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An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming

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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.

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 990.

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Length: 13 pages
Date of creation: Aug 1991
Publication status: Published in ORSA Journal of Computing (spring 1993), 5(2): 206-221
Handle: RePEc:cwl:cwldpp:990
Note: CFP 906.
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Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. László Lovász & Herbert E. Scarf, 1992. "The Generalized Basis Reduction Algorithm," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 751-764, August.
  2. 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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