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An Implicit Enumeration Algorithm for Quadratic Integer Programming

Author

Listed:
  • R. D. McBride

    (University of Southern California)

  • J. S. Yormark

    (University of Southern California)

Abstract

We present an implicit enumeration algorithm for a nonseparable quadratic integer programming problem. We utilize fathoming criteria derived from Lemke's complementary pivot algorithm, and compare the use of pseudo-costs versus generalized penalties as a guide to branching. Computational experience is provided.

Suggested Citation

  • R. D. McBride & J. S. Yormark, 1980. "An Implicit Enumeration Algorithm for Quadratic Integer Programming," Management Science, INFORMS, vol. 26(3), pages 282-296, March.
    • Handle: RePEc:inm:ormnsc:v:26:y:1980:i:3:p:282-296
    DOI: 10.1287/mnsc.26.3.282
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    Citations

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    Cited by:

    1. Bahman Kalantari & Ansuman Bagchi, 1990. "An algorithm for quadratic zero‐one programs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 527-538, August.
    2. Lodi, Andrea & Allemand, Kim & Liebling, Thomas M., 1999. "An evolutionary heuristic for quadratic 0-1 programming," European Journal of Operational Research, Elsevier, vol. 119(3), pages 662-670, December.
    3. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
    4. Alkhamis, Talal M. & Hasan, Merza & Ahmed, Mohamed A., 1998. "Simulated annealing for the unconstrained quadratic pseudo-Boolean function," European Journal of Operational Research, Elsevier, vol. 108(3), pages 641-652, August.
    5. Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2010. "A hybrid metaheuristic approach to solving the UBQP problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1254-1262, December.
    6. Gupta, Renu & Bandopadhyaya, Lakshmisree & Puri, M. C., 1996. "Ranking in quadratic integer programming problems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 231-236, November.
    7. Glover, Fred & Alidaee, Bahram & Rego, Cesar & Kochenberger, Gary, 2002. "One-pass heuristics for large-scale unconstrained binary quadratic problems," European Journal of Operational Research, Elsevier, vol. 137(2), pages 272-287, March.
    8. Katayama, Kengo & Narihisa, Hiroyuki, 2001. "Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem," European Journal of Operational Research, Elsevier, vol. 134(1), pages 103-119, October.
    9. Wang, Yang & Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2012. "Path relinking for unconstrained binary quadratic programming," European Journal of Operational Research, Elsevier, vol. 223(3), pages 595-604.
    10. Gary Kochenberger & Fred Glover & Bahram Alidaee & Cesar Rego, 2005. "An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem," Annals of Operations Research, Springer, vol. 139(1), pages 229-241, October.

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    Keywords

    quadratic integer programming;

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