In this paper we address the following probabilistic version (PSC) of the set covering problem: $min \{ cx \ |\ {\mathbb P} (Ax\ge \xi) \ge p,\ x_{j}\in \{0,1\}^N\}$ where $A$ is a 0-1 matrix, $\xi$ is a random 0-1 vector and $p\in (0,1]$ is the threshold probability level. We formulate (PSC) as a mixed integer … Read more
The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up … Read more
We introduce orbital branching, an effective branching method for integer programs containing a great deal of symmetry. The method is based on computing groups of variables that are equivalent with respect to the symmetry remaining in the problem after branching, including symmetry which is not present at the root node. These groups of equivalent variables, … Read more
We present new valid inequalities that work in similar ways to well known cover inequalities.The differences exist in three aspects. First difference is in the generation of the inequalities. The method used in generation of the new cuts is more practical in contrast to classical cover inequalities. Second difference is the more general applicability, i.e., … Read more
Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it … Read more
In this paper, we study the set of 0-1 integer solutions to a single knapsack constraint and a set of non-overlapping cardinality constraints (MCKP). This set is a generalization of the traditional 0-1 knapsack polytope and the 0-1 knapsack polytope with generalized upper bounds. We derive strong valid inequalities for the convex hull of its … Read more
Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs G where the stable set polytope STAB(G) coincides with the clique constraint stable set polytope QSTAB(G). For all imperfect graphs STAB(G) \subset QSTAB(G) holds and, therefore, it is … Read more
The task of scheduling communications between satellites and ground control stations is getting more and more critical since an increasing number of satellites must be controlled by a small set of stations. In such a congested scenario, the current practice, in which experts build hand-made schedules, often leaves a large number of communication requests unserved. … Read more
While dealing with uncertainty in linear programs, the robust optimization framework proposed by Bertsimas and Sim appears as relevant. In particular, it can readily be extended for integer linear programming. This paper outlines the polyhedral impacts of this robust model for the 0-1 knapsack problem. It shows especially how the classical cover cuts can be … Read more
We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal sub ject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain … Read more