Abstract. In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm which constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard notion of sequential cutting planes with ideas underlying the convex hull tree algorithm to help guide the choice of disjunctions to use within a cutting plane method. This algorithm, which we refer to as the cutting plane tree algorithm, is shown to converge to an integral optimal solution in finitely many iterations. Finally, we illustrate the proposed algorithm on three well-known examples in the literature that require an infinite number of elementary or split disjunctions in a rudimentary cutting plane algorithm.
Abstract. The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obtain the solution of general mixed-integer linear programs (MILP) with bounded integer variables. In this paper, we present our computational experience with variants of the CPT algorithm. Because the CPT algorithm is based on discovering multi-term disjunctions, this paper is the first to present computational results with multi-term disjunctions. We implement two variants for cut generation using alternative normalization schemes. Our results demonstrate that even a preliminary implementation of the CPT algorithm (with either normalization) is able to close a significant portion of the integrality gap without resorting to branch-and-cut. As a by-product of our experiments, we also conclude that one of the cut generation schemes (namely minimizing the 1 norm of cut coefficients) appears to have an edge over the other.
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