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High Performance Optimization pp 349–366Cite as

Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm

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Part of the book series: Applied Optimization ((APOP,volume 33))

Abstract

We describe a cutting plane algorithm for solving linear ordering problems. The algorithm uses a primal-dual interior point method to solve the first few relaxations and then switches to a simplex method to solve the last few relaxations. The simplex method uses CPLEX 4.0. We compare the algorithm with one that uses only an interior point method and with one that uses only a simplex method. We solve integer programming problems with as many as 31125 binary variables. Computational results show that the combined approach can dramatically outperform the other two methods.

Supported in part by ONR grant N00014-94-1-0391.

Supported in part by a grant from the Dutch N WO and Delft University of Technology for the 1997-98 academic year, while visiting TW1/SSOR at Delft University of Technology.

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Authors
  1. John E. Mitchell
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  2. Brian Borchers
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Editor information

Editors and Affiliations

  1. Erasmus University, Rotterdam, The Netherlands

    Hans Frenk  & Shuzhong Zhang  & 

  2. Delft University of Technology, The Netherlands

    Kees Roos  & Tamás Terlaky  & 

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© 2000 Springer Science+Business Media Dordrecht

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Mitchell, J.E., Borchers, B. (2000). Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds) High Performance Optimization. Applied Optimization, vol 33. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3216-0_14

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  • DOI: https://doi.org/10.1007/978-1-4757-3216-0_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4819-9

  • Online ISBN: 978-1-4757-3216-0

  • eBook Packages: Springer Book Archive

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