We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of valid inequalities, called cycle inequalities, valid for the problem and show that this inequalities together with the so-called cut inequalities yield an integ...

The Manickam-Miklós-Singhi Conjecture states that when n ≥ 4k, every multiset of n real numbers with nonnegative total sum has at least ( n−1 k−1 ) k-subsets with nonnegative sum. We develop a branch-and-cut strategy using a linear programming formulation to show that verifying the conjecture for fixed values of k is a finite problem. To improve our search, we develop a zero-error randomized pr...

This paper presents a branch-and-cut algorithm for the Time Window Assignment Vehicle Routing Problem (TWAVRP), the problem of assigning time windows for delivery before demand volume becomes known. A novel set of valid inequalities, the precedence inequalities, is introduced and multiple separation heuristics are presented. In our numerical experiments the branch-and-cut algorithm is 3.8 times...

Prior work on training the IBM-3 translation model is based on suboptimal methods for computing Viterbi alignments. In this paper, we present the first method guaranteed to produce globally optimal alignments. This not only results in improved alignments, it also gives us the opportunity to evaluate the quality of standard hillclimbing methods. Indeed, hillclimbing works reasonably well in prac...

Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bi-layer networks, comparing with Knippel’s previous results.

The Robust Network Loading Problem (RNL) can be stated as follows. Given a graph and a set of traffic matrices, install minimum cost integer capacities on the edges such that all the matrices can be routed non simultaneously on the network. The routing scheme is said to be dynamic if we can choose a (possibly) different routing for every matrix, it is called static if the routing must be the sa...

We present a branch-and-cut algorithm to solve capacitated network design problems. Given a capacitated network and point-to-point traac demands, the objective is to install more capacity on the edges of the network and route traac simultaneously, so that the overall cost is minimized. We study a mixed-integer programming formulation of the problem and identify some new facet deening inequaliti...

The Capacitated m-ring-star Problem is a variant of the classical one-depot capacitated vehicle routing problem in which a customer is either on a route or is connected to another customer or to some Steiner point present in a route. We develop a new exact algorithm for this problem using a branch-and-cut-and-price approach and compare its performance with that of a branch-and-cut algorithm pro...

We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose two scenario-based Steiner cut formulations, study the strength of the proposed valid inequalities, a...

Branch-and-cut methods are very successful techniques for solving a wide variety of integer programming problems, and they can provide a guarantee of optimality. We describe how a branch-and-cut method can be tailored to a specific integer programming problem, and how families of general cutting planes can be used to solve a wide variety of problems. Other important aspects of successful implem...