithm.

Zusammenfassung

In dieser Arbeit beschreiben wir rechnerische Erfahrungen bei der Lösung von unbeschränkten quadratischen Null-Eins-Problemen mit einem “Branch and Bound”-Algorithmus. Der Algorithmus erlaubt dynamische Vorbereitungs-Techniken zur Erzwingung ausgewählter Variablen und Heuristiken zur Wahl von guten Startpunkten. Resultate von Berechnungen und Vergleiche mit früheren Arbeiten mit mehreren hundert Testproblemen mit Dimensionen bis 200 zeigen die Effizienz unseres Algorithmus.

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References

  1. Barahona, F., A Solvable Case of Quadratic 0–1 Programming, Discrete Applied Mathematics13 (1986), 23–26.

    Google Scholar 

  2. Barahona, F., Jünger, M., Reinelt, G., Experiments in Quadratic 0–1 Programming, Mathematical Programming44 (1989), 127–137.

    Google Scholar 

  3. Carter, M. W., The Indefinite Zero-One Quadratic Problem, Discrete Applied Mathematics7 (1984), 23–44.

    Google Scholar 

  4. Cooper, M., A Survey of Methods for Pure Nonlinear Integer Programming, Management Science3 (1981), 356–361.

    Google Scholar 

  5. Gallo, G., Hammer, P. L., Simeone, B., Quadratic Knapsack Problems, Mathematical Programming12 (1980), 132–149.

    Google Scholar 

  6. Gulati, V. P., Gupta, S. K., Mittal, A. K., Unconstrained Quadratic Bivalent Programming Problem, European Journal of Operational Research,15 (1984), 121–125.

    Google Scholar 

  7. Hansen, P., Hammer, P. L., Logical relations in quadratic 0–1 programming, Revue Roumaine de Mathematiques Pures et Appliques,20 (1984), 418–427.

    Google Scholar 

  8. Hammer, P. L., Hansen, P., Simeone, B., Roof Duality, Complementation, and Persistency in Quadratic 0–1 Optimization, Mathematical Programming,28(2), (1984), 121–155.

    Google Scholar 

  9. Hansen, P., Methods of Nonlinear 0–1 Programming, Annals of Discrete Mathematics5 (1979), 53–70.

    Google Scholar 

  10. Shi Hui, L., An Improved Enumerative Algorithm for Solving Quadratic Zero-One Programming, European Journal of Operational Research15 (1984), 110–120.

    Google Scholar 

  11. Jha, S., Pardalos, P. M., Graph Separation Techniques for Quadratic Zero-One Programming, Technical Report CS-87-39, Computer Science Department, The Pennsylvania State University (1987).

  12. Körner, F., An Efficient Branch and Bound Algorithm to Solve the Quadratic Integer Programming Problem, Computing30 (1983), 253–260.

    Google Scholar 

  13. Krarup, J., Pruza, P. A., Computer Aided Layout Design, Mathematical Programming Study9 (1978), 75–94.

    Google Scholar 

  14. Lewis, P., Goodman, A. S., Miller, J. M., Pseudo-Random Number Generator for the System/360, IBM Systems Journal,8(2), (1969), 300–312.

    Google Scholar 

  15. McBride, R. D., Yormark, J. S., An Implicit Enumeration Algorithm for Quadratic Integer Programming, Management Science26(3) (1980), 282–296.

    Google Scholar 

  16. Pardalos, P. M., Construction of test problems in quadratic bivalent programming, To appear in ACM TOMS (1990).

  17. Pardalos, P. M., Rodgers, G. P., Parallel branch and bound algorithms for unconstrained quadratic zero-one programming. In: Impacts of Recent Computer Advances on Operations Research, (eds R. Sharda et al. 1989), North-Holland, 131–143.

  18. Pardalos, P. M., Rodgers, G. P., A branch and bound algorithm for the maximum clique problem, To appear in Mathematical Programming.

  19. Pardalos, P. M., Rosen, J. B., Global Constrained Optimization: Algorithms and Applications, Lecture Notes in Computer Sciences268 Berlin-Heidelberg-New York: Springer (1987).

    Google Scholar 

  20. Picard, J. C., Ratliff, H. D., Minimum Cuts and Related Problems, Networks5 (1974), 357–370.

    Google Scholar 

  21. Rodgers, G. P. Algorithms for Unconstrained Quadratic 0–1 Programming and Related Problems on Contemporary Computer Architectures, Ph.D. Dissertation, The Pennsylvania State University, (1989).

  22. Williams, A. C., Quadratic 0–1 Programming Using the Roof Dual with Computational Results, RUTCOR Research Report #8-85, The State University of New Jersey, (1985).

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Authors and Affiliations

  1. Department of Computer Science, The Pennsylvania State University, 16802, University Park, PA, USA

    P. M. Pardalos

  2. General Technology Division, IBM Corporation, 05452, Burlington, Vermont, USA

    G. P. Rodgers

Authors
  1. P. M. Pardalos
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  2. G. P. Rodgers
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Pardalos, P.M., Rodgers, G.P. Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing 45, 131–144 (1990). https://doi.org/10.1007/BF02247879

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  • DOI: https://doi.org/10.1007/BF02247879

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