An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming
In recent years many advances have been made in solution techniques for specially structured 0-1 integer programming problems. In contrast, very little progress has been made on solving general (mixed integer) problems. This, of course, is not true when viewed from the theoretical side: Lenstra (1981) made a major breakthrough, obtaining a polynomial-time algorithm when the number of integer variables is fixed. We discuss a practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of Lovasz and Scarf (1988).This method allows us to avoid the ellipsoidal approximations required in Lenstra's algorithm. We report on the solution of a number of small (but difficult) examples, up to 100 integer variables. Our computer code uses the linear programming optimizer CPlex as a subroutine to solve the linear programming problems that arise.
|Date of creation:||Aug 1991|
|Publication status:||Published in ORSA Journal of Computing (spring 1993), 5(2): 206-221|
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- László Lovász & Herbert E. Scarf, 1992.
"The Generalized Basis Reduction Algorithm,"
Mathematics of Operations Research,
INFORMS, vol. 17(3), pages 751-764, August.
- Herbert E. Scarf & Laszlo Lovasz, 1990. "The Generalized Basis Reduction Algorithm," Cowles Foundation Discussion Papers 946, Cowles Foundation for Research in Economics, Yale University.
- Ravi Kannan & Lászlo Lovász & Herbert E. Scarf, 1990. "The Shapes of Polyhedra," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 364-380, May.
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