Abstract.
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 pre- and 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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Mathematics Subject Classification (2000): primary 90C11, secondary 65G20
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Neumaier, A., Shcherbina, O. Safe bounds in linear and mixed-integer linear programming. Math. Program., Ser. A 99, 283–296 (2004). https://doi.org/10.1007/s10107-003-0433-3
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DOI: https://doi.org/10.1007/s10107-003-0433-3