Separation of Mixing Inequalities in a Mixed Integer Programming Solver

This paper shows how valid inequalities based on the mixing set can be used in a mixed integer programming (MIP) solver. It discusses the relation of mixing inequalities to flow path and mixed integer rounding inequalities and how currently used separation algorithms already generate cuts implicitly that can be seen as mixing cuts. Further on, it describes two new separation algorithms that generate mixing cuts from mixed integer paths explicitly. A section with computational results discusses the importance of mixing cuts based on paths for solving MIP problems and reports results for the described separation algorithms.