A COMPUTATIONAL STUDY OF THE CUTTING PLANE TREE ALGORITHM FOR GENERAL MIXED-INTEGER LINEAR PROGRAMS BINYUAN CHEN, S ˙ IMGE K ¨ UC ¸ ¨ UKYAVUZ, AND SUVRAJEET SEN 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 im- plement two variants for cut generation using alternative normalization schemes. Our results demonstrate that even a preliminary implementation of the CPT algorithm (with either nor- malization) 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 gen- eration schemes (namely minimizing the ℓ1 norm of cut coefficients) appears to have an edge over the other. Key words: Mixed-integer programming, disjunctive programming, cutting planes. 1. Introduction This work constitutes a follow-on to a recent paper (Chen et al., 2009) in which the authors settled several questions related to finite convergence of cutting plane algorithms that use dis- junctive cuts for mixed-integer linear programs with general integer variables (MILP-G). The main algorithmic issue that was settled was an answer to the following question: If we are re- stricted to introducing only one (disjunctive) valid inequality in any iteration, is there a finitely convergent pure cutting plane algorithm that solves MILP-G? The main construct developed to answer this question affirmatively is the notion of a cutting plane tree (CPT). The CPT repre- sents an adaptive sequence of disjunctions involving multiple variables, and is able to discover the convex hull (closure) of any instance of a bounded MILP-G, without having to specify an a priori hierarchy. This characterization is a generalization of the sequential convexification process of Balas (1979) for MILP with binary variables (MILP-B). However, it is important to note that the same sequential process of convexification (one variable at a time) does not yield the convex hull of MILP-G in finitely many steps (Owen and Mehrotra, 2001). Prior to this, Date : September 14, 2010. Binyuan Chen: Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA. bychen@email.arizona.edu. Simge K¨ u¸c¨ ukyavuz: Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH 43210, USA. kucukyavuz.2@osu.edu. Supported, in part, by NSF-CMMI Grant 0917952. Suvrajeet Sen: (corresponding author) Department of Integrated Systems Engineering, The Ohio State Uni- versity, Columbus, OH 43210, USA. sen.22@osu.edu. Supported, in part, AFOSR grant FA9550-08-1-0117. 1