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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- Herbert E. Scarf & Laszlo Lovasz, 1990. "The Generalized Basis Reduction Algorithm," Cowles Foundation Discussion Papers 946, Cowles Foundation for Research in Economics, Yale University.
- Herbert E. Scarf & R. Kannan & Laszlo Lovasz, 1988. "The Shapes of Polyhedra," Cowles Foundation Discussion Papers 883, Cowles Foundation for Research in Economics, Yale University.
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