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Surrogate Dual Multiplier Search Procedures in Integer Programming

Author

Listed:
  • Mark H. Karwan

    (State University of New York, Buffalo, New York)

  • Ronald L. Rardin

    (Purdue University, West Lafayette, Indiana)

Abstract

Search procedures for optimal Lagrange multipliers are highly developed and provide good bounds in branch and bound procedures that have led to the successful application of Lagrangean duality in integer programming. Although the surrogate dual generally provides a better objective bound, there has been little development of surrogate multiplier search procedures. This paper develops and empirically analyzes several surrogate multiplier search procedures. Results indicate that the procedures can produce possibly superior bounds in an amount of time comparable to other techniques. Our discussion also highlights the similarity of the procedures to some well known Lagrangean search techniques.

Suggested Citation

  • Mark H. Karwan & Ronald L. Rardin, 1984. "Surrogate Dual Multiplier Search Procedures in Integer Programming," Operations Research, INFORMS, vol. 32(1), pages 52-69, February.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:1:p:52-69
    DOI: 10.1287/opre.32.1.52
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    Citations

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    Cited by:

    1. N. Boland & A. C. Eberhard & A. Tsoukalas, 2015. "A Trust Region Method for the Solution of the Surrogate Dual in Integer Programming," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 558-584, November.
    2. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.
    3. Sanjiv Sarin & Mark H. Karwan & Ronald L. Rardin, 1987. "A new surrogate dual multiplier search procedure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 431-450, June.
    4. S.-L. Kim & S. Kim, 1998. "Exact Algorithm for the Surrogate Dual of an Integer Programming Problem: Subgradient Method Approach," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 363-375, February.
    5. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    6. Hanafi, Said & Glover, Fred, 2007. "Exploiting nested inequalities and surrogate constraints," European Journal of Operational Research, Elsevier, vol. 179(1), pages 50-63, May.
    7. Saïd Hanafi & Christophe Wilbaut, 2011. "Improved convergent heuristics for the 0-1 multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 183(1), pages 125-142, March.
    8. Cesar Rego & Frank Mathew & Fred Glover, 2010. "RAMP for the capacitated minimum spanning tree problem," Annals of Operations Research, Springer, vol. 181(1), pages 661-681, December.
    9. Alidaee, Bahram, 2014. "Zero duality gap in surrogate constraint optimization: A concise review of models," European Journal of Operational Research, Elsevier, vol. 232(2), pages 241-248.
    10. M. A. Venkataramana & John J. Dinkel & John Mote, 1991. "Vector processing approach to constrained network problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 71-85, February.

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