@misc{BertholdHeinzLuebbeckeetal., author = {Berthold, Timo and Heinz, Stefan and L{\"u}bbecke, Marco and M{\"o}hring, Rolf and Schulz, Jens}, title = {A Constraint Integer Programming Approach for Resource-Constrained Project Scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11180}, number = {10-03}, abstract = {We propose a hybrid approach for solving the resource-constrained project scheduling problem which is an extremely hard to solve combinatorial optimization problem of practical relevance. Jobs have to be scheduled on (renewable) resources subject to precedence constraints such that the resource capacities are never exceeded and the latest completion time of all jobs is minimized. The problem has challenged researchers from different communities, such as integer programming (IP), constraint programming (CP), and satisfiability testing (SAT). Still, there are instances with 60 jobs which have not been solved for many years. The currently best known approach, lazyFD, is a hybrid between CP and SAT techniques. In this paper we propose an even stronger hybridization by integrating all the three areas, IP, CP, and SAT, into a single branch-and-bound scheme. We show that lower bounds from the linear relaxation of the IP formulation and conflict analysis are key ingredients for pruning the search tree. First computational experiments show very promising results. For five instances of the well-known PSPLIB we report an improvement of lower bounds. Our implementation is generic, thus it can be potentially applied to similar problems as well.}, language = {en} } @misc{BertholdHeinzVigerske, author = {Berthold, Timo and Heinz, Stefan and Vigerske, Stefan}, title = {Extending a CIP framework to solve MIQCPs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11371}, number = {09-23}, abstract = {This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.}, language = {en} } @misc{BertholdHeinzPfetsch, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc}, title = {Nonlinear pseudo-Boolean optimization: relaxation or propagation?}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11232}, number = {09-11}, abstract = {Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.}, language = {en} } @misc{HeinzStephanSchlechte, author = {Heinz, Stefan and Stephan, R{\"u}diger and Schlechte, Thomas}, title = {Solving Steel Mill Slab Problems with Branch and Price}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11260}, number = {09-14}, abstract = {The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.}, language = {en} } @misc{AchterbergBertholdHeinzetal., author = {Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Wolter, Kati}, title = {Constraint Integer Programming: Techniques and Applications}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10950}, number = {08-43}, abstract = {This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques.}, language = {en} } @misc{HeinzSachenbacher, author = {Heinz, Stefan and Sachenbacher, Martin}, title = {Using Model Counting to Find Optimal Distinguishing Tests}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10832}, number = {08-32}, abstract = {Testing is the process of stimulating a system with inputs in order to reveal hidden parts of the system state. In the case of non-deterministic systems, the difficulty arises that an input pattern can generate several possible outcomes. Some of these outcomes allow to distinguish between different hypotheses about the system state, while others do~not. In this paper, we present a novel approach to find, for non-deterministic systems modeled as constraints over variables, tests that allow to distinguish among the hypotheses as good as possible. The idea is to assess the quality of a test by determining the ratio of distinguishing (good) and not distinguishing (bad) outcomes. This measure refines previous notions proposed in the literature on model-based testing and can be computed using model counting techniques. We propose and analyze a greedy-type algorithm to solve this test optimization problem, using existing model counters as a building block. We give preliminary experimental results of our method, and discuss possible improvements.}, language = {en} } @misc{AchterbergHeinzKoch, author = {Achterberg, Tobias and Heinz, Stefan and Koch, Thorsten}, title = {Counting solutions of integer programs using unrestricted subtree detection}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10632}, number = {08-09}, abstract = {In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection.}, language = {en} } @misc{BertholdHeinzPfetsch, author = {Berthold, Timo and Heinz, Stefan and Pfetsch, Marc}, title = {Solving Pseudo-Boolean Problems with SCIP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10671}, number = {08-12}, abstract = {Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method.}, language = {en} } @misc{HarksHeinzPfetsch, author = {Harks, Tobias and Heinz, Stefan and Pfetsch, Marc}, title = {Competitive Online Multicommodity Routing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9212}, number = {06-27}, abstract = {We study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining the routing weights. We discuss an online algorithm that routes each commodity by minimizing a convex cost function that depends on the demands that are previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is \$4K/2+K\$-competitive, where \$K\$ is the number of commodities. For the parallel arc case this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.}, language = {en} } @misc{HarksHeinzPfetsch, author = {Harks, Tobias and Heinz, Stefan and Pfetsch, Marc}, title = {Competitive Online Multicommodity Routing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9599}, number = {07-16}, abstract = {In this paper we study online multicommodity routing problems in networks, in which commodities have to be routed sequentially. The flow of each commodity can be split on several paths. Arcs are equipped with load dependent price functions defining routing costs, which have to be minimized. We discuss a greedy online algorithm that routes each commodity by minimizing a convex cost function that only depends on the demands previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is 4K2 (1+K)2 -competitive, where K is the number of commodities. For the single-source single-destination case, this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.}, language = {en} }