An exact rational mixed-integer programming solver

Authors:
William Cook;Thorsten Koch;Daniel E.;Kati Wolter
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA;Zuse Institute Berlin, Germany;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA;Zuse Institute Berlin, Germany
Venue:
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Year:
2011

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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.