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An Adaptive Group Theoretic Algorithm for Integer Programming Problems

Author

Listed:
  • G. Anthony Gorry

    (Massachusetts Institute of Technology)

  • Jeremy F. Shapiro

    (Massachusetts Institute of Technology)

Abstract

Group theory is used to integrate a wide variety of integer programming methods into a common computational process. Included are group optimization algorithms, Lagrangian methods, the cutting plane method, and the method of surrogate constraints. These methods are controlled by a supervisor which performs four main functions: set-up, directed search, subproblem analysis, and prognosis. Some computational experience is given. One appendix contains an algorithm for dynamically solving unconstrained group problems. A second appendix gives an algorithm for solving zero-one group problems.

Suggested Citation

  • G. Anthony Gorry & Jeremy F. Shapiro, 1971. "An Adaptive Group Theoretic Algorithm for Integer Programming Problems," Management Science, INFORMS, vol. 17(5), pages 285-306, January.
    • Handle: RePEc:inm:ormnsc:v:17:y:1971:i:5:p:285-306
    DOI: 10.1287/mnsc.17.5.285
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    Cited by:

    1. Gérard Cornuéjols & Milind Dawande, 1999. "A Class of Hard Small 0-1 Programs," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 205-210, May.
    2. Roe, Terry L. & Shane, Mathew, 1973. "A Heuristic Fixed-Charge Quadratic Algorithm," Staff Papers 13466, University of Minnesota, Department of Applied Economics.

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