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 - Dahl, Geir A1 - Martin, Alexander A1 - Stoer, Mechthild T1 - Routing through virtual paths in layered telecommunication networks N2 - 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. T3 - ZIB-Report - SC-95-41 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2070 ER - TY - GEN A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Solving Steiner Tree Problems in Graphs to Optimality N2 - In this paper we present the implementation of a branch-and-cut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms and primal heuristics. We are able to solve all problem instances discussed in literature to optimality, including one to our knowledge not yet solved problem. We also report on our computational experiences with some very large Steiner tree problems arising from the design of electronic circuits. All test problems are gathered in a newly introduced library called {\em SteinLib} that is accessible via World Wide Web. T3 - ZIB-Report - SC-96-42 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2526 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - Packing Paths and Steiner Trees: Routing of Electronic Circuits. N2 - One of the challenging problems in the design of electronic circuits is the so-called routing problem. Roughly speaking, the task is to connect so-called terminal sets via wires on a predefined area. In addition, certain design rules are to be taken into account and an objective function such as the wiring length must be minimized. The routing problem in general is too complex to be solved in one step. Depending on the user's choice of decomposing the chip design problem into a hierarchy of stages, on the underlying technology, and on the given design rules, various subproblems arise. We discuss several variants of practically relevant routing problems and give a short overview on the underlying technologies and design rules. Many of the routing problems that come up this way can be formulated as the problem of packing so-called Steiner trees in certain graphs. We consider the Steiner tree packing problem from a polyhedral point of view and present three possibilities to define an appropriate polyhedron. Weighing their pros and cons we decide for one of these polytopes and sketch some of our investigations. T3 - ZIB-Report - SC-93-15 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1113 ER - TY - GEN A1 - Ferreira, Carlos E. A1 - Martin, Alexander A1 - Souza, Cid C. de A1 - Weismantel, Robert A1 - Wolsey, Laurence T1 - Formulations and Valid Inequalities for the Node Capacitated Graph Partitioning Problem. N2 - 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. T3 - ZIB-Report - SC-94-16 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1450 ER - TY - GEN A1 - Ferreira, Carlos E. A1 - Martin, Alexander A1 - Souza, Cid C. de A1 - Weismantel, Robert A1 - Wolsey, Laurence T1 - The Node Capacitated Graph Partitioning Problem: A Computational Study. N2 - 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. T3 - ZIB-Report - SC-94-17 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1469 ER - TY - GEN A1 - Weismantel, Robert A1 - Ferreira, Carlos E. A1 - Martin, Alexander T1 - A Cutting Plane Based Algorithm for the Multiple Knapsack Problem. N2 - In this paper we describe a cutting plane based algorithm for the multiple knapsack problem. We use our algorithm to solve some practical problem instances arising in the layout of electronic circuits and in the design of main frame computers, and we report on our computational experience. This includes a discussion and evaluation of separation algorithms, an LP-based primal heuristic and some implementation details. The paper is based on the polyhedral theory for the multiple knapsack polytope developed in our companion paper SC 93-04 and meant to turn this theory into an algorithmic tool for the solution of practical problems. T3 - ZIB-Report - SC-93-07 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1031 ER - TY - GEN A1 - Jünger, Michael A1 - Martin, Alexander A1 - Reinelt, Gerhard A1 - Weismantel, Robert T1 - Quadratic 0/1 Optimization and a Decomposition Approach for the Placement of Electronic Circuits. N2 - The placement in the layout design of electronic circiuts consists of finding a non- overlapping assignment of rectangular cells to positions on the chip so what wireability is guaranteed and certain technical constraints are met.This problem can be modelled as a quadratic 0/1- program subject to linear constraints. We will present a decomposition approach to the placement problem and give results about $NP$-hardness and the existence of $\varepsilon$-approximative algorithms for the involved optimization problems. A graphtheoretic formulation of these problems will enable us to develop approximative algorithms. Finally we will present details of the implementation of our approach and compare it to industrial state of the art placement routines. {\bf Keywords:} Quadratic 0/1 optimization, Computational Complexity, VLSI-Design. T3 - ZIB-Report - SC-92-10 KW - quadratic 0/1 optimization KW - computational complexity KW - VLSI-Design Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-803 ER - TY - GEN A1 - Ferreira, Carlos E. A1 - Martin, Alexander A1 - Weismantel, Robert T1 - Facets for the Multiple Knapsack Problem. N2 - 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. T3 - ZIB-Report - SC-93-04 Y1 - 1993 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1007 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - Conjunctive Cuts for Integer Programs N2 - This paper deals with a family of conjunctive inequalities. Such inequalities are needed to describe the polyhedron associated with all the integer points that satisfy several knapsack constraints simultaneously. Here we demonstrate the strength and potential of conjunctive inequalities in connection with lifting from a computational point of view. T3 - ZIB-Report - SC-98-18 KW - Polyhedral Combinatorics KW - Integer Programming KW - Separation Algorithm Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3618 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - Contributions to General Mixed Integer Knapsack Problems N2 - This paper deals with a general mixed integer knapsack polyhedron for which we introduce and analyze a new family of inequalities. We discuss the value of this family both from a theoretic and a computational point of view. T3 - ZIB-Report - SC-97-38 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3075 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Kniasew, Dimitri A1 - Schlögel, Dominik A1 - Martin, Alexander A1 - Weninger, Dieter T1 - Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming JF - Journal of Computational Mathematics N2 - The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of robust and future-proof decision support systems. The complexity of industrial-scale supply chain optimization, however, often poses limits to the application of general mixed-integer programming solvers. In this paper we describe algorithmic innovations that help to ensure that MIP solver performance matches the complexity of the large supply chain problems and tight time limits encountered in practice. Our computational evaluation is based on a diverse set, modeling real-world scenarios supplied by our industry partner SAP. Y1 - 2019 U6 - https://doi.org/10.4208/jcm.1905-m2019-0055 VL - 37 SP - 866 EP - 888 ER - TY - GEN A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Miltenberger, Matthias A1 - Weninger, Dieter T1 - Progress in Presolving for Mixed Integer Programming N2 - Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice. T3 - ZIB-Report - 13-48 KW - mixed-integer programming KW - presolving KW - preprocessing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42530 SN - 1438-0064 ER - TY - GEN A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Voß, Stefan T1 - SteinLib: An Updated Library on Steiner Tree Problems in Graphs N2 - In this paper we present the {\em SteinLib}, a library of data sets for the Steiner tree problem in graphs. This library extends former libraries on Steiner tree problems by many new interesting and difficult instances, most of them arising from real-world applications. We give a survey on the difficulty of these problem instances by giving references to state-of-the-art software packages that were the first or are currently among the best to solve these instances. T3 - ZIB-Report - 00-37 KW - Steiner Trees KW - Mathematical Programming Testdata Library Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6056 ER - TY - GEN A1 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Koch, Thorsten A1 - Koster, Arie M.C.A. A1 - Martin, Alexander A1 - Pfender, Tobias A1 - Wegel, Oliver A1 - Wessäly, Roland T1 - Modelling Feasible Network Configurations for UMTS N2 - 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. T3 - ZIB-Report - 02-16 KW - UMTS KW - radio interface KW - network planning KW - configuration KW - perfect power control KW - mathematical model KW - mixed integer programming KW - MOMENTUM KW - IST-20 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6837 ER - 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 - Eisenblätter, Andreas A1 - Fügenschuh, Armin A1 - Geerdes, Hans-Florian A1 - Junglas, Daniel A1 - Koch, Thorsten A1 - Martin, Alexander T1 - Optimization Methods for UMTS Radio Network Planning N2 - 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. T3 - ZIB-Report - 03-41 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7637 ER - TY - THES A1 - Martin, Alexander T1 - Packen von Steinerbäumen: Polyedrische Studien und Anwendung. N2 - Gegeben sei ein Graph $G=(V,E)$ mit positiven Kantenkapazitäten $c_e$ und Knotenmengen $T_1,\ldots,T_N$. Das Steinerbaumpackungs-Problem besteht darin, Kantenmengen $S_1,\ldots,S_N$ zu finden, so da\ss\ jedes $S_k$ die Knoten aus $T_k$ verbindet und jede Kante $e$ in höchstens $c_e$ Kantenmengen aus $S_1,\ldots,S_N$ vorkommt. Eine zulässige Lösung dieses Problems nennen wir eine Steinerbaumpackung. Ist zusätzlich eine Gewichtung der Kanten gegeben und nach einer bezüglich dieser Gewichtung minimalen Steinerbaumpackung gesucht, so sprechen wir vom gewichteten Steinerbaumpackungs-Problem. Die Motivation zum Studium dieses Problems kommt aus dem Entwurf elektronischer Schaltungen. Ein dort auftretendes Teilproblem ist das sogenannte Verdrahtungsproblem, das im wesentlichen darin besteht, gegebene Punktmengen unter bestimmten Nebenbedingungen und Optimalitätskriterien auf einer Grundfläche zu verbinden. Wir studieren das Steinerbaumpackungs-Problem aus polyedrischer Sicht und definieren ein Polyeder, dessen Ecken genau den Steinerbaumpackungen entsprechen. Anschlie\ss end versuchen wir, dieses Polyeder durch gute'' beziehungsweise facetten-definierenden Ungleichungen zu beschreiben. Basierend auf diesen Ungleichungen entwickeln wir ein Schnittebenenverfahren. Die Lösung des Schnittebenenverfahrens liefert eine untere Schranke für die Optimallösung und dient als Grundlage für die Entwicklung guter Primalheuristiken. Wir haben das von uns implementierte Schnittebenenverfahren an einem Spezialfall des Verdrahtungsproblems, dem sogenannten Switchbox-Verdrahtungsproblem, getestet und vielversprechende Ergebnisse erzielt. T3 - ZIB-Report - TR-92-04 Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4894 ER - TY - GEN A1 - Marchand, Hugues A1 - Martin, Alexander A1 - Weismantel, Robert A1 - Wolsey, Laurence T1 - Cutting Planes in Integer and Mixed Integer Programming N2 - This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, such as network design, is explored. T3 - ZIB-Report - SC-99-44 KW - Mixed Integer Programming KW - Cutting Planes Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4339 ER - TY - GEN A1 - Martin, Alexander A1 - Weismantel, Robert T1 - The Intersection of Knapsack Polyhedra and Extensions N2 - This paper introduces a scheme of deriving strong cutting planes for a general integer programming problem. The scheme is related to Chvatal-Gomory cutting planes and important special cases such as odd hole and clique inequalities for the stable set polyhedron or families of inequalities for the knapsack polyhedron. We analyze how relations between covering and incomparability numbers associated with the matrix can be used to bound coefficients in these inequalities. For the intersection of several knapsack polyhedra, incomparabilities between the column vectors of the associated matrix will be shown to transfer into inequalities of the associated polyhedron. Our scheme has been incorporated into the mixed integer programming code SIP. About experimental results will be reported. T3 - ZIB-Report - SC-97-61 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3300 ER -