Polyhedral investigations on stable multi-sets

Stable multi-sets are an evident generalization of the well-known stable sets. As integer programs, they constitute a general structure which allows for a wide applicability of the results. Moreover, the study of stable multi-sets provides new insights to well-known properties of stable sets. In this paper, we continue our investigations started in Koster and Zymolka … Read more

Polyhedral Analysis for Concentrator Location Problems

The concentrator location problem is to choose a subset of a given terminal set to install concentrators and to assign each remaining terminal node to a concentrator to minimize the cost of installation and assignment. The concentrators may have capacity constraints. We study the polyhedral properties of concentrator location problems with different capacity structures. We … Read more

Computational study of a cutting plane algorithm for University Course Timetabling

In this paper we describe a successful case-study where a Branch-and-Cut algorithm yields the \lq\lq optimal” solution of a real-world timetabling problem of University courses \emph{(University Course Timetabling problem)}. The problem is formulated as a \emph{Set Packing problem} with side constraints. To tighten the initial formulation, we utilize well-known valid inequalities of the Set Packing … Read more

A Branch and Cut Algorithm for Hub Location Problems with Single Assignment

The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. … Read more

Computational study of large-scale p-Median problems

Given a directed graph G(V,A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a Branch-and-Cut algorithm yielding provably good solutions for instances up to 3795 nodes (14,402,025 variables). Key ingredients of our approach are: lagrangian relaxation, a simple procedure … Read more

Parallel Interval Continuous Global Optimization Algorithms

We theorically study, on a distributed memory architecture, the parallelization of Hansen’s algorithm for the continuous global optimization with inequality constraints, using interval arithmetic. We propose a parallel algorithm based on a dynamic redistribution of the working list among the processors. On the other hand, we exploit the reduction technique, developped by Hansen, for computing … Read more

Two-connected networks with rings of bounded cardinality

We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli. In this paper, we compute a lower bound on the … Read more

Branch and cut based on the volume algorithm: Steiner trees in graphs and max-cut

We present a Branch-and-Cut algorithm where the Volume Algorithm is applied to the linear programming relaxations arising at each node of the search tree. This means we use fast approximate solutions to these linear programs instead of exact but slower solutions given by the traditionally used dual simplex method. Our claim is that such a … Read more

A Polyhedral Study of the Cardinality Cosntrained Knapsack Problem

A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. This structure occurs, for example, in areas as finance, location, and scheduling. Traditionally, cardinality constraints are modeled by introducing auxiliary 0-1 variables and additional constraints that relate the continuous … Read more

Polyhedral results for two-connected networks with bounded rings

We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a “ring”) does not exceed a given length K. We present here a new formulation of the problem and derive facet results for different classes … Read more