Can cut generating functions be good and efficient?
Abstract: Making cut generating functions (CGFs) computationally viable is a central question in modern integer programming research. One would like to nd CGFs that are simultaneously good, i.e., there are good guarantees for the cutting planes they generate, and ecient, meaning that the values of the CGFs can be computed cheaply (with procedures that have some hope of being implemented in current solvers). We investigate in this paper to what extent this balance can be struck. We propose a family of CGFs which, in a sense, achieves this harmony between good and ecient. In particular, we show that our proposed CGFs give a good approximation of the closure given by CGFs obtained from maximal lattice-free sets and their so-called trivial liftings, and simultaneously, show that these CGFs can be computed with explicit, ecient procedures. We close the paper with some computational experiments with this family of cuts. Our proposed family of cuts seem to give some concrete advantage on randomly generated instances; however, their performance on MIPLIB 3.0 problems is not comparable to CPLEX or a simple GMI cut generator, except for a specic family of problems.
Keywords: Integer programming, lattice-free convex sets, multi-row cuts
Category 1: Integer Programming (Cutting Plane Approaches )
Category 2: Integer Programming
Category 3: Combinatorial Optimization (Polyhedra )
Citation: Johns Hopkins University March 2018
Entry Submitted: 03/01/2018
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