Safe bounds in linear and mixed-integer linear programming

نویسندگان

  • Arnold Neumaier
  • Oleg Shcherbina
چکیده

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic, cheap preand postprocessing of the linear programs arising in a branch-and-cut framework can guarantee that no solution is lost, at least for mixed-integer programs in which all variables can be bounded rigorously by bounds of reasonable size.

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عنوان ژورنال:
  • Math. Program.

دوره 99  شماره 

صفحات  -

تاریخ انتشار 2004