Marco Lübbecke - Academia.edu (original) (raw)

Papers by Marco Lübbecke

Discrete Optimization, Feb 1, 2021

When solving the linear programming (LP) relaxation of a mixed-integer program (MIP) with column ... more When solving the linear programming (LP) relaxation of a mixed-integer program (MIP) with column generation, columns might be generated that are not needed to express any integer optimal solution. Such columns are called strongly redundant and the dual bound obtained by solving the LP relaxation is potentially stronger if these columns are not generated. We introduce a sufficient condition for strong redundancy that can be checked by solving a compact LP. Using a dual solution of this compact LP we generate classical Benders cuts for the subproblem so that the generation of strongly redundant columns can be avoided. The potential of these cuts to improve the dual bound of the column generation master problem is evaluated computationally using an implementation in the branch-price-and-cut solver GCG. While their efficacy is limited on classical problems, the benefits of applying the cuts is demonstrated on structured models to which a temporal decomposition can be applied.

HAL (Le Centre pour la Communication Scientifique Directe), Feb 23, 2022

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Zuse Institute Berlin, Jul 2, 2018

The SCIP Optimization Suite provides a collection of software packages for mathematical optimizat... more The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders' decomposition in a generic framework. GCG's detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders' framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver So-Plex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP.

Mathematical Programming, 2017

Even and odd pairs are important tools in the study of perfect graphs and were instrumental in th... more Even and odd pairs are important tools in the study of perfect graphs and were instrumental in the proof of the Strong Perfect Graph Theorem. We suggest that such pairs impose a lot of structure also in arbitrary, not just perfect graphs. To this end, we show that the presence of even or odd pairs in graphs imply a special structure of the stable set polytope. In fact, we give a polyhedral characterization of even and odd pairs.

The SCIP Optimization Suite is a powerful collection of optimization software that consists of th... more The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences.

DESSLib provides benchmark instances obtained by real world data for synthesis problems of decent... more DESSLib provides benchmark instances obtained by real world data for synthesis problems of decentralized energy supply systems (DESS). In this paper, the considered optimization problem is described in detail.

Algorithmic Approaches for Transportation Modeling, Optimization, and Systems, 2010

Titlepage, Table of Contents, Preface, Organization

Lecture Notes in Computer Science, 2005

We consider the problem of covering an orthogonal polygon with a minimum number of axisparallel r... more We consider the problem of covering an orthogonal polygon with a minimum number of axisparallel rectangles from a computational point of view. We propose an integer program which is the first general approach to obtain provably optimal solutions to this well-studied N P-hard problem. It applies to common variants like covering only the corners or the boundary of the polygon, and also to the weighted case. In experiments it turns out that the linear programming relaxation is extremely tight, and rounding a fractional solution is an immediate high quality heuristic. We obtain excellent experimental results for polygons originating from VLSI design, fax data sheets, black and white images, and for random instances. Making use of the dual linear program, we propose a stronger lower bound on the optimum, namely the cardinality of a fractional stable set. Furthermore, we outline ideas how to make use of this bound in primal-dual based algorithms. We give partial results which make us believe that our proposals have a strong potential to settle the main open problem in the area: To find a constant factor approximation algorithm for the rectangle cover problem.

Lecture Notes in Computer Science, 2017

Applying a Dantzig-Wolfe decomposition to a mixed-integer program (MIP) aims at exploiting an emb... more Applying a Dantzig-Wolfe decomposition to a mixed-integer program (MIP) aims at exploiting an embedded model structure and can lead to significantly stronger reformulations of the MIP. Recently, automating the process and embedding it in standard MIP solvers have been proposed, with the detection of a decomposable model structure as key element. If the detected structure reflects the (usually unknown) actual structure of the MIP well, the solver may be much faster on the reformulated model than on the original. Otherwise, the solver may completely fail. We propose a supervised learning approach to decide whether or not a reformulation should be applied, and which decomposition to choose when several are possible. Preliminary experiments with a MIP solver equipped with this knowledge show a significant performance improvement on structured instances, with little deterioration on others.

IEEE robotics and automation letters, Jul 1, 2017

Future production systems must meet the continual demands for improved productivity and energy ef... more Future production systems must meet the continual demands for improved productivity and energy efficiency. Being flexible and adaptable, reconfigurable systems offer great opportunities to face these challenges. Against this background, this study is concerned with the reconfiguration planning of Delta-like parallel robots. Following the trend of equipping the original Delta robot with additional rotational dof, a potential analysis reveals a great variety of dimensional and functional reconfiguration possibilities. Based on this, the reconfiguration planning is optimized applying operations research techniques. In this approach, a fixed number of configurations is optimally selected from the entire configuration space and simultaneously allocated to a set of handling tasks in a most energy efficient way. Each allocation's energy consumption is efficiently computed using Kane's inverse dynamics formulation. The outcome of a case study demonstrates the general applicability and energysaving potential of the proposed method.

ACM Journal of Experimental Algorithms, Jan 29, 2016

The cut packing problem in an undirected graph is to find a largest cardinality collection of pai... more The cut packing problem in an undirected graph is to find a largest cardinality collection of pairwise edgedisjoint cuts. We provide the first experimental study of this NP-hard problem that is interesting from a pure theorist's viewpoint as well as from the standpoint of scientific applications (e.g., in bioinformatics and network reliability). So far it could not be solved exactly. We propose a branch-price-and-cut algorithm to optimally solve instances from various graph classes, random and from the literature, with up to several hundred vertices. In particular, we investigate how complexity results match computational experience and how combinatorial properties help improve the algorithm's performance.

Symposium on Discrete Algorithms, Jan 11, 2004

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segm... more The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the original 30 outstanding open problems in computational geometry on the list by Demaine, Mitchell, and O'Rourke. The answer we provide is negative for a number of minimum stabbing problems by showing them N P-hard by means of a general proof technique. It implies non-trivial lower bounds on the approximability. On the positive side we propose a cut-based integer programming formulation for minimizing the stabbing number of matchings and spanning trees. We obtain lower bounds (in polynomial time) from the corresponding linear programming relaxations, and show that an optimal fractional solution always contains an edge of at least constant weight. This result constitutes a crucial step towards a constant-factor approximation via an iterated rounding scheme. In computational experiments we demonstrate that our approach allows for actually solving problems with up to several hundred points optimally or near-optimally.

Operations research proceedings, 2016

Want to get experience? Want to get any ideas to create new things in your life? Read operations ... more Want to get experience? Want to get any ideas to create new things in your life? Read operations research proceedings 2014 selected papers of the annual international conference of the german operations research society gor rwth aachen university germany september 2 5 2014 now! By reading this book as soon as possible, you can renew the situation to get the inspirations. Yeah, this way will lead you to always think more and more. In this case, this book will be always right for you. When you can observe more about the book, you will know why you need this. When reading the PDF, you can see how the author is very reliable in using the words to create sentences. It will be also the ways how the author creates the diction to influence many people. But, it's not nonsense, it is something. Something that will lead you is thought to be better. Something that will make your feel so better. And something that will give you new things. This is it, the operations research proceedings 2014 selected papers of the annual international conference of the german operations research society gor rwth aachen university germany september 2 5 2014.

Symposium on Experimental and Efficient Algorithms, 2018

In Dantzig-Wolfe reformulation of an integer program one convexifies a subset of the constraints,... more In Dantzig-Wolfe reformulation of an integer program one convexifies a subset of the constraints, leading to potentially stronger dual bounds from the respective linear programming relaxation. As the subset can be chosen arbitrarily, this includes the trivial cases of convexifying no and all constraints, resulting in a weakest and strongest reformulation, respectively. Our computational study aims at better understanding of what happens in between these extremes. For a collection of integer programs with few constraints we compute, optimally solve, and evaluate the relaxations of all possible (exponentially many) Dantzig-Wolfe reformulations (with mild extensions to larger models from the MIPLIBs). We observe that only a tiny number of different dual bounds actually occur and that only a few inclusion-wise minimal representatives exist for each. This aligns with considerably different impacts of individual constraints on the strengthening the relaxation, some of which have almost no influence. In contrast, types of constraints that are convexified in textbook reformulations have a larger effect. We relate our experiments to what could be called a hierarchy of Dantzig-Wolfe reformulations.

Mathematical Programming Computation, Sep 9, 2019

We exactly solve the N P-hard combinatorial optimization problem of finding a minimum cardinality... more We exactly solve the N P-hard combinatorial optimization problem of finding a minimum cardinality vertex separator with k (or arbitrarily many) capacitated shores in a hypergraph. We present an exponential size integer programming formulation which we solve by branch-and-price. The pricing problem, an interesting optimization problem on its own, has a decomposable structure that we exploit in preprocessing. We perform an extensive computational study, in particular on hypergraphs coming from the application of rearranging a matrix into single-bordered block-diagonal form. Our experimental results show that our proposal complements the previous exact approaches in terms of applicability for larger k, and significantly outperforms them in the case k = ∞.

2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR), 2018

Data availability and modular design of modern production systems allow companies to respond flex... more Data availability and modular design of modern production systems allow companies to respond flexibly to changing market conditions and process requirements. Against this background, this contribution presents tools to automatically identify energy efficient (re)configuration patterns. Therefore, market studies are used to reveal industrially relevant demandrelated handling tasks and potential configurations for the wellknown Delta parallel robot, as well as recent design modifications extending its field of application. In this context, optimization approaches are innovatively employed to effectively reduce the configuration space by discarding infeasible candidates and eventually solve the problem of simultaneous selection and allocation of configurations, such that a set of given handling tasks is performed in the most energy efficient way. Additionally, kinematic constraints are included in order to maintain the throughput rates of the underlying system. The approach is easily transferable to a system layout with reconfigurable, but also predetermined subsystems.

Computers & Chemical Engineering, 2016

Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to ... more Decentralized energy supply systems (DESS) are highly integrated and complex systems designed to meet time-varying energy demands, e.g., heating, cooling, and electricity. The synthesis problem of DESS addresses combining various types of energy conversion units, choosing their sizing and operations to maximize an objective function, e.g., the net present value. In practice, investment costs and part-load performances are nonlinear. Thus, this optimization problem can be modeled as a nonconvex mixed-integer nonlinear programming (MINLP) problem. We present an adaptive discretization algorithm to solve such synthesis problems containing an iterative interaction between mixedinteger linear programs (MIPs) and nonlinear programs (NLPs). The proposed algorithm outperformes state-of-the-art MINLP solvers as well as linearization approaches with regard to solution quality and computation times on a test set obtained from real industrial data, which we made available online.