New computer-based search strategies for extreme functions of the Gomory--Johnson infinite group problem

We describe new computer-based search strategies for extreme functions for the Gomory--Johnson infinite group problem. They lead to the discovery of new extreme functions, whose existence settles several open questions.Comment: 54 pages, many figure

Bayesian network learning with cutting planes

The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach -the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning

When Lift-and-Project Cuts are Different

In this paper, we present a method to determine if a lift-and-project cut for a mixed-integer linear program is irregular, in which case the cut is not equivalent to any intersection cut from the bases of the linear relaxation. This is an important question due to the intense research activity for the past decade on cuts from multiple rows of simplex tableau as well as on lift-and-project cuts from non-split disjunctions. While it is known since Balas and Perregaard (2003) that lift-and-project cuts from split disjunctions are always equivalent to intersection cuts and consequently to such multi-row cuts, Balas and Kis (2016) have recently shown that there is a necessary and sufficient condition in the case of arbitrary disjunctions: a lift-and-project cut is regular if, and only if, it corresponds to a regular basic solution of the Cut Generating Linear Program (CGLP). This paper has four contributions. First, we state a result that simplifies the verification of regularity for basic CGLP solutions from Balas and Kis (2016). Second, we provide a mixed-integer formulation that checks whether there is a regular CGLP solution for a given cut that is regular in a broader sense, which also encompasses irregular cuts that are implied by the regular cut closure. Third, we describe a numerical procedure based on such formulation that identifies irregular lift-and-project cuts. Finally, we use this method to evaluate how often lift-and-project cuts from simple $t$-branch split disjunctions are irregular, and thus not equivalent to multi-row cuts, on 74 instances of the MIPLIB benchmarks.Comment: INFORMS Journal on Computing (to appear

Optimization in Telecommunication Networks

Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Menger’s disjoint paths theorem, and Ford-Fulkerson’s max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;

A New Framework for Network Disruption

Traditional network disruption approaches focus on disconnecting or lengthening paths in the network. We present a new framework for network disruption that attempts to reroute flow through critical vertices via vertex deletion, under the assumption that this will render those vertices vulnerable to future attacks. We define the load on a critical vertex to be the number of paths in the network that must flow through the vertex. We present graph-theoretic and computational techniques to maximize this load, firstly by removing either a single vertex from the network, secondly by removing a subset of vertices.Comment: Submitted for peer review on September 13, 201

Algorithms for Highly Symmetric Linear and Integer Programs

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension. Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension.Comment: 21 pages, 1 figure; some references and further comments added, title slightly change