@misc{AchterbergKochMartin, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching on History Information}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6990}, number = {02-32}, abstract = {Mixed integer programs (\$MIPs\$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in \$SIP\$, a state-of-the-art \$MIP\$ solver. We give computational results that show the superiority of the new strategy.}, language = {en} } @misc{AchterbergKochMartin, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {Branching rules revisited}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7886}, number = {04-13}, abstract = {Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on. We present a new generalization called {\sl reliability branching} of today's state-of-the-art {\sl strong branching} and {\sl pseudocost branching} strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed newstrategy.}, language = {en} } @misc{AchterbergKochMartin, author = {Achterberg, Tobias and Koch, Thorsten and Martin, Alexander}, title = {MIPLIB 2003}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8625}, number = {05-28}, abstract = {This paper reports on the fourth version of the Mixed Integer Programming Library. Since ({\sc miplib}) is to provide a concise set of challenging problems, it became necessary to purge instances that became too easy. We present an overview of the 27 new problems and statistical data for all 60 instances.}, language = {en} } @misc{BixbyMartin, author = {Bixby, Robert E. and Martin, Alexander}, title = {Parallelizing the Dual Simplex Method}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2112}, number = {SC-95-45}, abstract = {We study the parallelization of the steepest-edge version of the dual simplex algorithm. Three different parallel implementations are examined, each of which is derived from the CPLEX dual simplex implementation. One alternative uses PVM, one general-purpose System V shared-memory constructs, and one the PowerC extension of C on a Silicon Graphics multi-processor. These versions were tested on different parallel platforms, including heterogeneous workstation clusters, Sun S20-502, Silicon Graphics multi-processors, and an IBM SP2. We report on our computational experience.}, language = {en} } @misc{BorndoerferEisenblaetterGroetscheletal., author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {The Orientation Model for Frequency Assignment Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5627}, number = {TR-98-01}, abstract = {Mobile telecommunication systems establish a large number of communication links with a limited number of available frequencies; reuse of the same or adjacent frequencies on neighboring links causes interference. The task to find an assignment of frequencies to channels with minimal interference is the frequency assignment problem. The frequency assignment problem is usually treated as a graph coloring problem where the number of colors is minimized, but this approach does not model interference minimization correctly. We give in this paper a new integer programming formulation of the frequency assignment problem, the orientation model, and develop a heuristic two-stage method to solve it. The algorithm iteratively solves an outer and an inner optimization problem. The outer problem decides for each pair of communication links which link gets the higher frequency and leads to an acyclic subdigraph problem with additional longest path restrictions. The inner problem to find an optimal assignment respecting an orientation leads to a min-cost flow problem.}, language = {en} } @misc{BorndoerferEisenblaetterGroetscheletal., author = {Bornd{\"o}rfer, Ralf and Eisenbl{\"a}tter, Andreas and Gr{\"o}tschel, Martin and Martin, Alexander}, title = {Frequency Assignment in Cellular Phone Networks}, doi = {10.1023/A:1018908907763}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3044}, number = {SC-97-35}, abstract = {We present a graph-theoretic model for the \emph{frequency assignment problem} in Cellular Phone Networks: Obeying several technical and legal restrictions, frequencies have to be assigned to transceivers so that interference is as small as possible. This optimization problem is NP-hard. Good approximation cannot be guaranteed, unless P = NP. We describe several assignment heuristics. These heuristics are simple and not too hard to implement. We give an assessment of the heuristics' efficiency and practical usefulness. For this purpose, typical instances of frequency assignment problems with up to 4240 transceivers and 75 frequencies of a German cellular phone network operator are used. The results are satisfying from a practitioner's point of view. The best performing heuristics were integrated into a network planning system used in practice.}, language = {en} } @misc{BorndoerferFerreiraMartin, author = {Bornd{\"o}rfer, Ralf and Ferreira, Carlos E. and Martin, Alexander}, title = {Matrix Decomposition by Branch-and-Cut}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2839}, number = {SC-97-14}, abstract = {In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix \$A\$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the \%LP- and MIP-libraries \Netlib{} and MIPLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem.}, language = {en} } @misc{BorndoerferFerreiraMartin, author = {Bornd{\"o}rfer, Ralf and Ferreira, Carlos E. and Martin, Alexander}, title = {Decomposing Matrices into Blocks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2849}, number = {SC-97-15}, abstract = {In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix \$A\$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the LP- and MIP-libraries NETLIB and MITLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem. In practice, however, one would use heuristics to find a good decomposition. We present several heuristic ideas and test their performance. Finally, we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch-and-cut code for general mixed integer programs.}, language = {en} } @misc{BorndoerferHoangKarbsteinetal., author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Karbstein, Marika and Koch, Thorsten and Martin, Alexander}, title = {How Many Steiner Terminals Can You Connect in 20 Years?}, issn = {1438-0064}, doi = {10.1007/978-3-642-38189-8_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42524}, abstract = {Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful approaches to many relevant variants, from both a theoretical and a computational point of view. This article illustrates the theoretical and algorithmic progress on Steiner tree type problems on two examples, the Steiner connectivity and the Steiner tree packing problem.}, language = {en} } @misc{BrunsGubeladzeHenketal., author = {Bruns, Winfried and Gubeladze, Joseph and Henk, Martin and Martin, Alexander and Weismantel, Robert}, title = {A counterexample to an integer analogue of Caratheodorys theorem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3718}, number = {SC-98-28}, abstract = {For \$n\geq 6\$ we provide a counterexample to the conjecture that every integral vector of a \$n\$-dimensional integral polyhedral pointed cone \$C\$ can be written as a nonnegative integral combination of at most \$n\$ elements of the Hilbert basis of \$C\$. In fact, we show that in general at least \$\lfloor 7/6 \cdot n \rfloor\$ elements of the Hilbert basis are needed.}, language = {en} } @misc{DahlMartinStoer, author = {Dahl, Geir and Martin, Alexander and Stoer, Mechthild}, title = {Routing through virtual paths in layered telecommunication networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2070}, number = {SC-95-41}, abstract = {We study a network configuration problem in telecommunications where one wants to set up paths in a capacitated network to accommodate given point-to-point traffic demand. The problem is formulated as an integer linear programming model where 0-1 variables represent different paths. An associated integral polytope is studied and different classes of facets are described. These results are used in a cutting plane algorithm. Computational results for some realistic problems are reported.}, language = {en} } @misc{DittelFuegenschuhMartin, author = {Dittel, Agnes and F{\"u}genschuh, Armin and Martin, Alexander}, title = {Polyhedral Aspects of Self-Avoiding Walks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12576}, number = {11-11}, abstract = {In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this problem one is interested in optimal configurations, where an energy function measures the benefit if certain path elements are placed on adjacent vertices of the graph. The most prominent application of this problem is the protein folding problem in biochemistry. On a set of selected instances, we demonstrate the computational merits of our approach.}, language = {en} } @misc{EisenblaetterFuegenschuhGeerdesetal., author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Geerdes, Hans-Florian and Junglas, Daniel and Koch, Thorsten and Martin, Alexander}, title = {Optimization Methods for UMTS Radio Network Planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7637}, number = {03-41}, abstract = {The UMTS radio network planning problem poses the challenge of designing a cost-effective network that provides users with sufficient coverage and capacity. We describe an optimization model for this problem that is based on comprehensive planning data of the EU project MOMENTUM. We present heuristic mathematical methods for this realistic model, including computational results.}, language = {en} } @misc{EisenblaetterFuegenschuhKochetal., author = {Eisenbl{\"a}tter, Andreas and F{\"u}genschuh, Armin and Koch, Thorsten and Koster, Arie M.C.A. and Martin, Alexander and Pfender, Tobias and Wegel, Oliver and Wess{\"a}ly, Roland}, title = {Modelling Feasible Network Configurations for UMTS}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6837}, number = {02-16}, abstract = {A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations.}, language = {en} } @misc{EisenblaetterGeerdesKochetal., author = {Eisenbl{\"a}tter, Andreas and Geerdes, Hans-Florian and Koch, Thorsten and Martin, Alexander and Wess{\"a}ly, Roland}, title = {UMTS Radio Network Evaluation and Optimization beyond Snapshots}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7903}, number = {04-15}, abstract = {This paper is concerned with UMTS radio network design. Our task is to reconfigure antennas and the related cells as to improve network quality. In contrast to second generation GSM networks, \emph{interference} plays a paramount role when designing third generation radio networks. A known compact formulation for assessing the interference characteristics of a radio network as coupling relations between cells based on user snapshots is generalized to statistical average load. This enables us to overcome the notorious difficulties of snapshot-based network optimization approaches. We recall a mixed-integer programming model for the network design problem that is based on user snapshots and contrast it with a new network design model based on the average coupling formulation. Exemplarily focusing on the important problem of optimizing antenna tilts, we give computational results for a fast local search algorithm and the application of a MIP solver to both models. These results demonstrate that our new average-based approaches outperform state-of-the-art snapshot models for UMTS radio network optimization.}, language = {en} } @misc{FerreiraGroetschelKiefletal., author = {Ferreira, Carlos E. and Gr{\"o}tschel, Martin and Kiefl, Stefan and Krispenz, Ludwig and Martin, Alexander and Weismantel, Robert}, title = {Some Integer Programs Arising in the Design of Main Frame Computers.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-957}, number = {SC-92-25}, abstract = {In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult -- at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are also \$NP\$-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.}, language = {en} } @misc{FerreiraMartinSouzaetal., author = {Ferreira, Carlos E. and Martin, Alexander and Souza, Cid C. de and Weismantel, Robert and Wolsey, Laurence}, title = {Formulations and Valid Inequalities for the Node Capacitated Graph Partitioning Problem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1450}, number = {SC-94-16}, abstract = {We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts. In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem parameters change.}, language = {en} } @misc{FerreiraMartinSouzaetal., author = {Ferreira, Carlos E. and Martin, Alexander and Souza, Cid C. de and Weismantel, Robert and Wolsey, Laurence}, title = {The Node Capacitated Graph Partitioning Problem: A Computational Study.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1469}, number = {SC-94-17}, abstract = {In this paper we consider the problem of \$k\$-partitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition, and the objective of minimizing the sum of the costs of the edges between the subsets of the partition. Based on a study of valid inequalities, we present a variety of separation heuristics for so-called cycle, cycle with ears, knapsack tree and path-block-cycle inequalities. The separation heuristics, plus primal heuristics, have been implemented in a branch-and-cut routine using a formulation including the edges with nonzero costs and node variables. Results are presented for three classes of problems: equipartitioning problems arising in finite element methods and partitioning problems associated with electronic circuit layout and compiler design.}, language = {en} } @misc{FerreiraMartinWeismantel, author = {Ferreira, Carlos E. and Martin, Alexander and Weismantel, Robert}, title = {Facets for the Multiple Knapsack Problem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1007}, number = {SC-93-04}, abstract = {In this paper we consider the multiple knapsack problem which is defined as follows: given a set \$N\$ of items with weights \$f_i\$, \$i \in N\$, a set \$M\$ of knapsacks with capacities \$F_k\$, \$k \in M\$, and a profit function \$c_{ik}, i \in N, k \in M\$; find an assignment of a subset of the set of items to the set of knapsacks that yields maximum profit (or minimum cost). With every instance of this problem we associate a polyhedron whose vertices are in one to one correspondence to the feasible solutions of the instance. This polytope is the subject of our investigations. In particular, we present several new classes of inequalities and work out necessary and sufficient conditions under which the corresponding inequality defines a facet. Some of these conditions involve only properties of certain knapsack constraints, and hence, apply to the generalized assignment polytope as well. The results presented here serve as the theoretical basis for solving practical problems. The algorithmic side of our study, i.e., separation algorithms, implementation details and computational experience with a branch and cut algorithm are discussed in the companion paper SC 93-07.}, language = {en} } @misc{FuegenschuhGeisslerGollmeretal., author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Rene and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Willert, Bernhard}, title = {Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets}, issn = {1438-0064}, doi = {10.1007/s12667-013-0099-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17821}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.}, language = {en} }