An Exact Rational Mixed-Integer Programming Solver

  • William Cook
  • Thorsten Koch
  • Daniel E. Steffy
  • Kati Wolter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6655)

Abstract

We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the Miplib and Mittelmann collections.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • William Cook
    • 1
  • Thorsten Koch
    • 2
  • Daniel E. Steffy
    • 1
  • Kati Wolter
    • 2
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Zuse Institute BerlinGermany

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