Over the past decade, Decision Diagrams (DDs) have risen as a powerful modeling tool to solve discrete optimization problems. The extension of this emerging concept to continuous problems, however, has remained a challenge, posing a limitation on its applicability scope. In this paper, we introduce a novel framework that utilizes DDs to model continuous programs. … Read more
Cutting planes have been an important factor in the impressive progress made by integer programming (IP) solvers in the past two decades. However, cutting planes have had little impact on improving performance for symmetric IPs. Rather, the main breakthroughs for solving symmetric IPs have been achieved by cleverly exploiting symmetry in the enumeration phase of … Read more
We present new theory, heuristics and algorithms for preprocessing instances of the Stable Marriage with Ties and Incomplete lists (SMTI), the Hospitals/Residents with Ties (HRT), and the Worker-Firms with Ties (WFT) problems. We show that instances of these problems can be preprocessed by removing from the preference lists of some agents entries that correspond to … Read more
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a binary decision diagram (BDD) encoding of their constraints. We present a general framework that can be applied to a large range of … Read more
We consider minimization problems with bisubmodular objective functions. We propose a class of valid inequalities, which we call the poly-bimatroid inequalities and prove that these inequalities, along with trivial bound constraints, fully describe the convex hull of the epigraph of a bisubmodular function. We develop a cutting plane algorithm for general bisubmodular minimization problems using … Read more
We introduce a new facility layout problem, the so-called T-Row Facility Layout Problem (TRFLP). The TRFLP consists of a set of one-dimensional departments with pairwise transport weights between them and two orthogonal rows which form a T such that departments in different rows cannot overlap. The aim is to find a non-overlapping assignment of the … Read more
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash to the nonlinear setting which shows that for convex 0/1 problems, CP … Read more
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete, optimization problems arise in applications from biology and material science among others, and are known to be NP-Hard for … Read more
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size. Article Download View Split cuts in the plane
We translate the algorithmic question of whether to linearize convex Mixed-Integer Quadratic Programming problems (MIQPs) into a classification task, and use machine learning (ML) techniques to tackle it. We represent MIQPs and the linearization decision by careful target and feature engineering. Computational experiments and evaluation metrics are designed to further incorporate the optimization knowledge in … Read more