We consider semi-continuous network flow problems, that is, a class of network flow problems where some of the variables are restricted to be semi-continuous. We introduce the semi-continuous inflow set with variable upper bounds as a relaxation of general semi-continuous network flow problems. Two particular cases of this set are considered, for which we present … Read more
We present a new method for solving bin packing problems, including two-constraint variants, based on an arc flow formulation with side constraints. Conventional formulations for bin packing problems are usually highly symmetric and provide very weak lower bounds. The arc flow formulation proposed provides a very strong lower bound, and is able to break symmetry … Read more
In this paper, we study the hop-constrained survivable network design problem with reliable edges. Given a graph with non-negative edge weights and node pairs Q, the hop-constrained survivable network design problem consists of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L … Read more
In this paper we consider a cardinality-constrained quadratic program that minimizes a convex quadratic function subject to a cardinality constraint and linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality … Read more
Many combinatorial optimization problems have natural formulations as submodular minimization problems over well-studied combinatorial structures. A standard approach to these problems is to linearize the objective function by introducing new variables and constraints, yielding an extended formulation. We propose two new approaches for constrained submodular minimization problems. The first is a linearization approach that requires … Read more
We study scheduling as a means to address the increasing energy concerns in manufacturing enterprises. In particular, we consider a flow shop scheduling problem with a restriction on peak power consumption, in addition to the traditional time-based objectives. We investigate both mathematical programming and combinatorial approaches to this scheduling problem, and test our approaches with … Read more
We present a new tree-search algorithm for solving mixed-integer nonlinear programs (MINLPs). Rather than relying on computationally expensive nonlinear solves at every node of the branch-and-bound tree, our algorithm solves a quadratic approximation at every node. We show that the resulting algorithm retains global convergence properties for convex MINLPs, and we present numerical results on … Read more
In recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MILPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MILPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is … Read more
Given the steady increase in cores per CPU, it is only a matter of time until supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise … Read more
We introduce a natural strengthening of Gomory-Chvátal cutting planes for the important class of 0/1-integer programming problems and study the properties of the elementary closure that arises from the new class of cuts. Most notably, we prove that the new closure is polyhedral, we characterize the family of all facet-defining inequalities, and we compare it … Read more