A primal all-integer algorithm based on irreducible solutions |
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Authors: | Utz-Uwe Haus Matthias Köppe Robert Weismantel |
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Institution: | 1.Otto-von-Guericke-Universit?t Magdeburg, Department of Mathematics/IMO, Universit?tsplatz 2, 39106 Magdeburg, Germany. e-mail: {haus, mkoeppe, weismant}@imo.math.uni-magdeburg.de,DE |
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Abstract: | This paper introduces an exact primal augmentation algorithm for solving general linear integer programs. The algorithm iteratively
substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine
inequalities. We prove that various versions of our algorithm are finite. It is a major concern in this paper to show how
the subproblem of replacing a column can be accomplished effectively. An implementation of the presented algorithms is given.
Computational results for a number of hard 0/1 integer programs from the MIPLIB demonstrate the practical power of the method.
Received: April 23, 2001 / Accepted: May 2002
Published online: March 21, 2003
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ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
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ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
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ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
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ID="#"Supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET
program TMR ERB FMRX-CT98-0202.
Mathematics Subject Classification (1991): 90C10 |
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