TY - JOUR A1 - Breuer, Thomas A1 - Bussieck, Michael A1 - Fiand, Frederik A1 - Cao, Karl-Kiên A1 - Gils, Hans Christian A1 - Wetzel, Manuel A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Khabi, Dmitry T1 - BEAM-ME: Ein interdisziplinärer Beitrag zur Erreichung der Klimaziele JF - OR-News : das Magazin der GOR Y1 - 2019 IS - 66 SP - 6 EP - 8 ER - TY - GEN A1 - Rössig, Ansgar T1 - Verification of Neural Networks T3 - ZIB-Report - 19-40 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74174 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian T1 - New Perspectives on PESP: T-Partitions and Separators N2 - In the planning process of public transportation companies, designing the timetable is among the core planning steps. In particular in the case of periodic (or cyclic) services, the Periodic Event Scheduling Problem (PESP) is well-established to compute high-quality periodic timetables. We are considering algorithms for computing good solutions for the very basic PESP with no additional extra features as add-ons. The first of these algorithms generalizes several primal heuristics that had been proposed in the past, such as single-node cuts and the modulo network simplex algorithm. We consider partitions of the graph, and identify so-called delay cuts as a structure that allows to generalize several previous heuristics. In particular, when no more improving delay cut can be found, we already know that the other heuristics could not improve either. The second of these algorithms turns a strategy, that had been discussed in the past, upside-down: Instead of gluing together the network line-by-line in a bottom-up way, we develop a divide-and-conquer-like top-down approach to separate the initial problem into two easier subproblems such that the information loss along their cutset edges is as small as possible. We are aware that there may be PESP instances that do not fit well the separator setting. Yet, on the RxLy-instances of PESPlib in our experimental computations, we come up with good primal solutions and dual bounds. In particular, on the largest instance (R4L4), this new separator approach, which applies a state-of-the-art solver as subroutine, is able to come up with better dual bounds than purely applying this state-of-the-art solver in the very same time. T3 - ZIB-Report - 19-35 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Graph Partitioning KW - Graph Separators KW - Balanced Cuts Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73853 SN - 1438-0064 ER - TY - GEN A1 - Serrano, Felipe T1 - Visible points, the separation problem, and applications to MINLP N2 - In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point to restrict the feasible region in order to obtain a tighter domain. To ensure validity, we require that every valid cut separating the infeasible point from the restricted feasible region is still valid for the original feasible region. We translate this requirement in terms of the separation problem and the reverse polar. In particular, if the reverse polar of the restricted feasible region is the same as the reverse polar of the feasible region, then any cut valid for the restricted feasible region that \emph{separates} the infeasible point, is valid for the feasible region. We show that the reverse polar of the \emph{visible points} of the feasible region from the infeasible point coincides with the reverse polar of the feasible region. In the special where the feasible region is described by a single non-convex constraint intersected with a convex set we provide a characterization of the visible points. Furthermore, when the non-convex constraint is quadratic the characterization is particularly simple. We also provide an extended formulation for a relaxation of the visible points when the non-convex constraint is a general polynomial. Finally, we give some conditions under which for a given set there is an inclusion-wise smallest set, in some predefined family of sets, whose reverse polars coincide. T3 - ZIB-Report - 19-38 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74016 SN - 1438-0064 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Schlechte, Thomas T1 - Re-optimizing ICE Rotations after a Tunnel Breakdown near Rastatt N2 - Planning rolling stock movements in industrial passenger railway applications isa long-term process based on timetables which are also often valid for long periods of time. For these timetables and rotation plans, i.e., plans of railway vehicle movements are constructed as templates for these periods. During operation the rotation plans are affected by all kinds of unplanned events. An unusal example for that is the collapse of a tunnel ceiling near Rastatt in southern Germany due to construction works related to the renewal of the central station in Stuttgart. As a result the main railway connection between Stuttgart and Frankfurt am Main, located on top of the tunnel, had to be closed from August 12th to October 2nd 2017. This had a major impact on the railway network in southern Germany. Hence, all rotation plans and train schedules for both passenger and cargo traffic had to be revised. In this paper we focus on a case study for this situation and compute new rotation plans via mixed integer programming for the ICE high speed fleet of DB Fernverkehr AG one of the largest passenger railway companies in Europe. In our approach we take care of some side constraints to ensure a smooth continuation of the rotation plans after the disruption has ended. T3 - ZIB-Report - 19-02 KW - case study KW - re-optimization KW - railway rolling stock optimization KW - mixed integer programming Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73976 SN - 1438-0064 ER - TY - GEN A1 - Löbel, Fabian A1 - Lindner, Niels A1 - Borndörfer, Ralf T1 - The Restricted Modulo Network Simplex Method for Integrated Periodic Timetabling and Passenger Routing N2 - The Periodic Event Scheduling Problem is a well-studied NP-hard problem with applications in public transportation to find good periodic timetables. Among the most powerful heuristics to solve the periodic timetabling problem is the modulo network simplex method. In this paper, we consider the more difficult version with integrated passenger routing and propose a refined integrated variant to solve this problem on real-world-based instances. T3 - ZIB-Report - 19-36 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Integrated Passenger Routing KW - Shortest Routes in Public Transport Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73868 SN - 1438-0064 ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Schlechte, Thomas T1 - Re-optimizing ICE Rotations after a Tunnel Breakdown near Rastatt T2 - Proceedings of the 8th International Conference on Railway Operations Modelling and Analysis - RailNorrköping 2019 N2 - Planning rolling stock movements in industrial passenger railway applications isa long-term process based on timetables which are also often valid for long periods of time. For these timetables and rotation plans, i.e., plans of railway vehicle movements are constructed as templates for these periods. During operation the rotation plans are affected by all kinds of unplanned events. An unusal example for that is the collapse of a tunnel ceiling near Rastatt in southern Germany due to construction works related to the renewal of the central station in Stuttgart. As a result the main railway connection between Stuttgart and Frankfurt am Main, located on top of the tunnel, had to be closed from August 12th to October 2nd 2017. This had a major impact on the railway network in southern Germany. Hence, all rotation plans and train schedules for both passenger and cargo traffic had to be revised. In this paper we focus on a case study for this situation and compute new rotation plans via mixed integer programming for the ICE high speed fleet of DB Fernverkehr AG one of the largest passenger railway companies in Europe. In our approach we take care of some side constraints to ensure a smooth continuation of the rotation plans after the disruption has ended. Y1 - 2019 UR - http://www.ep.liu.se/ecp/article.asp?issue=069&article=011&volume= SN - 978-91-7929-992-7 SN - 1650-3686 VL - Linköping Electronic Conference Proceedings IS - 069 SP - 160 EP - 168 PB - Linköping University Electronic Press, Linköpings universitet CY - Linköping, Sweden ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Optimization of handouts for rolling stock rotations JF - Journal of Rail Transport Planning & Management N2 - A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach. Y1 - 2019 U6 - https://doi.org/10.1016/j.jrtpm.2019.02.001 IS - 10 SP - 1 EP - 8 ER - TY - CHAP A1 - Gleixner, Ambros A1 - Kempke, Nils-Christian A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Uslu, Svenja T1 - First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method T2 - Operations Research Proceedings 2019 N2 - In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix. KW - block structure KW - energy system models KW - interior-point method KW - high performance computing KW - linear programming KW - parallelization KW - presolving KW - preprocessing Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-48439-2_13 SP - 105 EP - 111 PB - Springer International Publishing ET - 1 ER - TY - CHAP A1 - Berthold, Timo A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - Strategic Planning of Rolling Stock Rotations for Public Tenders T2 - Proceedings of the 8th International Conference on Railway Operations Modelling and Analysis - RailNorrköping 2019 N2 - Since railway companies have to apply for long-term public contracts to operate railway lines in public tenders, the question how they can estimate the operating cost for long-term periods adequately arises naturally. We consider a rolling stock rotation problem for a time period of ten years, which is based on a real world instance provided by an industry partner. We use a two stage approach for the cost estimation of the required rolling stock. In the first stage, we determine a weekly rotation plan. In the second stage, we roll out this weekly rotation plan for a longer time period and incorporate scheduled maintenance treatments. We present a heuristic approach and a mixed integer programming model to implement the process of the second stage. Finally, we discuss computational results for a real world tendering scenario. Y1 - 2019 UR - http://www.ep.liu.se/ecp/article.asp?issue=069&article=009&volume= SN - 978-91-7929-992-7 SN - 1650-3686 VL - Linköping Electronic Conference Proceedings IS - 069 SP - 148 EP - 159 PB - Linköping University Electronic Press, Linköpings universitet ER - TY - JOUR A1 - Müller, Benjamin A1 - Serrano, Felipe A1 - Gleixner, Ambros T1 - Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms JF - SIAM Journal on Optimization N2 - One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly. Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-72767 VL - 30 IS - 2 SP - 1339 EP - 1365 ER - TY - GEN A1 - Müller, Benjamin A1 - Serrano, Felipe A1 - Gleixner, Ambros T1 - Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms N2 - One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly. T3 - ZIB-Report - 19-15 KW - mixed-integer quadratically constrained programs KW - nonconvex KW - global optimization KW - separation KW - propagation KW - projection KW - bilinear terms Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-72759 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gamrath, Gerald A1 - Salvagnin, Domenico T1 - Exploiting Dual Degeneracy in Branching N2 - Branch-and-bound methods for mixed-integer programming (MIP) are traditionally based on solving a linear programming (LP) relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. In this paper, we study branching strategies for mixed-integer programs that exploit the knowledge of multiple alternative optimal solutions (a cloud ) of the current LP relaxation. These strategies naturally extend common methods like most infeasible branching, strong branching, pseudocost branching, and their hybrids, but we also propose a novel branching rule called cloud diameter branching. We show that dual degeneracy, a requirement for alternative LP optima, is present for many instances from common MIP test sets. Computational experiments show significant improvements in the quality of branching decisions as well as reduced branching effort when using our modifications of existing branching rules. We discuss different ways to generate a cloud of solutions and present extensive computational results showing that through a careful implementation, cloud modifications can speed up full strong branching by more than 10 % on standard test sets. Additionally, by exploiting degeneracy, we are also able to improve the state-of-the-art hybrid branching rule and reduce the solving time on affected instances by almost 20 % on average. T3 - ZIB-Report - 19-17 KW - mixed integer programming KW - branching rule KW - search strategy KW - dual degeneracy Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73028 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Galley, Tristan T1 - An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-libraries N2 - Branch-and-bound (B&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature. T3 - ZIB-Report - 19-14 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-72804 SN - 1438-0064 ER - TY - GEN A1 - Serrano, Felipe A1 - Schwarz, Robert A1 - Gleixner, Ambros T1 - On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley’s Cutting Plane Algorithm N2 - Recently, Kronqvist et al. (2016) rediscovered the supporting hyperplane algorithm of Veinott (1967) and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by general, not necessarily convex, differentiable functions that satisfy a mild condition. T3 - ZIB-Report - 19-18 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73253 SN - 1438-0064 ER - TY - GEN A1 - Hoppmann, Kai T1 - On the Complexity of the Maximum Minimum Cost Flow Problem N2 - Consider a flow network, i.e., a directed graph where each arc has a nonnegative capacity and an associated length, together with nonempty supply-intervals for the sources and nonempty demand-intervals for the sinks. The goal of the Maximum Minimum Cost Flow Problem (MMCF) is to find fixed supply and demand values within these intervals, such that the optimal objective value of the induced Minimum Cost Flow Problem (MCF) is maximized. In this paper, we show that MMCF is APX-hard and remains NP-hard in the uncapacitated case. T3 - ZIB-Report - 19-19 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73359 SN - 1438-0064 ER - TY - CHAP A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Building Optimal Steiner Trees on Supercomputers by Using up to 43,000 Cores T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019 N2 - SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively parallel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best-known solutions to instances from the benchmark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been considerably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB. Y1 - 2019 U6 - https://doi.org/10.1007/978-3-030-19212-9_35 VL - 11494 SP - 529 EP - 539 PB - Springer ER - TY - JOUR A1 - Bernal, David E. A1 - Vigerske, Stefan A1 - Trespalacios, Francisco A1 - Grossmann, Ignacio E. T1 - Improving the performance of DICOPT in convex MINLP problems using a feasibility pump JF - Optimization Methods and Software N2 - The solver DICOPT is based on an outer-approximation algorithm used for solving mixed- integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, there are certain problems that are diffcult to solve with this algorithm. One of these problems is when the nonlinear constraints are so restrictive that the nonlinear subproblems produced by the algorithm are infeasible. This problem is addressed in this paper with a feasibility pump algorithm, which modifies the objective function in order to efficiently find feasible solutions. It has been implemented as a preprocessing algorithm for DICOPT. Computational comparisons with previous versions of DICOPT and other MINLP solvers on a set of convex MINLPs demonstrate the effectiveness of the proposed algorithm in terms of solution quality and solving time. Y1 - 2017 ER - TY - JOUR A1 - Sagnol, Guillaume A1 - Pauwels, Edouard T1 - An unexpected connection between Bayes A-optimal designs and the group lasso JF - Statistical Papers N2 - We show that the A-optimal design optimization problem over m design points in R^n is equivalent to minimizing a quadratic function plus a group lasso sparsity inducing term over n x m real matrices. This observation allows to describe several new algorithms for A-optimal design based on splitting and block coordinate decomposition. These techniques are well known and proved powerful to treat large scale problems in machine learning and signal processing communities. The proposed algorithms come with rigorous convergence guarantees and convergence rate estimate stemming from the optimization literature. Performances are illustrated on synthetic benchmarks and compared to existing methods for solving the optimal design problem. Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73059 VL - 60 IS - 2 SP - 215 EP - 234 ER - TY - GEN A1 - Witzig, Jakob A1 - Berthold, Timo A1 - Heinz, Stefan T1 - Computational Aspects of Infeasibility Analysis in Mixed Integer Programming N2 - The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The result of this analysis is one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept is called conflict graph analysis and has its origin in solving satisfiability problems and is similarly used in constraint programming. The second concept is to analyze infeasible linear programming (LP) relaxations. Every ray of the dual LP provides a set of multipliers that can be used to generate a single new globally valid linear constraint. This method is called dual proof analysis. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide an intense computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first integrated approach to use both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set MIPLIB 2017; the presented algorithms have been implemented within the non-commercial MIP solver SCIP and the commercial MIP solver FICO Xpress. T3 - ZIB-Report - 19-54 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74962 SN - 1438-0064 ER - TY - GEN A1 - Hoppmann, Kai A1 - Hennings, Felix A1 - Lenz, Ralf A1 - Gotzes, Uwe A1 - Heinecke, Nina A1 - Spreckelsen, Klaus A1 - Koch, Thorsten T1 - Optimal Operation of Transient Gas Transport Networks T3 - ZIB-Report - 19-23 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73639 SN - 1438-0064 ER - TY - GEN A1 - Hennings, Felix A1 - Anderson, Lovis A1 - Hoppmann, Kai A1 - Turner, Mark A1 - Koch, Thorsten T1 - Controlling transient gas flow in real-world pipeline intersection areas N2 - Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach. T3 - ZIB-Report - 19-24 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73645 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Elijazyfer, Ziena A1 - Schwartz, Stephan T1 - Approximating Balanced Graph Partitions N2 - We consider the problem of partitioning a weighted graph into k connected components of similar weight. In particular, we consider the two classical objectives to maximize the lightest part or to minimize the heaviest part. For a partitioning of the vertex set and for both objectives, we give the first known approximation results on general graphs. Specifically, we give a $\Delta$-approximation where $\Delta$ is the maximum degree of an arbitrary spanning tree of the given graph. Concerning the edge partition case, we even obtain a 2-approximation for the min-max and the max-min problem, by using the claw-freeness of line graphs. T3 - ZIB-Report - 19-25 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73675 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Inken A1 - Petkovic, Milena T1 - Prediction of Intermitted Flows in Large Gas Networks T3 - ZIB-Report - 19-29 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73717 SN - 1438-0064 ER - TY - CHAP A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Gally, Tristan T1 - An Easy Way to Build Parallel State-of-the-art Combinatorial Optimization Problem Solvers: A Computational Study on Solving Steiner Tree Problems and Mixed Integer Semidefinite Programs by using ug[SCIP-*,*]-libraries T2 - Proceedings of the 9th IEEE Workshop Parallel / Distributed Combinatorics and Optimization N2 - Branch-and-bound (B&B) is an algorithmic framework for solving NP-hard combinatorial optimization problems. Although several well-designed software frameworks for parallel B&B have been developed over the last two decades, there is very few literature about successfully solving previously intractable combinatorial optimization problem instances to optimality by using such frameworks.The main reason for this limited impact of parallel solvers is that the algorithmic improvements for specific problem types are significantly greater than performance gains obtained by parallelization in general. Therefore, in order to solve hard problem instances for the first time, one needs to accelerate state-of-the-art algorithm implementations. In this paper, we present a computational study for solving Steiner tree problems and mixed integer semidefinite programs in parallel. These state-of-the-art algorithm implementations are based on SCIP and were parallelized via the ug[SCIP-*,*]-libraries---by adding less than 200 lines of glue code. Despite the ease of their parallelization, these solvers have the potential to solve previously intractable instances. In this paper, we demonstrate the convenience of such a parallelization and present results for previously unsolvable instances from the well-known PUC benchmark set, widely regarded as the most difficult Steiner tree test set in the literature. Y1 - 2019 U6 - https://doi.org/10.1109/IPDPSW.2019.00095 SP - 530 EP - 541 PB - IEEE ER - TY - JOUR A1 - Chen, Ying A1 - Chua, Wee Song A1 - Koch, Thorsten T1 - Forecasting day-ahead high-resolution natural-gas demand and supply in Germany JF - Applied Energy N2 - Forecasting natural gas demand and supply is essential for an efficient operation of the German gas distribution system and a basis for the operational decisions of the transmission system operators. The German gas market is moving towards more short-term planning, in particular, day-ahead contracts. This increases the difficulty that the operators in the dispatching centre are facing, as well as the necessity of accurate forecasts. This paper presents a novel predictive model that provides day-ahead forecasts of the high resolution gas flow by developing a Functional AutoRegressive model with eXogenous variables (FARX). The predictive model allows the dynamic patterns of hourly gas flows to be described in a wide range of historical profiles, while also taking the relevant determinants data into account. By taking into account a richer set of information, FARX provides stronger performance in real data analysis, with both accuracy and high computational efficiency. Compared to several alternative models in out-of-sample forecasts, the proposed model can improve forecast accuracy by at least 12% and up to 5-fold for one node, 3% to 2-fold and 2-fold to 4-fold for the other two nodes. The results show that lagged 1-day gas flow and nominations are important predictors, and with their presence in the forecast model, temperature becomes insignificant for short-term predictions. Y1 - 2018 U6 - https://doi.org/https://doi.org/10.1016/j.apenergy.2018.06.137 IS - Volume 228 SP - 1091 EP - 1110 ER - TY - CHAP A1 - Rehfeldt, Daniel A1 - Shinano, Yuji A1 - Koch, Thorsten T1 - SCIP-Jack: An exact high performance solver for Steiner tree problems in graphs and related problems BT - Proceedings of the 7th International Conference on High Performance Scientific Computing T2 - Modeling, Simulation and Optimization of Complex Processes HPSC 2018 N2 - The Steiner tree problem in graphs is one of the classic combinatorial optimization problems. Furthermore, many related problems, such as the rectilinear Steiner tree problem or the maximum-weight connected subgraph problem, have been described in the literature—with a wide range of practical applications. To embrace this wealth of problem classes, the solver SCIP-JACK has been developed as an exact framework for classic Steiner tree and 11 related problems. Moreover, the solver comes with both shared- and distributed memory extensions by means of the UG framework. Besides its versatility, SCIP-JACK is highly competitive for most of the 12 problem classes it can solve, as for instance demonstrated by its top ranking in the recent PACE 2018 Challenge. This article describes the current state of SCIP-JACK and provides up-to-date computational results, including several instances that can now be solved for the first time to optimality. Y1 - 2021 U6 - https://doi.org/10.1007/978-3-030-55240-4_10 PB - Springer ER - TY - THES A1 - Scheizel, Jenia T1 - A fast Flow based Heuristic for MIP modelled SCM Problems Y1 - 2018 ER - TY - GEN A1 - Anderson, Daniel A1 - Hendel, Gregor A1 - Le Bodic, Pierre A1 - Viernickel, Jan Merlin T1 - Clairvoyant Restarts in Branch-and-Bound Search Using Online Tree-Size Estimation N2 - We propose a simple and general online method to measure the search progress within the Branch-and-Bound algorithm, from which we estimate the size of the remaining search tree. We then show how this information can help solvers algorithmically at runtime by designing a restart strategy for Mixed-Integer Programming (MIP) solvers that decides whether to restart the search based on the current estimate of the number of remaining nodes in the tree. We refer to this type of algorithm as clairvoyant. Our clairvoyant restart strategy outperforms a state-of-the-art solver on a large set of publicly available MIP benchmark instances. It is implemented in the MIP solver SCIP and will be available in future releases. T3 - ZIB-Report - 19-11 KW - Mixed-Integer Programming solvers KW - Restart KW - Progress measures KW - tree-size estimates Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-72653 SN - 1438-0064 ER - TY - BOOK A1 - Abbink, Erwin A1 - Bärmann, Andreas A1 - Bešinovic, Nikola A1 - Bohlin, Markus A1 - Cacchiani, Valentina A1 - Caimi, Gabrio A1 - de Fabris, Stefano A1 - Dollevoet, Twan A1 - Fischer, Frank A1 - Fügenschuh, Armin A1 - Galli, Laura A1 - Goverde, Rob M.P. A1 - Hansmann, Ronny A1 - Homfeld, Henning A1 - Huisman, Dennis A1 - Johann, Marc A1 - Klug, Torsten A1 - Törnquist Krasemann, Johanna A1 - Kroon, Leo A1 - Lamorgese, Leonardo A1 - Liers, Frauke A1 - Mannino, Carlo A1 - Medeossi, Giorgio A1 - Pacciarelli, Dario A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Schmidt, Marie A1 - Schöbel, Anita A1 - Schülldorf, Hanno A1 - Stieber, Anke A1 - Stiller, Sebastian A1 - Toth, Paolo A1 - Zimmermann, Uwe ED - Borndörfer, Ralf ED - Klug, Torsten ED - Lamorgese, Leonardo ED - Mannino, Carlo ED - Reuther, Markus ED - Schlechte, Thomas T1 - Handbook of Optimization in the Railway Industry N2 - This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art. There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover: Simulation Capacity Assessment Network Design Train Routing Robust Timetabling Event Scheduling Track Allocation Blocking Shunting Rolling Stock Crew Scheduling Dispatching Delay Propagation Y1 - 2018 SN - 978-3-319-72152-1 U6 - https://doi.org/10.1007/978-3-319-72153-8 VL - 268 PB - Springer Verlag ER - TY - JOUR A1 - Berthold, Timo A1 - Farmer, James A1 - Heinz, Stefan A1 - Perregaard, Michael T1 - Parallelization of the FICO Xpress Optimizer JF - Optimization Methods and Software N2 - Computing hardware has mostly thrashed out the physical limits for speeding up individual computing cores. Consequently, the main line of progress for new hardware is growing the number of computing cores within a single CPU. This makes the study of efficient parallelization schemes for computation-intensive algorithms more and more important. A natural precondition to achieving reasonable speedups from parallelization is maintaining a high workload of the available computational resources. At the same time, reproducibility and reliability are key requirements for software that is used in industrial applications. In this paper, we present the new parallelization concept for the state-of-the-art MIP solver FICO Xpress-Optimizer. MIP solvers like Xpress are expected to be deterministic. This inevitably results in synchronization latencies which render the goal of a satisfying workload a challenge in itself. We address this challenge by following a partial information approach and separating the concepts of simultaneous tasks and independent threads from each other. Our computational results indicate that this leads to a much higher CPU workload and thereby to an improved, almost linear, scaling on modern high-performance CPUs. As an added value, the solution path that Xpress takes is not only deterministic in a fixed environment, but also, to a certain extent, thread-independent. This paper is an extended version of Berthold et al. [Parallelization of the FICO Xpress-Optimizer, in Mathematical Software – ICMS 2016: 5th International Conference, G.-M. Greuel, T. Koch, P. Paule, and A. Sommere, eds., Springer International Publishing, Berlin, 2016, pp. 251–258] containing more detailed technical descriptions, illustrative examples and updated computational results. Y1 - 2018 U6 - https://doi.org/10.1080/10556788.2017.1333612 VL - 33 IS - 3 SP - 518 EP - 529 ER - TY - JOUR A1 - Tawfik, Christine A1 - Limbourg, Sabine T1 - A Bilevel Model for Network Design and Pricing Based on a Level-of-Service Assessment JF - Transportation Science N2 - Within a wide view to stimulate intermodal transport, this paper is devoted to the examination of the intrinsically related problems of designing freight carrying services and determining their associated prices as observed by the shipper firms. A path-based multicommodity formulation is developed for a medium-term planning horizon, from the perspective of an intermodal operator. In the quest of incorporating nonprice attributes, two approaches are proposed to depict a realistic assessment of the service quality. First, frequency delay constraints are added to the upper level problem. Second, based on a random utility model, behavioural concepts are integrated in the expression of the lower level as a logistics costs minimization problem. Exact tests are invoked on real-world instances, demonstrating the capability of the presented approaches of reaching reasonable results within acceptable computation times and optimality gaps. The broader level-of-service perspective imposes additional costs on the service providers, although to a lesser extent on long-distance freight corridors, as indicated by the computed market share and net profit. Further experiments are conducted to test the impact of certain transport management instruments (e.g. subsidies and service capacities) on the modal split, as well as to assess the intermodality’s future based on a scenario analysis methodology. Y1 - 2019 U6 - https://doi.org/10.1287/trsc.2019.0906 VL - 53 IS - 6 SP - 1609 EP - 1626 PB - Informs CY - Transportation Science ER - TY - JOUR A1 - Munguia, Lluis-Miquel A1 - Oxberry, Geoffrey A1 - Rajan, Deepak A1 - Shinano, Yuji T1 - Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs JF - Computational Optimization and Applications N2 - PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch & Bound (B&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores. Y1 - 2019 U6 - https://doi.org/10.1007/s10589-019-00074-0 ER - TY - JOUR A1 - Achterberg, Tobias A1 - Bixby, Robert E. A1 - Gu, Zonghao A1 - Rothberg, Edward A1 - Weninger, Dieter T1 - Presolve Reductions in Mixed Integer Programming JF - INFORMS Journal on Computing N2 - Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed-integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the ``strength'' of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed-integer programs, and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed-integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature. Y1 - 2019 ER - TY - CHAP A1 - Péron, Martin A1 - Bartlett, Peter L. A1 - Becker, Kai-Helge A1 - Helmstedt, Kate A1 - Chadès, Iadine T1 - Two Approximate Dynamic Programming Algorithms for Managing Complete SIS Networks T2 - COMPASS '18 Proceedings of the 1st ACM SIGCAS Conference on Computing and Sustainable Societies N2 - Inspired by the problem of best managing the invasive mosquito Aedes albopictus across the 17 Torres Straits islands of Australia, we aim at solving a Markov decision process on large Susceptible-Infected-Susceptible (SIS) networks that are highly connected. While dynamic programming approaches can solve sequential decision-making problems on sparsely connected networks, these approaches are intractable for highly connected networks. Inspired by our case study, we focus on problems where the probability of nodes changing state is low and propose two approximate dynamic programming approaches. The first approach is a modified version of value iteration where only those future states that are similar to the current state are accounted for. The second approach models the state space as continuous instead of binary, with an on-line algorithm that takes advantage of Bellman's adapted equation. We evaluate the resulting policies through simulations and provide a priority order to manage the 17 infested Torres Strait islands. Both algorithms show promise, with the continuous state approach being able to scale up to high dimensionality (50 nodes). This work provides a successful example of how AI algorithms can be designed to tackle challenging computational sustainability problems. Y1 - 2018 U6 - https://doi.org/10.1145/3209811.3209814 PB - ACM ER - TY - CHAP A1 - Berthold, Timo A1 - Perregaard, Michael A1 - Mészáros, Csaba T1 - Four Good Reasons to Use an Interior Point Solver Within a MIP Solver T2 - Kliewer N., Ehmke J., Borndörfer R. (eds) Operations Research Proceedings 2017 N2 - “Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex” This is the common conception which disregards that an interior point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of the benefits that an interior point solver brings to the solution of difficult MIPs within FICO Xpress. This includes many different components of the MIP solver such as branching variable selection, primal heuristics, preprocessing, and of course the solution of the LP relaxation. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_22 SP - 159 EP - 164 ER - TY - GEN A1 - Gleixner, Ambros A1 - Berthold, Timo A1 - Müller, Benjamin A1 - Weltge, Stefan T1 - Three Enhancements for Optimization-Based Bound Tightening N2 - Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper is to discuss algorithmic techniques for an efficient implementation of OBBT. Most state-of-the-art MINLP solvers apply some restricted version of OBBT and it seems to be common belief that OBBT is beneficial if only one is able to keep its computational cost under control. To this end, we introduce three techniques to increase the efficiency of OBBT: filtering strategies to reduce the number of solved LPs, ordering heuristics to exploit simplex warm starts, and the generation of Lagrangian variable bounds (LVBs). The propagation of LVBs during tree search is a fast approximation to OBBT without the need to solve auxiliary LPs. We conduct extensive computational experiments on MINLPLib2. Our results indicate that OBBT is most beneficial on hard instances, for which we observe a speedup of 17% to 19% on average. Most importantly, more instances can be solved when using OBBT. T3 - ZIB-Report - 15-16 KW - MINLP KW - optimization-based bound tightening KW - optimality-based bound tightening KW - OBBT KW - propagation KW - bound tightening Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57803 SN - 1438-0064 ER - TY - THES A1 - Gleixner, Ambros T1 - Solving Large-scale Open Pit Mining Production Scheduling Problems by Integer Programming N2 - Since the initial application of mathematical optimisation methods to mine planning in 1965, the Lerchs-Grossmann algorithm for computing the ultimate pit limit, operations researchers have worked on a variety of challenging problems in the area of open pit mining. This thesis focuses on the open pit mining production scheduling problem: Given the discretisation of an orebody as a block model, determine the sequence in which the blocks should be removed from the pit, over the lifespan of the mine, such that the net present value of the mining operation is maximised. In practise, when some material has been removed from the pit, it must be processed further in order to extract the valuable elements contained therein. If the concentration of valuable elements is not sufficiently high, the material is discarded as waste or stockpiled. Realistically-sized block models can contain hundreds of thousands of blocks. A common approach to render these problem instances computationally tractable is the aggregation of blocks to larger scheduling units. The thrust of this thesis is the investigation of a new mixed-integer programming formulation for the open pit mining production scheduling problem, which allows for processing decisions to be made at block level, while the actual mining schedule is still computed at aggregate level. A drawback of this model in its full form is the large number of additional variables needed to model the processing decisions. One main result of this thesis shows how these processing variables can be aggregated efficiently to reduce the problem size significantly, while practically incurring no loss in net present value. The second focus is on the application of lagrangean relaxation to the resource constraints. Using a result of Möhring et al. (2003) for project scheduling, the lagrangean relaxation can be solved efficiently via minimum cut computations in a weighted digraph. Experiments with a bundle algorithm implementation by Helmberg showed how the lagrangean dual can be solved within a small fraction of the time required by standard linear programming algorithms, while yielding practically the same dual bound. Finally, several problem-specific heuristics are presented together with computational results: two greedy sub-MIP start heuristics and a large neighbourhood search heuristic. A combination of a lagrangean-based start heuristic followed by a large neighbourhood search proved to be effective in generating solutions with objective values within a 0.05% gap of the optimum. Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11389 ER - TY - GEN A1 - Vigerske, Stefan A1 - Gleixner, Ambros T1 - SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework N2 - This paper describes the extensions that were added to the constraint integer programming framework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithm based on a linear outer-approximation, which is computed by convex over- and underestimation of nonconvex functions. An expression graph representation of nonlinear constraints allows for bound tightening, structure analysis, and reformulation. Primal heuristics are employed throughout the solving process to find feasible solutions early. We provide insights into the performance impact of individual MINLP solver components via a detailed computational study over a large and heterogeneous test set. T3 - ZIB-Report - 16-24 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59377 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover: a primal MINLP heuristic exploring a largest sub-MIP N2 - We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. We apply domain propagation and conflict analysis to try to avoid infeasibilities and learn from them, respectively. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib. It turns out that the majority of these instances allow for small covers. Although general in nature, the heuristic appears most promising for MIQCPs, and complements nicely with existing root node heuristics in different state-of-the-art solvers. T3 - ZIB-Report - 12-07 KW - Primal Heuristic KW - Mixed-Integer Nonlinear Programming KW - Large Neighborhood Search KW - Mixed-Integer Quadratically Constrained Programming KW - Nonconvex Optimization Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14631 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Hobbie, Hannes A1 - Schönheit, David A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Möst, Dominik T1 - A massively parallel interior-point solver for linear energy system models with block structure N2 - Linear energy system models are often a crucial component of system design and operations, as well as energy policy consulting. Such models can lead to large-scale linear programs, which can be intractable even for state-of-the-art commercial solvers|already the available memory on a desktop machine might not be sufficient. Against this backdrop, this article introduces an interior-point solver that exploits common structures of linear energy system models to efficiently run in parallel on distributed memory systems. The solver is designed for linear programs with doubly bordered block-diagonal constraint matrix and makes use of a Schur complement based decomposition. Special effort has been put into handling large numbers of linking constraints and variables as commonly observed in energy system models. In order to handle this strong linkage, a distributed preconditioning of the Schur complement is used. In addition, the solver features a number of more generic techniques such as parallel matrix scaling and structure-preserving presolving. The implementation is based on the existing parallel interior-point solver PIPS-IPM. We evaluate the computational performance on energy system models with up to 700 million non-zero entries in the constraint matrix, and with more than 200 million columns and 250 million rows. This article mainly concentrates on the energy system model ELMOD, which is a linear optimization model representing the European electricity markets by the use of a nodal pricing market clearing. It has been widely applied in the literature on energy system analyses during the recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models. T3 - ZIB-Report - 19-41 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74321 SN - 1438-0064 N1 - In the meantime, this report got published as a journal article: https://opus4.kobv.de/opus4-zib/frontdoor/index/index/searchtype/authorsearch/author/Hannes+Hobbie/docId/8191/start/1/rows/10 Please use this journal reference when citing this work. ER - TY - GEN A1 - D'Andreagiovanni, Fabio A1 - Gleixner, Ambros T1 - Towards an accurate solution of wireless network design problems N2 - The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads to mixed-integer linear programs with constraint matrices containing tiny coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models. T3 - ZIB-Report - 16-12 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59010 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Kempke, Nils-Christian A1 - Koch, Thorsten A1 - Rehfeldt, Daniel A1 - Uslu, Svenja T1 - First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method N2 - In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix. T3 - ZIB-Report - 19-39 KW - block structure KW - energy system models KW - interior-point method KW - high performance computing KW - linear programming KW - parallelization KW - presolving KW - preprocessing Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74084 SN - 1438-0064 ER - TY - CHAP A1 - Sofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices T2 - 2020 IEEE/ACM 10th Workshop on Irregular Applications: Architectures and Algorithms (IA3) N2 - Fast domain propagation of linear constraints has become a crucial component of today's best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, more generally, on parallel architectures challenging. This is one of the main reasons why domain propagation in state-of-the-art solvers is single thread only. In this paper, we present a new algorithm for domain propagation which (a) avoids these problems and allows for an efficient implementation on GPUs, and is (b) capable of running propagation rounds entirely on the GPU, without any need for synchronization or communication with the CPU. We present extensive computational results which demonstrate the effectiveness of our approach and show that ample speedups are possible on practically relevant problems: on state-of-the-art GPUs, our geometric mean speed-up for reasonably-large instances is around 10x to 20x and can be as high as 195x on favorably-large instances. Y1 - 2020 U6 - https://doi.org/10.1109/IA351965.2020.00007 N1 - URL of the Slides: https://app.box.com/s/qy0pjmhtbm7shk2ypxjxlh2sj4nudvyu N1 - URL of the Abstract: http://www.pokutta.com/blog/research/2020/09/20/gpu-prob.html SP - 1 EP - 11 ER - TY - THES A1 - Gleixner, Ambros T1 - Exact and Fast Algorithms for Mixed-Integer Nonlinear Programming N2 - Mixed-integer nonlinear programming (MINLP) comprises the broad class of finite-dimensional mathematical optimization problems from mixed-integer linear programming and global optimization. The combination of the two disciplines allows us to construct more accurate models of real-world systems, while at the same time it increases the algorithmic challenges that come with solving them. This thesis presents new methods that improve the numerical reliability and the computational performance of global MINLP solvers. Since state-of-the-art algorithms for nonconvex MINLP fundamentally rely on solving linear programming (LP) relaxations, we address numerical accuracy directly for LP by means of LP iterative refinement: a new algorithm to solve linear programs to arbitrarily high levels of precision. The thesis is supplemented by an exact extension of the LP solver SoPlex, which proves on average 1.85 to 3 times faster than current state-of-the-art software for solving general linear programs exactly over the rational numbers. These methods can be generalized to quadratic programming. We study their application to numerically difficult multiscale LP models for metabolic networks in systems biology. To improve the computational performance of LP-based MINLP solvers, we show how the expensive, but effective, bound-tightening technique called optimization-based bound tightening can be approximated more efficiently via feasibility-based bound tightening. The resulting implementation increases the number of instances that can be solved and reduces the average running time of the MINLP solver SCIP by 17-19% on hard mixed-integer nonlinear programs. Last, we present branching rules that exploit the presence of nonlinear integer variables, i.e., variables both contained in nonlinear terms and required to be integral. The new branching rules prefer integer variables when performing spatial branching, and favor variables in nonlinear terms when resolving integer infeasibility. They reduce the average running time of SCIP by 17% on affected instances. Most importantly, all of the new methods enable us to solve problems which could not be solved before, either due to their numerical complexity or because of limited computing resources. Y1 - 2015 UR - http://dx.doi.org/10.14279/depositonce-4938 SN - 978-3-8325-4190-3 PB - Logos Verlag Berlin ER - TY - JOUR A1 - Šofranac, Boro A1 - Gleixner, Ambros A1 - Pokutta, Sebastian T1 - Accelerating domain propagation: An efficient GPU-parallel algorithm over sparse matrices JF - Parallel Computing N2 - • Currently, domain propagation in state-of-the-art MIP solvers is single thread only. • The paper presents a novel, efficient GPU algorithm to perform domain propagation. • Challenges are dynamic algorithmic behavior, dependency structures, sparsity patterns. • The algorithm is capable of running entirely on the GPU with no CPU involvement. • We achieve speed-ups of around 10x to 20x, up to 180x on favorably-large instances. Y1 - 2022 U6 - https://doi.org/10.1016/j.parco.2021.102874 VL - 109 SP - 102874 ER - TY - GEN A1 - Gleixner, Ambros A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gemander, Patrick A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 5.0 N2 - This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 % faster overall and 23 % faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG. T3 - ZIB-Report - 17-61 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66297 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Lindner, Niels A1 - Roth, Sarah T1 - A Concurrent Approach to the Periodic Event Scheduling Problem N2 - We introduce a concurrent solver for the periodic event scheduling problem (PESP). It combines mixed integer programming techniques, the modulo network simplex method, satisfiability approaches, and a new heuristic based on maximum cuts. Running these components in parallel speeds up the overall solution process. This enables us to significantly improve the current upper and lower bounds for all benchmark instances of the library PESPlib. T3 - ZIB-Report - 19-07 KW - Periodic Event Scheduling Problem KW - Periodic Timetabling KW - Mixed Integer Programming Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71907 SN - 1438-0064 ER - TY - JOUR A1 - Hendel, Gregor T1 - Adaptive Large Neighborhood Search for Mixed Integer Programming JF - Mathematical Programming Computation N2 - Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver learns adaptively which LNS heuristics work best for the MIP problem at hand in order to concentrate its limited computational budget. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) for MIP, a primal heuristic that acts a framework for eight popular LNS heuristics such as Local Branching and Relaxation Induced Neighborhood Search (RINS). We distinguish the available LNS heuristics by their individual search domains, which we call neighborhoods. The decision which neighborhood should be executed is guided by selection strategies for the multi armed bandit problem, a related optimization problem during which suitable actions have to be chosen to maximize a reward function. In this paper, we propose an LNS-specific reward function to learn to distinguish between the available neighborhoods based on successful calls and failures. A second, algorithmic enhancement is a generic variable fixing priorization, which ALNS employs to adjust the subproblem complexity as needed. This is particularly useful for some neighborhoods which do not fix variables by themselves. The proposed primal heuristic has been implemented within the MIP solver SCIP. An extensive computational study is conducted to compare different LNS strategies within our ALNS framework on a large set of publicly available MIP instances from the MIPLIB and Coral benchmark sets. The results of this simulation are used to calibrate the parameters of the bandit selection strategies. A second computational experiment shows the computational benefits of the proposed ALNS framework within the MIP solver SCIP. Y1 - 2018 ER - TY - CHAP A1 - Witzig, Jakob A1 - Berthold, Timo A1 - Heinz, Stefan T1 - A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming T2 - Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019 N2 - Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis. The main contribution of this short paper is twofold. Firstly, we present the first computational study regarding the impact of dual ray analysis on convex and nonconvex MINLPs. In that context, we introduce a modified generation of infeasibility proofs that incorporates linearization cuts that are only locally valid. Secondly, we describe an extension of conflict analysis that works directly with the nonlinear relaxation of convex MINLPs instead of considering a linear relaxation. This is work-in-progress, and this short paper is meant to present first theoretical considerations without a computational study for that part. Y1 - 2019 U6 - https://doi.org/10.1007/978-3-030-19212-9_6 VL - 11494 SP - 84 EP - 94 PB - Springer ER - TY - CHAP A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakayamaa, Yuji A1 - Wakui, Tetsuya T1 - Optimal Design of a Gas Turbine Cogeneration Plant by a Hierarchical Optimization Method With Parallel Computing T2 - ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition N2 - To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. The authors have proposed a MILP method utilizing the hierarchical relationship between design and operation variables to solve the optimal design problems of energy supply systems efficiently. In addition, some strategies to enhance the computation efficiency have been adopted: bounding procedures at both the levels and ordering of the optimal operation problems at the lower level. In this paper, as an additional strategy to enhance the computation efficiency, parallel computing is adopted to solve multiple optimal operation problems in parallel at the lower level. In addition, the effectiveness of each and combinations of the strategies adopted previously and newly is investigated. This hierarchical optimization method is applied to an optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified through some case studies. Y1 - 2018 UR - http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=2700845 VL - 3 ER - TY - CHAP A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakayama, Yuki A1 - Wakui, Tetsuya T1 - Model Reduction by Time Aggregation for Optimal Design of Energy Supply Systems by an MILP Hierarchical Branch and Bound Method T2 - Proceedings of the 31st International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2018) N2 - Mixed-integer linear programming (MILP) methods have been applied widely to optimal design of energy supply systems. A hierarchical MILP method has been proposed to solve such optimal design problems effi- ciently. An original problem has been solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of one another at the lower level. In addition, some strategies have been proposed to enhance the computation efficiency furthermore. In this paper, a method of reducing model by time aggregation is proposed as a novel strategy to search design candidates efficiently in the relaxed optimal design problem at the upper level. In addition, the previous strategies are modified in accordance with the novel strategy. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solu- tion. The method can decrease the number of design variables and constraints at the upper level, and thus may decrease the computation time at the upper level. Through a case study on the optimal design of a gas turbine cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency in comparison and combination with the modified previous strategies. Y1 - 2018 ER - TY - CHAP A1 - Berthold, Timo A1 - Stuckey, Peter A1 - Witzig, Jakob T1 - Local Rapid Learning for Integer Programs T2 - Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019 N2 - Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn information to support the remaining MIP solve. This has been demonstrated to be beneficial for binary programs. In this paper, we extend the idea of Rapid Learning to integer programs, where not all variables are restricted to the domain {0, 1}, and rather than just running a rapid CP search at the root, we will apply it repeatedly at local search nodes within the MIP search tree. To do so efficiently, we present six heuristic criteria to predict the chance for local Rapid Learning to be successful. Our computational experiments indicate that our extended Rapid Learning algorithm significantly speeds up MIP search and is particularly beneficial on highly dual degenerate problems. Y1 - 2019 U6 - https://doi.org/10.1007/978-3-030-19212-9_5 VL - 11494 SP - 67 EP - 83 PB - Springer ER - TY - JOUR A1 - Bestuzheva, Ksenia A1 - Hijazi, Hassan A1 - Coffrin, Carleton T1 - Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching JF - INFORMS Journal on Computing N2 - This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the Convex Quadratic relaxation of the Optimal Transmission Switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the Optimal Transmission Switching problem in Power Systems. Using the proposed improvements, along with bound propagation, on 23 medium-size test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on 5 instances. The tightened model has promising computational results when compared to state-of-the-art formulations. Y1 - 2019 U6 - https://doi.org/https://doi.org/10.1287/ijoc.2019.0900 VL - 32 IS - 3 SP - 682 EP - 696 PB - INFORMS Institute for Operations Research and the Management Sciences CY - 5521 Research Park Drive, Suite 200, Catonsville, MD 21228 USA ER - TY - CHAP A1 - Anderson, Daniel A1 - Hendel, Gregor A1 - Le Bodic, Pierre A1 - Viernickel, Jan Merlin T1 - Clairvoyant Restarts in Branch-and-Bound Search Using Online Tree-Size Estimation T2 - AAAI-19: Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence N2 - We propose a simple and general online method to measure the search progress within the branch-and-bound algorithm, from which we estimate the size of the remaining search tree. We then show how this information can help solvers algorithmically at runtime by designing a restart strategy for Mixed-Integer Programming (MIP) solvers that decides whether to restart the search based on the current estimate of the number of remaining nodes in the tree. We refer to this type of algorithm as clairvoyant. Our clairvoyant restart strategy outperforms a state-of-the-art solver on a large set of publicly available MIP benchmark instances. It is implemented in the MIP solver SCIP and will be available in future releases. Y1 - 2018 ER - TY - CHAP A1 - Gleixner, Ambros A1 - Steffy, Daniel T1 - Linear Programming using Limited-Precision Oracles T2 - A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019 N2 - Linear programming is a foundational tool for many aspects of integer and combinatorial optimization. This work studies the complexity of solving linear programs exactly over the rational numbers through use of an oracle capable of returning limited-precision LP solutions. It is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. Previous work has often considered oracles that provide solutions of an arbitrary specified precision. While this leads to polynomial-time algorithms, the level of precision required is often unrealistic for practical computation. In contrast, our work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly. Y1 - 2019 U6 - https://doi.org/10.1007/978-3-030-17953-3_30 SP - 399 EP - 412 ER - TY - CHAP A1 - Serrano, Felipe T1 - Intersection cuts for factorable MINLP T2 - A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019 N2 - Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables. Y1 - 2019 U6 - https://doi.org/10.1007/978-3-030-17953-3_29 VL - 11480 SP - 385 EP - 398 ER - TY - THES A1 - Anderson, Lovis T1 - The Computation of the Volume of the Union of Polytopes via a Sweep-Plane Algorithm N2 - Das Thema dieser Arbeit ist ein Volumen-Algorithmus für die Vereinigung von Polytopen. Der Algorithmus basiert auf der Arbeit von Bieri und Nef. Er berechnet das Volumen der Vereinigung von Polytopen mit einem Sweep-Verfahren. Dabei wird eine Hyperebene im Raum verschoben und das Volumen auf der einen Seite der Hyperebene berechnet. Umso weiter die Hyperebene verschobe wird, desto größer ist auch der Halbraum. Unser Algorithmus berechnet das Volumen einer Vereinigung von Polytopen geschnitten mit dem Halbraum der Sweep-Ebene als eine Funktion abhängig von der Veschiebung. Ab einem gewissen Punkt liegt der Körper dabei komplett im Halbraum der Sweep-Ebene und das Volumen bleibt konstant. Unser Algorithmus unterscheidet sich in zwei Punkten von dem Algorithmus von Bieri und Nef. Erstens funktioniert er nur auf der Vereinigung von Polytopen, wohingegen der Algorithmus von Bieri und Nef für Nef-Polyeder funktioniert. Diese sind eine Verallgemeinerung von Polyedern, die auch die Klasse der Vereinigung von Polytopen umfasst. Für uns ist das allerdings kein Nachteil, da unsere Datensätze zu Vereinigungen von Polytopen führen. Zweitens ist unser Algorithmus in zwei Teile aufgeteilt. Im ersten Teil wird eine Datenstruktur entwickelt, aus der im zweiten Teil zusammen mit einer Richtung die Sweep-Ebenen-Volumenfunktion berechnet wird. Der Großteil der Komplexität liegt im ersten Teil des Algorithmus. Das hat den Vorteil, dass wir die Volumenfunktionen für viele verschiedene Richtungen berechnen können. So können Einblicke in die Struktur des Körpers gewonnen werden. Der Algorithmus beruht auf zwei verschiedenen Zerlegungsansätzen. Zuerst können wir mit Hilfe von Anordnungen von Hyperebenen eine Vereinigung von Polytopen in ihre Zellen zerlegen. Dabei berufen wir uns auf die Arbeit von Gerstner und Holtz, in der das Konzept der Positionsvektoren eingeführt wird. Diese nutzen wir um die Ecken und ihre benachbarten Zellen zu bestimmen. So erhalten wir eine Zerlegung unserer Vereinigung in Zellen, deren paarweise Schnitte kein Volumen haben. Das zweite Zerlegungskonzept ist die konische Zerlegung, wie sie von Lawrence eingeführt wurde. Mit Hilfe dieser können wir die Indikatorfunktion eines Polytops als die Summe der Indikatorfunktionen seiner Vorwärtskegel schreiben. Die Sweep-Ebenen Volumenfunktionen können dann leicht mit Hilfe einer altbekannten Formel für das Volumen von Simplices berechnet werden. Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71829 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores N2 - This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances. T3 - ZIB-Report - 15-53 KW - Mixed Integer Programming KW - Parallel processing KW - Node merging KW - Racing ParaSCIP KW - Ubiquity Generator Framework KW - MIPLIB Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56404 SN - 1438-0064 ER - TY - GEN A1 - Munguia, Lluis-Miquel A1 - Oxberry, Geoffrey A1 - Rajan, Deepak A1 - Shinano, Yuji T1 - Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs N2 - PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch & Bound (B&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores. T3 - ZIB-Report - 17-58 KW - PIPS-SBB, UG, Parallel Branch and Bound Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65517 SN - 1438-0064 IS - ZIB-Report 17-58 ER - TY - GEN ED - Borndörfer, Ralf ED - Storandt, Sabine T1 - Proceedings of the 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems N2 - Running and optimizing transportation systems give rise to very complex and large-scale optimization problems requiring innovative solution techniques and ideas from mathematical optimization, theoretical computer science, and operations research. Since 2000, the series of Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) workshops brings together researchers and practitioners who are interested in all aspects of algorithmic methods and models for transportation optimization and provides a forum for the exchange and dissemination of new ideas and techniques. The scope of ATMOS comprises all modes of transportation. The 18th ATMOS workshop (ATMOS’18) was held in connection with ALGO’18 and hosted by Aalto University in Helsinki, Finland, on August 23–24, 2018. Topics of interest were all optimization problems for passenger and freight transport, including, but not limited to, demand forecasting, models for user behavior, design of pricing systems, infrastructure planning, multi-modal transport optimization, mobile applications for transport, congestion modelling and reduction, line planning, timetable generation, routing and platform assignment, vehicle scheduling, route planning, crew and duty scheduling, rostering, delay management, routing in road networks, traffic guidance, and electro mobility. Of particular interest were papers applying and advancing techniques like graph and network algorithms, combinatorial optimization, mathematical programming, approximation algorithms, methods for the integration of planning stages, stochastic and robust optimization, online and real-time algorithms, algorithmic game theory, heuristics for real-world instances, and simulation tools. There were twenty-nine submissions from eighteen countries. All of them were reviewed by at least three referees in ninety-one reviews, among them five external ones, and judged on their originality, technical quality, and relevance to the topics of the workshop. Based on the reviews, the program committee selected sixteen submissions to be presented at the workshop (acceptance rate: 55%), which are collected in this volume in the order in which they were presented. Together, they quite impressively demonstrate the range of applicability of algorithmic optimization to transportation problems in a wide sense. In addition, Dennis Huisman kindly agreed to complement the program with an invited talk on Railway Disruption Management: State-of-the-art in practice and new research directions. Based on the reviews, Ralf Borndörfer, Marika Karbstein, Christian Liebchen, and Niels Lindner won the Best Paper Award of ATMOS’18 with their paper A simple way to compute the number of vehicles that Are required to operate a periodic timetable. In addition, we awarded Tomas Lidén the Best VGI Paper Award of ATMOS’18 for his paper Reformulations for railway traffic and maintenance planning. We would like to thank the members of the Steering Committee of ATMOS for giving us the opportunity to serve as Program Chairs of ATMOS’18, all the authors who submitted papers, Dennis Huisman for accepting our invitation to present an invited talk, the members of the Program Committee and the additional reviewers for their valuable work in selecting the papers appearing in this volume, our sponsors MODAL, TomTom, and VGIscience for their support of the prizes, and the local organizers for hosting the workshop as part of ALGO’18. We acknowledge the use of the EasyChair system for the great help in managing the submission and review processes, and Schloss Dagstuhl for publishing the proceedings of ATMOS’18 in its OASIcs series. Y1 - 2018 SN - ISBN 978-3-95977-096-5 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2018.0 PB - Dagstuhl Publishing, Saarbrücken/Wadern, Germany ER - TY - THES A1 - Nöckel, Celine T1 - Bidirectional A* Search on Time-Dependent Airway Networks N2 - This thesis deals with a new algorithm for finding Shortest Paths on Airway Networks. It is about a Bidirectional A* Search, a Greedy algorithm exploring a network from two sides instead of one. We will use it to solve the so-called 'Horizontal Flight Trajectory Problem', where one searches for an aircraft trajectory between two airports of minimal costs on an Airway Network. The given network will be modeled as a directed graph and in order to reflect reality we concentrate on the dynamic version. Here a timedependent cost function for all arcs is integrated, that shall represent the winds blowing. This way we model the Horizontal Flight Trajectory Problem mathematically as a Time-Dependent Shortest Path Problem. The basic algorithm idea derives from the algorithm presented in 'Bidirectional A* Search on Time-Dependent Road Networks' [1], where a similar setting is elaborated for road networks. The algorithm procedure bears on a modified generalization of Dijkstra's algorithm, made bidirectional and improved in several aspects. As for the backwards search the arrival times are not known in advance, the reversed graph it occurs on has to be weighted by a lower bound. Contrary to the static case the forwards search still has to go on, when they 'meet' in one node. In the static case, the shortest path would have been found at this point. For road networks the TDSPP is well-studied, for airway networks cannot be found as much in literature. In order to test efficiency, we implement Dijkstra's algorithm, unidirectional A* Search and Bidirectional A* Search. We draw up how potential functions for the static case could look like and that with a suitable potential A* Search with works approx. 7 times faster than Dijkstra in the dynamic case. Our computations lead also to the result, that the unidirectional A* Search works even better on the network than our new bidirectional approach does. On average it labels fewer nodes and also yields 1,7 times faster to the solutions. For assessing the efficiency of the different algorithms we compare the running times and to exclude processor characteristics we consider also the set labels relative to the labels on the resulting optimal path. In addition, we present examples of routes visually and explain shortly why there appear local differences regarding performance of A* Search and Bidirectional A* Search. Y1 - 2018 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Winkler, Michael T1 - Structure-driven fix-and-propagate heuristics for mixed integer programming JF - Mathematical Programming Computation N2 - Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved first as an LP, and then as an auxiliary MIP if the rounded LP solution does not provide a feasible solution already. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about 60 % of the instances and by this, help to improve several performance measures for MIP solvers, including the primal integral and the average solving time. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-019-00159-1 VL - 11 IS - 4 SP - 675 EP - 702 PB - Springer CY - Berlin Heidelberg ER - TY - THES A1 - Elijazyfer, Ziena T1 - Längenbeschränkte Teilgraphenbildung zur Maut-Kontrollstreckenoptimierung Y1 - 2018 ER - TY - THES A1 - Schreck, Vanessa T1 - Algorithmic Analysis of the Graph Segmentation Problem Y1 - 2018 ER - TY - THES A1 - Vornberger, Leo T1 - Approximation von Windkomponenten in der Luftfahrt durch lineare Interpolation N2 - Das Wind-Interpolation-Problem (WIP) ist ein bisher selten diskutiertes Problem der Flugplanungsoptimierung, bei dem es darum geht, Wind-Komponenten auf einer Luftstraße zu approximieren. Anhand von Winddaten, die vektoriell an den Gitterpunkten eines den Globus umspannenden Gitters vorliegen, soll bestimmt werden, wie viel Wind entlang der Luftstraße und quer zu ihr weht. Thema dieser Arbeit ist ein Spezialfall des WIP, nämlich das statische WIP auf einer Planfläche (SWIPP). Dazu wird zuerst ein Algorithmus besprochen, der das SWIPP zwar löst, aber einem Ansatz zugrunde liegt, der bei genauerem Hinsehen nicht sinnvoll erscheint: hier wird Wind zwischen vier Punkten interpoliert, wozu es keine triviale Methode gibt. Ähnlich zu diesem Algorithmus, der heute als State-of-the-Art gilt, wird als Ergebnis dieser Arbeit ein neuer Algorithmus vorgestellt, der das SWIPP akkurater und schneller löst. Hier wird deutlich seltener auf die Interpolation zwischen vier Punkten zurückgegriffen - stattdessen wird fast immer linear zwischen zwei Punkten interpoliert. Die Algorithmen zum Lösen des SWIPP werden auf ihre Genauigkeit, asymptotische Laufzeit und Geschwindigkeit untersucht und verglichen. Als Testareal dienen zum einen echte Wetterdaten sowie das Luftstraßennetz, das die Erde umspannt, und zum anderen ein eigens generiertes Windfeld und fiktive Luftstraßen. Es wird gezeigt, dass der hier vorgestellte Algorithmus die State-of-the-Art-Variante in allen genannten Aspekten übertrifft. Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71570 ER - TY - THES A1 - Akil, Fatima T1 - Lineare Gleichungssysteme modulo T N2 - Mit dem Voranschreiten der Technologie erhalten die öffentlichen Verkehrsmittel eine größere Bedeutung. Die Beförderung mehrerer Personen eröffnet der Gesellschaft viele Möglichkeiten, unter Anderem den Vorteil der Zeitersparnis. Die Dauer des Verkehrswegs mit öffentlichen Verkehrsmitteln ist häufig geringer, als die mit individuellen Verkehrsmitteln. Jedes öffentliche Transportmittel ist mit einem Fahrplan versehen. Dieser bietet Passagieren, die öffentliche Verkehrsmittel öfter nutzen, eine Strukturierung und Planung ihrer Zeit. Dabei lassen sich Taktfahrpläne aufgrund ihres periodischen Verhaltens leicht einprägen. Dieses periodische Verhalten ist durch mathematische Modellierungen darstellbar. Das persönliche Nutzverhalten vieler Bürger im Personenverkehr ist auf die öffentlichen Verkehrsmittel beschränkt. Diese beinhalten im Gegensatz zum individuellen Verkehrsmittel eine Wartezeit. Dabei stellt sich die Frage, ob man anhand mathematischer Modelle diese Wartezeit minimieren kann. Eine bekannte mathematische Modellierung dieses Problems ist das Periodic Event Scheduling Problem (PESP). Die optimale Planung eines periodischen Taktfahrplanes steht im Vordergrund. Während ich dieses Problem betrachtet habe, wurde ich auf das Rechnen mit linearen Gleichungssystemen modulo T aufmerksam. Bei periodischen Taktfahrplänen wird ein einheitliches zeitliches Muster, welches sich nach T Minuten wiederholt, betrachtet. Das dabei zu betrachtende Lösungsproblem eröffnet ein Teilgebiet der Mathematik, welches bislang nicht im Vordergrund stand: Das Lösen linearer Gleichungen modulo T, wobei T für die Zeit in Minuten steht und somit 60 ist. Da 60 keine Primzahl ist, kann – wie im Laufe der Arbeit präsentiert – das lineare Gleichungssystem nicht mehr über einen Körper gelöst werden. Lineare Gleichungssysteme werden nun über Nicht-Körpern betrachtet. Die Literatur weist sowohl im deutschsprachigem als auch im englischsprachigen Raum wenig Umfang bezüglich linearer Gleichungssysteme über Nicht-Körper auf. Der Bestand an Fachliteratur bezüglich den Themen lineare diophantische Gleichungssysteme, Hermite- Normalform und Smith-Normalform ist zurzeit gering, dennoch erreichbar, beispielsweise in [1], welches in dieser Bachelorarbeit genutzt wurde. Insbesondere wurde ich bei der Suche nach geeigneter Literatur zu linearen Gleichungssystemen über Restklassenringe, die keinen Körper bilden, nicht fündig. Dabei recherchierte ich sowohl in den Universitätsbibliotheken als auch in webbasierenden Suchmaschinen. Aufgrund dem geringen Bestand an Fachliteratur in diesem Kontext, war ich gezwungen, an vielen Stellen eigene logische Verknüpfungen zu konzipieren und zu beweisen. Dies brachte viele Schwierigkeiten mit sich, die mit bestmöglichem Verständnis bearbeitet wurden. Abseits der Zugänglichkeit der Literatur, finde ich es sehr überraschend, dass sich viele Professoren der Mathematik mit diesem Themenbereich nicht beschäftigten. Insbesondere gingen von den Dozenten, die ich um Literaturempfehlung bat, kein Werk aus. Damit wurde das Thema "Lineare Gleichungssysteme Modulo T" einerseits eine große Herausforderung, andererseits eine große Motivation, da ich mit dieser Bachelorarbeit vielen Interessenten der Mathematik als Sekundärliteratur dienen kann. Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71560 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika A1 - Liebchen, Christian A1 - Lindner, Niels T1 - A Simple Way to Compute the Number of Vehicles That Are Required to Operate a Periodic Timetable N2 - We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [9], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem. In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same. T3 - ZIB-Report - 18-38 KW - Vehicle scheduling KW - Periodic timetabling KW - Bipartite matching Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69688 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Weider, Steffen T1 - A Hypergraph Model for Railway Vehicle Rotation Planning N2 - We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the ``regularity'' of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved. T3 - ZIB-Report - 11-36 KW - Rolling Stock Planning, Hypergraph Modeling, Integer Programming, Column Generation, Rapid Branching Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0030-drops-32746 SN - 1438-0064 ER - TY - THES A1 - Oleynikova, Ekaterina T1 - Mathematical optimization of joint order batching and picker routing problems N2 - In this thesis we study order picking optimization problems for a two-blocks rectangle warehouse layout. We present combinatorial formulations and linear programming models based on the Steiner graph representation for order batching, picker routing, and joint order batching and picker routing problems. A special case of the latter is considered. This case assumes that each order contains exactly one item and each item can be picked from different possible locations in a warehouse. The underlying optimization problem is called joint multi-location order batching and picker routing problem (JMLOBPRP). Since having only one-item orders turns the JMLOBPRP into a special case of a capacitated vehicle routing problem, we suggest to implement algorithmic approaches for those to solve the JMLOBPRP. In particular, we define the JMLOBPRP as a generalization of the resource constrained assignment problem, for which a regional search method exists. The intention of the thesis is to investigate how a relaxation of the JMLOBPRP, a so-called group assignment problem (GrAP), can be solved following the ideas of regional search. We present a mathematical model of the GrAP and prove that it is NP-hard. Furthermore, we propose a novel heuristic algorithm for the GrAP. We call this method a network search algorithm, as it is based on a Lagrangian relaxation of the GrAP, which is solved by the network simplex method. On each its iteration network search examines a solution region suggested by the network simplex algorithm and improves the incumbent solution. Numerical experiments are conducted to assess a performance of the network search method. We create more realistic problem instances. The proposed algorithm is compared to the integer optimal solution of the GrAP and optimal fractional solution of its linear relaxation. Both computed using the commercial linear solver Gurobi. Our experiments show that the developed network search algorithm leads to the hight-quality solution within a short computing time. The results obtained testing large problem instances which cannot be solved by Gurobi within a reasonable computing time, show that the network search method provides a solution approach which can be used in practice. Y1 - 2018 ER - TY - THES A1 - Wyczik, Christopher T1 - Optimierung von Deployment- und Umgebungs-Integrität durch ein dezentrales Konfigurationsrepository auf Basis einer Blockchain N2 - Viele Firmen nutzen für ihre eigenen Softwareentwicklungen verschiedene Server mit unterschiedlichen Konfigurationen. Manche Server werden dazu eingestzt das Verhalten einer Software in einer bestimmten Umgebung zu testen und andere dienen zur Bereitstellung der Software für den Endnutzer. Hierbei ist es wichtig, dass die Konfiguration der Server regelmäßig überprüft wird. Eine solche Sicherstellung der Deployment- und Umgebungs-Integrität wird meistens durch eine Mitarbeiter der Firma oder durch einen externen Dienstleister erbracht. D.h. die Firma muss sich auf die Zuverlässigkeit eines Mitarbeiters oder einer externen Dienstleistung verlassen, bie zunehmender Komplexität ist sie sogar abhängig. Das Ziel dieser Masterarbeit ist es, zu untersuchen, ob die Sicherstellung der Deployment- und Umgebungs-Integrität durch automatisierte kryptografische Beweise, anstelle externer Dienstleistungen oder anderer Mitarbeiter, gewährleistet werden kann. Als Anwendungsfall dient die Toll Collect GmbH. Im ersten Teil dieser Arbeit wird das Matheamtische Modell einer Blockchain erläutert. die Blockchain wurde erstmals in einem Dokument, welches unter dem Pseudonym Satoshi Nakamoto veröffentlicht wurde, beschrieben. Die erste große Anwendungen der Blockchain ist das dezentrale Zahlungssystem Bitcoin. Im zweiten Teil dieser Arbeit wird die Softwareimplementierung vorgestellt, welche im Rahmen dieser Arbeit entstanden ist. Mithilfe dieses Programms kann die Deployment- und Umgebungs-Integrität durch eine heirführ entwickelte Blockchainlösung dezentralisiert werden. Es wird außerdem der Übergang vom Mathematischen Modell zur Implementierung gezeigt. Y1 - 2018 ER - TY - THES A1 - Mett, Fabian T1 - Über die optimale Platzierung von Ladestationen für Elektrobusse N2 - In dieser Arbeit wird die Platzierung von Ladestationen für Elektrobusse untersucht. Dabei soll für eine Menge an gegebenen Linien eine Menge an Ladestationen gefunden werden, sodass jede Linie mit Nutzung der Ladestationen befahren werden kann und gleichzeitig die Kosten minimal sind. Zunächst wird der Fall betrachtet, dass die Batterie an jeder Station komplett vollgeladen werden könnte. Dieses Problem stellt sich als NP-schwer heraus. Für einige einfachere Fällewerden zudem Algorithmen entwickelt und untersucht. Anschließend wird der Fall einer unbegrenzt großen Batterie betrachtet, wobei an jeder Station derselbe Wert geladen werden kann. Auch dieses Problem ist NP-schwer. Erneut werden Algorithmen zur Lösung vereinfachter Problemstellungen gegeben und analysiert. Wird zudem angenommen, an jeder Station würde ein individueller Wert geladen, so ist das Problem schon für nur eine einzige Linie NP-schwer. Dennoch werden zwei exakte und ein approximierender Algorithmus entwickelt. Schließlich wird eine Batteriekapazität hinzugefügt und die zuvor entwickelten Algorithmen werden entsprechend angepasst. Für die abschließende Problemdefinition werden verschiedene Batteriegrößen betrachtet und es werden zwei gemischt-ganzzahlige Programme aufgestellt. Anhand von existierenden Buslinien aus Berlin werden diese untersucht. Dabei stellt sich heraus, dass die Batteriekosten einen deutlich größeren Teil der Kosten ausmachen als die Ladestationen. Zudem sollten kleinere Batterien statt größerer und mehr Ladestationen genutzt werden. Y1 - 2018 ER - TY - THES A1 - Husemann, Christoph T1 - Multimodales Routing mit Leihfahrradsystemen am Beispiel Berlins N2 - The aim of multimodal routing is to extract the best integrated journey of multiple transportation networks. The integration of bike rental networks is challenging particularly with respect to recognizing a valid path dependent on real-time availability of bike boarding and alighting places. In this work a common model for station-based bike rental networks extended with boarding possibilities for free floating bikes is presented. Moreover a new model for alighting inside a free floating area is introduced. In addition, a prototype of multimodal routing with a bike rental network in Berlin is developed by extending the OpenTripPlanner software. Due to recent public dispute about bike rental networks in Berlin, an examination about speed-up potential of an integrated bike rental network in the public transit of Berlin is provided. Y1 - 2018 ER - TY - THES A1 - Krug, Matthias T1 - Analysis of the Shortest Path Problem with Piecewise Constant Crossing Costs Y1 - 2018 ER - TY - GEN A1 - Berthold, Timo A1 - Stuckey, Peter A1 - Witzig, Jakob T1 - Local Rapid Learning for Integer Programs N2 - Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn information to support the remaining MIP solve. This has been demonstrated to be beneficial for binary programs. In this paper, we extend the idea of Rapid Learning to integer programs, where not all variables are restricted to the domain {0, 1}, and rather than just running a rapid CP search at the root, we will apply it repeatedly at local search nodes within the MIP search tree. To do so efficiently, we present six heuristic criteria to predict the chance for local Rapid Learning to be successful. Our computational experiments indicate that our extended Rapid Learning algorithm significantly speeds up MIP search and is particularly beneficial on highly dual degenerate problems. T3 - ZIB-Report - 18-56 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71190 SN - 1438-0064 ER - TY - GEN A1 - Hendel, Gregor T1 - Adaptive Large Neighborhood Search for Mixed Integer Programming N2 - Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver learns adaptively which LNS heuristics work best for the MIP problem at hand in order to concentrate its limited computational budget. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) for MIP, a primal heuristic that acts a framework for eight popular LNS heuristics such as Local Branching and Relaxation Induced Neighborhood Search (RINS). We distinguish the available LNS heuristics by their individual search domains, which we call neighborhoods. The decision which neighborhood should be executed is guided by selection strategies for the multi armed bandit problem, a related optimization problem during which suitable actions have to be chosen to maximize a reward function. In this paper, we propose an LNS-specific reward function to learn to distinguish between the available neighborhoods based on successful calls and failures. A second, algorithmic enhancement is a generic variable fixing priorization, which ALNS employs to adjust the subproblem complexity as needed. This is particularly useful for some neighborhoods which do not fix variables by themselves. The proposed primal heuristic has been implemented within the MIP solver SCIP. An extensive computational study is conducted to compare different LNS strategies within our ALNS framework on a large set of publicly available MIP instances from the MIPLIB and Coral benchmark sets. The results of this simulation are used to calibrate the parameters of the bandit selection strategies. A second computational experiment shows the computational benefits of the proposed ALNS framework within the MIP solver SCIP. T3 - ZIB-Report - 18-60 KW - mixed integer programming KW - primal heuristics KW - large neighborhood search KW - multi armed bandit problem Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71167 SN - 1438-0064 ER - TY - GEN A1 - Witzig, Jakob A1 - Berthold, Timo A1 - Heinz, Stefan T1 - A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming N2 - Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis. The main contribution of this short paper is twofold. Firstly, we present the first computational study regarding the impact of dual ray analysis on convex and nonconvex MINLPs. In that context, we introduce a modified generation of infeasibility proofs that incorporates linearization cuts that are only locally valid. Secondly, we describe an extension of conflict analysis that works directly with the nonlinear relaxation of convex MINLPs instead of considering a linear relaxation. This is work-in-progress, and this short paper is meant to present first theoretical considerations without a computational study for that part. T3 - ZIB-Report - 18-57 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71170 SN - 1438-0064 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Schulz, Christof A1 - Weider, Steffen T1 - The Rolling Stock Rotation Planning Problem under Revenue Considerations N2 - In many railway undertakings a railway timetable is offered that is valid for a longer period of time. At DB Fernverkehr AG, one of our industrial partners, this results in a summer and a winter timetable. For both of these timetables rotation plans, i.e., a detailed plan of railway vehicle movements is constructed as a template for this period. Sometimes there are be periods where you know for sure that vehicle capacities are not sufficient to cover all trips of the timetable or to transport all passenger of the trips. Reasons for that could be a heavy increase of passenger flow, a heavy decrease of vehicle availability, impacts from nature, or even strikes of some employees. In such events the rolling stock rotations have to be adapted. Optimization methods are particularly valuable in such situations in order to maintain a best possible level of service or to maximize the expected revenue using the resources that are still available. In most cases found in the literature, a rescheduling based on a timetable update is done, followed by the construction of new rotations that reward the recovery of parts of the obsolete rotations. We consider a different, novel, and more integrated approach. The idea is to guide the cancellation of the trips or reconfiguration of the vehicle composition used to operate a trip of the timetable by the rotation planning process, which is based on the mixed integer programming approach presented in Reuther (2017). The goal is to minimize the operating costs while cancelling or operating a trip with an insufficient vehicle configuration in sense of passenger capacities inflicts opportunity costs and loss of revenue, which are based on an estimation of the expected number of passengers. The performance of the algorithms presented in two case studies, including real world scenarios from DB Fernverkehr AG and a railway operator in North America. T3 - ZIB-Report - 19-01 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71339 SN - 1438-0064 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Schulz, Christof A1 - Weider, Steffen T1 - The Rolling Stock Rotation Planning Problem under Revenue Considerations T2 - Proceedings of the Rail Transport Demand Management Conference N2 - In many railway undertakings a railway timetable is offered that is valid for a longer period of time. At DB Fernverkehr AG, one of our industrial partners, this results in a summer and a winter timetable. For both of these timetables rotation plans, i.e., a detailed plan of railway vehicle movements is constructed as a template for this period. Sometimes there are be periods where you know for sure that vehicle capacities are not sufficient to cover all trips of the timetable or to transport all passenger of the trips. Reasons for that could be a heavy increase of passenger flow, a heavy decrease of vehicle availability, impacts from nature, or even strikes of some employees. In such events the rolling stock rotations have to be adapted. Optimization methods are particularly valuable in such situations in order to maintain a best possible level of service or to maximize the expected revenue using the resources that are still available. In most cases found in the literature, a rescheduling based on a timetable update is done, followed by the construction of new rotations that reward the recovery of parts of the obsolete rotations. We consider a different, novel, and more integrated approach. The idea is to guide the cancellation of the trips or reconfiguration of the vehicle composition used to operate a trip of the timetable by the rotation planning process, which is based on the mixed integer programming approach presented in Reuther (2017). The goal is to minimize the operating costs while cancelling or operating a trip with an insufficient vehicle configuration in sense of passenger capacities inflicts opportunity costs and loss of revenue, which are based on an estimation of the expected number of passengers. The performance of the algorithms presented in two case studies, including real world scenarios from DB Fernverkehr AG and a railway operator in North America. Y1 - 2018 ER - TY - CHAP A1 - Sagnol, Guillaume A1 - Schmidt genannt Waldschmidt, Daniel A1 - Tesch, Alexander T1 - The Price of Fixed Assignments in Stochastic Extensible Bin Packing T2 - WAOA 2018: Approximation and Online Algorithms N2 - We consider the stochastic extensible bin packing problem (SEBP) in which n items of stochastic size are packed into m bins of unit capacity. In contrast to the classical bin packing problem, the number of bins is fixed and they can be extended at extra cost. This problem plays an important role in stochastic environments such as in surgery scheduling: Patients must be assigned to operating rooms beforehand, such that the regular capacity is fully utilized while the amount of overtime is as small as possible. This paper focuses on essential ratios between different classes of policies: First, we consider the price of non-splittability, in which we compare the optimal non-anticipatory policy against the optimal fractional assignment policy. We show that this ratio has a tight upper bound of 2. Moreover, we develop an analysis of a fixed assignment variant of the LEPT rule yielding a tight approximation ratio of (1+e−1)≈1.368 under a reasonable assumption on the distributions of job durations. Furthermore, we prove that the price of fixed assignments, related to the benefit of adaptivity, which describes the loss when restricting to fixed assignment policies, is within the same factor. This shows that in some sense, LEPT is the best fixed assignment policy we can hope for. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-030-04693-4_20 VL - 11312 SP - 327 EP - 347 ER - TY - THES A1 - Jeschke, Björn-Marcel T1 - Alternativen zum Dijkstra Algorithmus in der (Nah-) Verkehrsoptimierung N2 - In dieser Arbeit betrachten wir das Problem, für den Fahrplan eines (Nah-) Verkehrsnetzes schnellste Wege zu berechnen. Da die Verkehrsmittel zu unterschiedlichen Zeiten von den einzelnen Haltestellen/Bahnhöfen abfahren, kann das Problem nicht ohne Weiteres mit einem „statischen“ Graphen modelliert werden. Es gibt zwei unterschiedliche Ansätze für dieses zeitabhängige Problem: Erstens können die verschiedenen An-/Abfahrtereignisse an einem Halt durch „Kopien“ dargestellt werden, das ist das zeit-expandierte Modell. Zweitens können die Gewichte der Kanten zeitabhängig sein, das ist das zeitabhängige Modell. Wir untersuchen in dieser Arbeit, wie der „klassische“ Dijkstra-Algorithmus und der A* Algorithmus mit einer geeigneten Heuristik im Vergleich abschneiden. Die gewählte Heuristik ist der Abstand zum Zielknoten, wenn die Abfahrtszeiten ignoriert werden. Nach unseren Untersuchungen zeigt sich, dass der A* Algorithmus dem Dijkstra-Algorithmus weit überlegen ist für genügend große Nahverkehrsnetze. Wir testen anhand der echten Verkehrsnetze von Berlin und Aachen. Unsere Berechnungen zeigen, dass die gewählte Heuristik besonders gut ist für Start- und Zielknoten, welche unabhängig von ihrer Distanz nur 1–2 verschiedene mögliche kürzeste Pfade für alle Zeitschritte haben. Dort ist der A* Algorithmus bis zu 20-mal schneller. Dies kommt aber nicht häufig in unseren Testinstanzen vor. Die einzelnen Laufzeitvergleich zeigen, dass der A* Algorithmus durchschnittlich 7-mal so schnell ist wie der Dikstra-Algorithmus. Y1 - 2017 ER - TY - THES A1 - Euler, Ricardo T1 - The Bienstock Zuckerberg Algorithm for the Rolling Stock Rotation Problem N2 - The design of rolling stock rotations is an important task in large-scale railway planning. This so-called rolling stock rotation problem (RSRP) is usually tackled using an integer programming approach. Markus Reuther did so in his dissertation [15] for the ICE railway network of DB ("Deutsche Bahn"). Due to the size of the network and the complexity of further technical requirements, the resulting integer problems tend to become very large and computationally involved. In this thesis, we tackle the linear programming relaxation of the RSRP integer program. We will do so by applying a modified version of an algorithm recently proposed by Dan Bienstock and Mark Zuckerberg [2] for the precedence constrained production scheduling problem that arises in open pit mine scheduling. This problem contains a large number of "easy" constraints and a relatively small number of "hard" constraints. We will see that a similar problem structure can also be found in the RSRP. The Bienstock-Zuckerberg algorithm relies on applying Lagrangian relaxation to the hard constraints as well as on partitioning the variable set. We propose three different partition schemes which try to exploit the specific problem structure of the RSRP. Furthermore, we will discuss the influence of primal degeneracy on the algorithm's performance, as well as possible merits of perturbating the right-hand side of the constraint matrix. We provide computational results to assess the performance of those approaches. Y1 - 2018 ER - TY - THES A1 - Wirsching, Marie T1 - Der Einfluss von Langzahlarithmetik auf das Gewichtsraumpolyeder in mehrkriterieller Optimierung N2 - Die Arbeit befasst sich mit einem gewichtsraumbasierten Algorithmus, der ganzzahlige und lineare Optimierungsprobleme mit mehreren Zielfunktionen löst und die Menge der unterstützt nicht dominierten Punkte ermittelt. Die dabei erzeugten Gewichtsraumpolyeder sind das entscheidende Mittel, um die gesuchte Lösungsmenge zu bestimmen. Aus softwaretechnischer Sicht sind numerische Ungenauigkeiten potentielle Fehlerquellen, die sich negativ auf das Endergebnis auswirken. Aus diesem Grund untersuchen wir anhand von Zuweisungs- und Rucksackinstanzen mit 3 Zielfunktionen, inwieweit der Gebrauch von Langzahlarithmetik die Gewichtsraumpolyeder und die damit verbundene Menge der unterstützt nicht dominierten Punkte beeinflusst. Y1 - 2018 ER - TY - GEN A1 - Beckenbach, Isabel A1 - Hatzel, Meike A1 - Wiederrecht, Sebastian T1 - The Tight Cut Decomposition of Matching Covered Uniformable Hypergraphs N2 - The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms. Kotzig, Lovász and Plummer developed a decomposition theory for graphs with perfect matchings and their corresponding polytopes known as the tight cut decomposition which breaks down every graph into a number of indecomposable graphs, so called bricks. For many properties that are of interest on graphs with perfect matchings, including the description of the perfect matching polytope, it suffices to consider these bricks. A key result by Lovász on the tight cut decomposition is that the list of bricks obtained is the same independent of the choice of tight cuts made during the tight cut decomposition procedure. This implies that finding a tight cut decomposition is polynomial time equivalent to finding a single tight cut. We generalise the notions of a tight cut, a tight cut contraction and a tight cut decomposition to hypergraphs. By providing an example, we show that the outcome of the tight cut decomposition on general hypergraphs is no longer unique. However, we are able to prove that the uniqueness of the tight cut decomposition is preserved on a slight generalisation of uniform hypergraphs. Moreover, we show how the tight cut decomposition leads to a decomposition of the perfect matching polytope of uniformable hypergraphs and that the recognition problem for tight cuts in uniformable hypergraphs is polynomial time solvable. T3 - ZIB-Report - 18-61 KW - uniform hypergraphs KW - perfect matchings KW - tight cuts Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71149 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Reduction-based exact solution of prize-collecting Steiner tree problems T3 - ZIB-Report - 18-55 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70958 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Building Optimal Steiner Trees on Supercomputers by using up to 43,000 Cores N2 - SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively par- allel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best known solutions to instances from the bench- mark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been con- siderably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB. T3 - ZIB-Report - 18-58 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71118 SN - 1438-0064 ER - TY - GEN A1 - Serrano, Felipe T1 - Intersection cuts for factorable MINLP N2 - Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables. T3 - ZIB-Report - 18-59 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71105 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Egerer, Ascan A1 - Karbstein, Marika A1 - Messerschmidt, Ralf A1 - Perez, Marc A1 - Pfisterer, Steven A1 - Strauß, Petra T1 - Kombilösung: Optimierung des Liniennetzes in Karlsruhe N2 - Wir beschreiben die Optimierung des Nahverkehrsnetzes der Stadt Karlsruhe im Zusammmenhang mit den Baumaßnahmen der sogenannten Kombilösung. T3 - ZIB-Report - 18-45 KW - ÖPNV KW - Linienplanung Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69677 SN - 1438-0064 ER - TY - THES A1 - Wegscheider, Fabian T1 - Exploiting Symmetry in Mixed-Integer Nonlinear Programming Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77055 ER - TY - GEN A1 - Becker, Kai-Helge A1 - Hiller, Benjamin T1 - Efficient Enumeration of Acyclic Graph Orientations with Sources or Sinks Revisited N2 - In a recent paper, Conte et al. [CGMR2017] presented an algorithm for enumerating all acyclic orientations of a graph G=(V,E) with a single source (and related orientations) with delay O(|V||E|). In this paper we revisit the problem by going back to an early paper by de Fraysseix et al. [FMR1995], who proposed an algorithm for enumerating all bipolar orientations of a graph based on a recursion formula. We first formalize de Fraysseix et al.'s algorithm for bipolar orientations and determine that its delay is also O(|V||E|). We then apply their recursion formula to the case of Conte et al.'s enumeration problem and show that this yields a more efficient enumeration algorithm with delay O(\sqrt(|V|)|E|). Finally, a way to further streamline the algorithm that leads to a particularly simple implementation is suggested. T3 - ZIB-Report - 20-05 KW - acyclic orientations KW - enumeration algorithm KW - multiple sources and sinks KW - bipolar orientations Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77684 SN - 1438-0064 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Olthoff, Mats T1 - A Solution Approach to the Vehicle Routing Problem with Perishable Goods N2 - This paper focuses on a special case of vehicle routing problem where perishable goods are considered. Deliveries have to be performed until a due date date, which may vary for different products. Storing products is prohibited. Since late deliveries have a direct impact on the revenues for these products, a precise demand prediction is important. In our practical case the product demands and vehicle driving times for the product delivery are dependent on weather conditions, i.e., temperatures, wind, and precipitation. In this paper the definition and a solution approach to the Vehicle Routing Problem with Perishable Goods is presented. The approach includes a procedure how historical weather data is used to predict demands and driving times. Its run time and solution quality is evaluated on different data sets given by the MOPTA Competition 2018. T3 - ZIB-Report - 20-03 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77020 SN - 1438-0064 ER - TY - JOUR A1 - Witzig, Jakob A1 - Gleixner, Ambros T1 - Conflict-Driven Heuristics for Mixed Integer Programming JF - INFORMS Journal on Computing N2 - Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. Here, we combine both concepts in two different ways. First, we develop a diving heuristic that targets the generation of valid conflict constraints from the Farkas dual. We show that in the primal this is equivalent to the optimistic strategy of diving towards the best bound with respect to the objective function. Secondly, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classical coefficient diving. The computational performance of both methods is evaluated using an implementation in the source-open MIP solver SCIP. Experiments are carried out on publicly available test sets including Miplib 2010 and Cor@l. Y1 - 2020 U6 - https://doi.org/10.1287/ijoc.2020.0973 VL - 33 IS - 2 SP - 706 EP - 720 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Hendel, Gregor A1 - Gamrath, Gerald A1 - Achterberg, Tobias A1 - Bastubbe, Michael A1 - Berthold, Timo A1 - Christophel, Philipp M. A1 - Jarck, Kati A1 - Koch, Thorsten A1 - Linderoth, Jeff A1 - Lübbecke, Marco A1 - Mittelmann, Hans A1 - Ozyurt, Derya A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Shinano, Yuji T1 - MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library JF - Mathematical Programming Computation N2 - We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of over 5,000 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, the compilation of these sets was done using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encoded requirements on diversity and balancedness with respect to instance features and performance data. Y1 - 2021 U6 - https://doi.org/10.1007/s12532-020-00194-3 VL - 13 IS - 3 SP - 443 EP - 490 ER - TY - CHAP A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Olthoff, Mats T1 - A Solution Approach to the Vehicle Routing Problem with Perishable Goods T2 - Operations Research 2019 Proceedings N2 - This paper focuses on a special case of vehicle routing problem where perishable goods are considered. Deliveries have to be performed until a due date date, which may vary for different products. Storing products is prohibited. Since late deliveries have a direct impact on the revenues for these products, a precise demand prediction is important. In our practical case the product demands and vehicle driving times for the product delivery are dependent on weather conditions, i.e., temperatures, wind, and precipitation. In this paper the definition and a solution approach to the Vehicle Routing Problem with Perishable Goods is presented. The approach includes a procedure how historical weather data is used to predict demands and driving times. Its run time and solution quality is evaluated on different data sets given by the MOPTA Competition 2018. Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77020 ER - TY - CHAP A1 - Serrano, Felipe A1 - Muñoz, Gonzalo T1 - Maximal Quadratic-Free Sets T2 - Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020 N2 - The intersection cut paradigm is a powerful framework that facilitates the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a simplicial conic relaxation of S and an S-free set: a convex zone whose interior does not intersect S. Ideally, such S-free set would be maximal inclusion-wise, as it would generate a deeper cutting plane. However, maximality can be a challenging goal in general. In this work, we show how to construct maximal S-free sets when S is defined as a general quadratic inequality. Our maximal S-free sets are such that efficient separation of a vertex in LP-based approaches to quadratically constrained problems is guaranteed. To the best of our knowledge, this work is the first to provide maximal quadratic-free sets. Y1 - 2020 U6 - https://doi.org/10.1007/978-3-030-45771-6_24 SP - 307 EP - 321 ER - TY - JOUR A1 - Sun, Yahui A1 - Rehfeldt, Daniel A1 - Brazil, Marcus A1 - Thomas, Doreen A1 - Halgamuge, Saman T1 - A Physarum-Inspired Algorithm for Minimum-Cost Relay Node Placement in Wireless Sensor Networks JF - IEEE/ACM Transactions on Networking Y1 - 2020 U6 - https://doi.org/10.1109/TNET.2020.2971770 ER - TY - THES A1 - Weltsch, André T1 - Fast Approximation of Equations of transient Gasflow Y1 - 2018 ER - TY - GEN A1 - Müller, Benjamin A1 - Muñoz, Gonzalo A1 - Gasse, Maxime A1 - Gleixner, Ambros A1 - Lodi, Andrea A1 - Serrano, Felipe T1 - On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming N2 - The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments. T3 - ZIB-Report - 19-55 KW - surrogate relaxation KW - MINLP KW - nonconvex optimization Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75179 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Steffy, Daniel T1 - Linear Programming using Limited-Precision Oracles N2 - Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly. T3 - ZIB-Report - 19-57 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-75316 SN - 1438-0064 ER - TY - GEN A1 - Georges, Alexander A1 - Gleixner, Ambros A1 - Gojic, Gorana A1 - Gottwald, Robert Lion A1 - Haley, David A1 - Hendel, Gregor A1 - Matejczyk, Bartlomiej T1 - Feature-Based Algorithm Selection for Mixed Integer Programming N2 - Mixed integer programming is a versatile and valuable optimization tool. However, solving specific problem instances can be computationally demanding even for cutting-edge solvers. Such long running times are often significantly reduced by an appropriate change of the solver's parameters. In this paper we investigate "algorithm selection", the task of choosing among a set of algorithms the ones that are likely to perform best for a particular instance. In our case, we treat different parameter settings of the MIP solver SCIP as different algorithms to choose from. Two peculiarities of the MIP solving process have our special attention. We address the well-known problem of performance variability by using multiple random seeds. Besides solving time, primal dual integrals are recorded as a second performance measure in order to distinguish solvers that timed out. We collected feature and performance data for a large set of publicly available MIP instances. The algorithm selection problem is addressed by several popular, feature-based methods, which have been partly extended for our purpose. Finally, an analysis of the feature space and performance results of the selected algorithms are presented. T3 - ZIB-Report - 18-17 KW - algorithm selection KW - mixed integer programming Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68362 SN - 1438-0064 ER -