In this paper we describe a novel way of generating an optimal clustering for coreference resolution. Where usually heuristics are used to generate a document-level clustering, based on the output of local pairwise classifiers, we propose a method that calculates an exact solution. We cast the clustering problem as an Integer Linear Programming (ILP) problem, and solve this by using a column ge...

Working in an extended variable space allows one to develop tight reformulations for mixed integer programs. However, the size of the extended formulation grows rapidly too large for a direct treatment by a MIP-solver. Then, one can use projection tools and derive valid inequalities for the original formulation, or consider an approximate extended formulation (f.i., by aggregating variables). B...

A slot allocation policy assigns a time slot for departure to each of a number of flights in order to avoid overload in control sectors and on runways. We present a new solution method for a basic version of the European slot allocation problem. The approach is based on an integer linear programming model, where for each flight there is a set of 0-1 variables each associated with one of its pos...

Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large scale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not yet found in textbooks. We emphasize the growing understanding of the dual point of view, which has brought considerable progress to the column generation theory and practice. It s...

In the past decade, significant progress has been achieved in developing generic primal heuristics that made their way into commercial mixed integer programming (MIP) solver. Extensions to the context of a column generation solution approach are not straightforward. The Dantzig-Wolfe decomposition principle can indeed be exploited in greedy, local search, rounding or truncated exact methods. Th...

Real-life planning problems are often complicated by the occurrence of disturbances, which imply that the original plan cannot be followed anymore and some recovery action must be taken to cope with the disturbance. In such a situation it is worthwhile to arm yourself against common disturbances. Well-known approaches to create plans that take possible, common disturbances into account are robu...

The classical column generation approach often shows a very slow convergence. Many different acceleration techniques have beenproposed recently to improve the convergence. Here, we briefly survey these methods and propose a novel algorithm based on the Chebyshev center of the dual polyhedron. The Chebyshev center can be obtained by solving a linear program; consequently, the proposed method can...

Identifying discrete patterns in binary data is an important dimensionality reduction tool machine learning and mining. In this paper, we consider the problem of low-rank matrix factorisation (BMF) under Boolean arithmetic. Due to hardness problem, most previous attempts rely on heuristic techniques. We formulate as a mixed integer linear program use large scale optimisation technique column ge...