A Computational Study of Finitely Convergent Polyhedral Methods for General Mixed-Integer Linear Programs

Recently, Chen et al. (2009) proposed a finite polyhedral characterization of the convex hull of solutions to general mixed integer linear programs with bounded integer variables and introduced finitely convergent algorithms to solve this class of problems. In this paper, we investigate whether these algorithms provide computational tools that go beyond the convergence results reported in the above paper. For one of the algorithms, namely the convex hull tree algorithm, we recast the method as a progressive reformulation-linearization technique, and sequentially construct higher dimensional convex hull approximations. The other finitely convergent procedure proposed in Chen et al. (2009) is the cutting plane tree algorithm, which provides an adaptive mechanism to discover multi-term disjunctive cuts. We present evidence that these schemes are, in their own right, powerful enough to close a significant fraction of the integrality gap associated with MIPLIB instances of moderate size, in addition to their desirable theoretical properties of guaranteed finite convergence.