@misc{KosterZymolkaKutschka, author = {Koster, Arie M.C.A. and Zymolka, Adrian and Kutschka, Manuel}, title = {Algorithms to Separate {0,1/2}-Chvatal-Gomory Cuts}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9531}, number = {07-10}, abstract = {Chvatal-Gomory cuts are among the most well-known classes of cutting planes for general integer linear programs (ILPs). In case the constraint multipliers are either 0 or \$\frac{1}{2}\$, such cuts are known as \$\{0,\frac{1}{2}\}\$-cuts. It has been proven by Caprara and Fischetti (1996) that separation of \$\{0,\frac{1}{2}\}\$-cuts is NP-hard. In this paper, we study ways to separate \$\{0,\frac{1}{2}\}\$-cuts effectively in practice. We propose a range of preprocessing rules to reduce the size of the separation problem. The core of the preprocessing builds a Gaussian elimination-like procedure. To separate the most violated \$\{0,\frac{1}{2}\}\$-cut, we formulate the (reduced) problem as integer linear program. Some simple heuristic separation routines complete the algorithmic framework. Computational experiments on benchmark instances show that the combination of preprocessing with exact and/or heuristic separation is a very vital idea to generate strong generic cutting planes for integer linear programs and to reduce the overall computation times of state-of-the-art ILP-solvers.}, language = {en} } @misc{KosterZymolka, author = {Koster, Arie M.C.A. and Zymolka, Adrian}, title = {Provably Good Solutions for Wavelength Assignment in Optical Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8155}, number = {04-40}, abstract = {In this paper, we study the minimum converter wavelength assignment problem in optical networks. To benchmark the quality of solutions obtained by heuristics, we derive an integer programming formula tion by generalizing the formulation of Mehrotra and Trick (1996) for the vertex coloring problem. To handle the exponential number of variables, we propose a column generation approach. Computational experiments show that the value of the linear relaxation states a good lower bound and can often prove optimality of the best solution generated heuristically.}, language = {en} } @misc{KosterZymolka, author = {Koster, Arie M.C.A. and Zymolka, Adrian}, title = {Linear Programming Lower Bounds for Minimum Converter Wavelength Assignment in Optical Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8160}, number = {04-41}, abstract = {In this paper, we study the conflict-free assignment of wavelengths to lightpaths in an optical network with the opportunity to place wavelength converters. To benchmark heuristics for the problem, we develop integer programming formulations and study their properties. Moreover, we study the computational performance of the column generation algorithm for solving the linear relaxation of the most promising formulation. In many cases, a non-zero lower bound on the number of required converters is generated this way. For several instances, we in fact prove optimality since the lower bound equals the best known solution value.}, language = {en} } @misc{ZymolkaKosterWessaely, author = {Zymolka, Adrian and Koster, Arie M.C.A. and Wess{\"a}ly, Roland}, title = {Transparent optical network design with sparse wavelength conversion}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7017}, number = {02-34}, abstract = {We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse wavelength conversion for efficient use of the capacities. In this paper, we investigate this extensive optical network design task. Using a flexible device-based model, we present an integer programming formulation that supports greenfield planning as well as expansion planning on top of an existing network. As solution method, we propose a suitable decomposition approach that separates the wavelength assignment from the dimensioning and routing. Our method in particular provides a lower bound on the total cost which allows to rate the solution quality. Computational experiments on realistic networks approve the solution approach to be appropriate.}, language = {en} }