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Separation of Mixing Inequalities in a Mixed Integer Programming Solver

Philipp Christophel(christophel***at***dsor.de)

Abstract: 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 in- equalities 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 in- teger 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.

Keywords: mixing set, mixed integer round, separation algorithms

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation: DS&OR Lab Workingpaper 0704, DS&OR Lab, University of Paderborn, Warburgerstr. 100, 33098 Paderborn, Germany

Download: [PDF]

Entry Submitted: 06/10/2008
Entry Accepted: 06/10/2008
Entry Last Modified: 06/10/2008

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