We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a novel formulation that introduces a modest number of additional variables and a class of inequalities that can be efficiently … Read more
We propose a dynamic version of the classical node packing problem, also called the stable set or independent set problem. The problem is defined by a node set, a node weight vector, and an edge probability vector. For every pair of nodes, an edge is present or not according to an independent Bernoulli random variable … Read more
In the well-known Hospitals/Residents problem (HR), the objective is to find a stable matching of doctors (or residents) to hospitals based on their preference lists. In this paper, we study HRCT, the extension of HR in which doctors are allowed to apply in couples, and in which doctors and hospitals can include ties in their … Read more
The celebrated Motzkin-Straus formulation for the maximum clique problem provides a nontrivial characterization of the clique number of a graph in terms of the maximum value of a nonconvex quadratic function over a standard simplex. It was originally developed as a way of proving Tur\'{a}n’s theorem in graph theory, but was later used to develop … 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
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 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 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
In this work we study the p-median problem with maximum distance constraints (PMPDC) which is a variant of the classical p-median problem (PMP). First of all, we provide some different formulations for (PMPDC) because the heuristics procedures for the (PMPDC) with a formulation based on the approach that modifies the distance matrix that leads to … Read more