TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Branching on History Information N2 - 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. T3 - ZIB-Report - 02-32 KW - Mixed Integer Programming KW - Branch-and-Bound KW - Branching Rules KW - Pseudocost Branching Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6990 ER - TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Branching rules revisited N2 - 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. T3 - ZIB-Report - 04-13 KW - Mixed-integer-programming KW - Branch-and-Bound KW - Variable selection KW - Pseudocost-Branching KW - Strong-Branching KW - Reliability-Branching Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7886 ER - TY - GEN A1 - Achterberg, Tobias A1 - Koch, Thorsten A1 - Martin, Alexander T1 - MIPLIB 2003 N2 - 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. T3 - ZIB-Report - 05-28 KW - Mathematical Programming KW - Mixed Integer Programming KW - IP KW - MIP KW - Optimization KW - Instances Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8625 ER - TY - GEN A1 - Bixby, Robert E. A1 - Martin, Alexander T1 - Parallelizing the Dual Simplex Method N2 - 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. T3 - ZIB-Report - SC-95-45 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2112 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Eisenblätter, Andreas A1 - Grötschel, Martin A1 - Martin, Alexander T1 - The Orientation Model for Frequency Assignment Problems N2 - 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. T3 - ZIB-Report - TR-98-01 KW - Minimum-Cost Flow Problems KW - Cellular Radio Telephone Systems KW - Frequency Assignment Problem KW - Integer Programming Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5627 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Eisenblätter, Andreas A1 - Grötschel, Martin A1 - Martin, Alexander T1 - Frequency Assignment in Cellular Phone Networks N2 - 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. T3 - ZIB-Report - SC-97-35 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3044 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Ferreira, Carlos E. A1 - Martin, Alexander T1 - Matrix Decomposition by Branch-and-Cut N2 - 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. T3 - ZIB-Report - SC-97-14 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2839 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Ferreira, Carlos E. A1 - Martin, Alexander T1 - Decomposing Matrices into Blocks N2 - 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. T3 - ZIB-Report - SC-97-15 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2849 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung A1 - Karbstein, Marika A1 - Koch, Thorsten A1 - Martin, Alexander T1 - How Many Steiner Terminals Can You Connect in 20 Years? N2 - 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. T3 - ZIB-Report - 13-57 KW - Steiner tree KW - Steiner connectivity KW - Steiner tree packing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42524 SN - 1438-0064 ER - TY - GEN A1 - Bruns, Winfried A1 - Gubeladze, Joseph A1 - Henk, Martin A1 - Martin, Alexander A1 - Weismantel, Robert T1 - A counterexample to an integer analogue of Caratheodorys theorem N2 - 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. T3 - ZIB-Report - SC-98-28 KW - Integral pointed cones KW - Hilbert basis KW - integral Carathéodory property Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3718 ER -