TY - JOUR A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Kniasew, Dimitri A1 - Schlögel, Dominik A1 - Martin, Alexander A1 - Weninger, Dieter T1 - Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming JF - Journal of Computational Mathematics N2 - The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of robust and future-proof decision support systems. The complexity of industrial-scale supply chain optimization, however, often poses limits to the application of general mixed-integer programming solvers. In this paper we describe algorithmic innovations that help to ensure that MIP solver performance matches the complexity of the large supply chain problems and tight time limits encountered in practice. Our computational evaluation is based on a diverse set, modeling real-world scenarios supplied by our industry partner SAP. Y1 - 2019 U6 - https://doi.org/10.4208/jcm.1905-m2019-0055 VL - 37 SP - 866 EP - 888 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Steffy, Daniel T1 - Linear Programming using Limited-Precision Oracles JF - Mathematical Programming 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. Y1 - 2020 U6 - https://doi.org/10.1007/s10107-019-01444-6 VL - 183 IS - 1-2 SP - 525 EP - 554 ER - TY - JOUR A1 - Pulaj, Jonad T1 - Cutting planes for families implying Frankl's conjecture JF - Mathematics of Computation N2 - We find previously unknown families of sets which ensure Frankl's conjecture holds for all families that contain them using an algorithmic framework. The conjecture states that for any nonempty finite union-closed (UC) family there exists an element of the ground set in at least half the sets of the considered UC family. Poonen's Theorem characterizes the existence of weights which determine whether a given UC family implies the conjecture for all UC families which contain it. We design a cutting-plane method that computes the explicit weights which satisfy the existence conditions of Poonen's Theorem. This method enables us to answer several open questions regarding structural properties of UC families, including the construction of a counterexample to a conjecture of Morris from 2006. Y1 - 2019 U6 - https://doi.org/10.1090/mcom/3461 ER - 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 - 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 - 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 - 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 - 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 - 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 - 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 - JOUR A1 - Hoppmann-Baum, Kai A1 - Hennings, Felix A1 - Zittel, Janina A1 - Gotzes, Uwe A1 - Spreckelsen, Eva-Maria A1 - Spreckelsen, Klaus A1 - Koch, Thorsten T1 - An Optimization Approach for the Transient Control of Hydrogen Transport Networks JF - Mathematical Methods of Operations Research Y1 - 2021 IS - Special Issue on Energy Networks ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem JF - SIAM Journal on Optimization N2 - Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver. The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced. Y1 - 2019 U6 - https://doi.org/10.1137/17M1145963 VL - 29 IS - 1 SP - 369 EP - 398 PB - Society for Industrial and Applied Mathematics ER - TY - JOUR A1 - Furini, Fabio A1 - Traversi, Emiliano A1 - Belotti, Pietro A1 - Frangioni, Antonio A1 - Gleixner, Ambros A1 - Gould, Nick A1 - Liberti, Leo A1 - Lodi, Andrea A1 - Misener, Ruth A1 - Mittelmann, Hans A1 - Sahinidis, Nikolaos V. A1 - Vigerske, Stefan A1 - Wiegele, Angelika T1 - QPLIB: A Library of Quadratic Programming Instances JF - Mathematical Programming Computation N2 - This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-018-0147-4 VL - 11 IS - 2 SP - 237 EP - 265 ER - TY - JOUR A1 - Vierhaus, Ingmar A1 - Fügenschuh, Armin A1 - Gottwald, Robert Lion A1 - Grösser, Stefan T1 - Using white-box nonlinear optimization methods in system dynamics policy improvement JF - System Dynamics Review N2 - We present a new strategy for the direct optimization of the values of policy functions. This approach is particularly well suited to model actors with a global perspective on the system and relies heavily on modern mathematical white-box optimization methods. We demonstrate our strategy on two classical models: market growth and World2. Each model is first transformed into an optimization problem by defining how the actor can influence the models' dynamics and by choosing objective functions to measure improvements. To improve comparability between different runs, we also introduce a comparison measure for possible interventions. We solve the optimization problems, discuss the resulting policies and compare them to the existing results from the literature. In particular, we present a run of the World2 model which significantly improves the published “towards a global equilibrium” run with equal cost of intervention. Y1 - 2017 U6 - https://doi.org/10.1002/sdr.1583 VL - 33 IS - 2 SP - 138 EP - 168 ER - TY - JOUR A1 - Weber, Tobias A1 - Sager, Sebastian A1 - Gleixner, Ambros T1 - Solving Quadratic Programs to High Precision using Scaled Iterative Refinement JF - Mathematical Programming Computation N2 - Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and Mészáros benchmark library. Y1 - 2019 U6 - https://doi.org/10.1007/s12532-019-00154-6 VL - 11 SP - 421 EP - 455 PB - Springer Berlin Heidelberg ER - TY - JOUR A1 - Koch, Thorsten A1 - Achterberg, Tobias A1 - Andersen, Erling A1 - Bastert, Oliver A1 - Berthold, Timo A1 - Bixby, Robert E. A1 - Danna, Emilie A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Lodi, Andrea A1 - Mittelmann, Hans A1 - Ralphs, Ted A1 - Salvagnin, Domenico A1 - Steffy, Daniel A1 - Wolter, Kati T1 - MIPLIB 2010 JF - Mathematical Programming Computation Y1 - 2011 UR - http://mpc.zib.de/index.php/MPC/article/view/56 U6 - https://doi.org/10.1007/s12532-011-0025-9 VL - 3 IS - 2 SP - 103 EP - 163 ER - TY - JOUR A1 - Gamrath, Gerald ED - Gomes, Carla ED - Sellmann, Meinolf T1 - Improving strong branching by propagation JF - Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems N2 - Strong branching is an important component of most variable selection rules in branch-and-bound based mixed-integer linear programming solvers. It predicts the dual bounds of potential child nodes by solving auxiliary LPs and thereby helps to keep the branch-and-bound tree small. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Computational experiments on standard MIP instances indicate that this is beneficial in three aspects: It helps to reduce the average number of LP iterations per strong branching call, the number of branch-and-bound nodes, and the overall solving time. Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38171-3_25 VL - 7874 SP - 347 EP - 354 PB - Springer Berlin Heidelberg ER - TY - JOUR A1 - Gamrath, Gerald T1 - Improving strong branching by domain propagation JF - EURO Journal on Computational Optimization N2 - One of the essential components of a branch-and-bound based mixed-integer linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs (LPs) and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique MIP solvers usually apply at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, the state-of-the-art hybrid branching rule can be improved this way as well. This paper extends previous work by the author published in the proceedings of the CPAIOR 2013. Y1 - 2014 U6 - https://doi.org/10.1007/s13675-014-0021-8 VL - 2 IS - 3 SP - 99 EP - 122 PB - Springer CY - Berlin Heidelberg ER - TY - JOUR A1 - Gleixner, Ambros A1 - Held, Harald A1 - Huang, Wei A1 - Vigerske, Stefan T1 - Towards globally optimal operation of water supply networks JF - Numerical Algebra, Control and Optimization N2 - This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to ε-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms. In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem. Y1 - 2012 U6 - https://doi.org/10.3934/naco.2012.2.695 VL - 2 IS - 4 SP - 695 EP - 711 ER - TY - JOUR A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Heinz, Stefan A1 - Vigerske, Stefan T1 - Analyzing the computational impact of MIQCP solver components JF - Numerical Algebra, Control and Optimization N2 - We provide a computational study of the performance of a state-of-the-art solver for nonconvex mixed-integer quadratically constrained programs (MIQCPs). Since successful general-purpose solvers for large problem classes necessarily comprise a variety of algorithmic techniques, we focus especially on the impact of the individual solver components. The solver SCIP used for the experiments implements a branch-and-cut algorithm based on a linear relaxation to solve MIQCPs to global optimality. Our analysis is based on a set of 86 publicly available test instances. Y1 - 2012 U6 - https://doi.org/10.3934/naco.2012.2.739 VL - 2 IS - 4 SP - 739 EP - 748 ER - TY - JOUR A1 - Heinz, Stefan A1 - Schlechte, Thomas A1 - Stephan, Rüdiger A1 - Winkler, Michael T1 - Solving steel mill slab design problems JF - Constraints N2 - The steel mill slab design problem from the CSPLIB is a combinatorial optimization problem motivated by an application of the steel industry. It has been widely studied in the constraint programming community. Several methods were proposed to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called the multiple knapsack problem with color constraints, originated from the same industrial problem, was discussed in the integer programming community. In particular, a simple integer program for this problem has been given by Forrest et al. (INFORMS J Comput 18:129–134, 2006). The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. (INFORMS J Comput 18:129–134, 2006) for the steel mill slab design problem. Using this model and a state-of-the-art integer program solver all instances of the steel mill slab library can be solved efficiently to optimality. We improved, thereby, the solution values of 76 instances compared to previous results (Schaus et al., Constraints 16:125–147, 2010). Finally, we consider a recently introduced variant of the steel mill slab design problem, where within all solutions which minimize the leftover one is interested in a solution which requires a minimum number of slabs. For that variant we introduce two approaches and solve all instances of the steel mill slab library with this slightly changed objective function to optimality. Y1 - 2012 U6 - https://doi.org/10.1007/s10601-011-9113-8 VL - 17 IS - 1 SP - 39 EP - 50 ER - TY - JOUR A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover: a primal MINLP heuristic exploring a largest sub-MIP JF - Mathematical Programming 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. Y1 - 2014 U6 - https://doi.org/10.1007/s10107-013-0635-2 VL - 144 IS - 1-2 SP - 315 EP - 346 ER - TY - JOUR A1 - Achterberg, Tobias A1 - Berthold, Timo T1 - Improving the Feasibility Pump JF - Discrete Optimization Y1 - 2007 VL - Special Issue 4 IS - 1 SP - 77 EP - 86 ER - TY - JOUR A1 - Berthold, Timo T1 - Heuristiken im Branch-and-Cut-Framework SCIP JF - OR News Y1 - 2008 IS - 32 SP - 24 EP - 25 ER - TY - JOUR A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Taniguchi, Syusuke A1 - Ohkura, Masashi A1 - Wakui, Tetsuya T1 - Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation JF - Energy Conversion and Management 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. In the combinatorial optimization method based on the mixed-integer linear programming (MILP), integer variables are used to express the selection, numbers, and on/off status of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. In this paper, a MILP method utilizing the hierarchical relationship between design and operation variables is proposed to solve the optimal design problem of energy supply systems efficiently: At the upper level, the optimal values of design variables are searched by the branch and bound method; At the lower level, the values of operation variables are optimized independently at each period by the branch and bound method under the values of design variables given tentatively during the search at the upper level; Lower bounds for the optimal value of the objective function to be minimized are evaluated, and are utilized for the bounding operations at both the levels. This method is implemented into open and commercial MILP solvers. Illustrative and practical case studies on the optimal design of cogeneration systems are conducted, and the validity and effectiveness of the proposed method are clarified. Y1 - 2015 U6 - https://doi.org/10.1016/j.enconman.2014.12.020 VL - 92 SP - 92 EP - 104 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - SCIP-Jack – A solver for STP and variants with parallelization extensions JF - Mathematical Programming Computation N2 - The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problem-specific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. Y1 - 2017 U6 - https://doi.org/10.1007/s12532-016-0114-x VL - 9 IS - 2 SP - 231 EP - 296 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Berthold, Timo A1 - Müller, Benjamin A1 - Weltge, Stefan T1 - Three Enhancements for Optimization-Based Bound Tightening JF - Journal of Global Optimization 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. Y1 - 2017 U6 - https://doi.org/10.1007/s10898-016-0450-4 VL - 67 IS - 4 SP - 731 EP - 757 ER - TY - JOUR A1 - Maher, Stephen J. A1 - Desaulniers, Guy A1 - Soumis, Francois T1 - The daily tail assignment problem under operational uncertainty using look-ahead maintenance constraints JF - European Journal of Operational Research N2 - The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to satisfy operational constraints. The aim of this paper is to develop an operationally flexible method, based upon the one-day routes business model, to compute tail assignments that satisfy short-range—within the next three days—aircraft maintenance requirements. While maintenance plans commonly span multiple days, the methods used to compute tail assignments for the given plans can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by using solutions from the one-day routes aircraft maintenance routing approach as input. The daily tail assignment problem is solved with an objective to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A computational study will be performed to assess the performance of exact and heuristic solution algorithms that modify the input lines-of-flight to reduce maintenance misalignments. The daily tail assignment problem and the developed algorithms are demonstrated to compute solutions that effectively satisfy maintenance requirements when evaluated using input data collected from three different airlines. Y1 - 2018 U6 - https://doi.org/10.1016/j.ejor.2017.06.041 VL - 264 IS - 2 SP - 534 EP - 547 ER - TY - JOUR A1 - Shinano, Yuji A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - FiberSCIP - A shared memory parallelization of SCIP JF - INFORMS Journal on Computing N2 - Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a mixed-integer linear programming solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, we present the basic concept of having two parallel extensions, and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator), including an implementation of deterministic parallelization. Second, we discuss the difficulties in achieving a good performance that utilizes all resources on an actual computing environment, and the difficulties of performance evaluation of the parallel solvers. Third, we present a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions. Finally, we demonstrate the current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer nonlinear programs (MINLPs) in parallel. Y1 - 2018 U6 - https://doi.org/10.1287/ijoc.2017.0762 VL - 30 IS - 1 SP - 11 EP - 30 ER - TY - JOUR A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Heinz, Stefan T1 - ParaXpress: An Experimental Extension of the FICO Xpress-Optimizer to Solve Hard MIPs on Supercomputers JF - Optimization Methods & Software N2 - The Ubiquity Generator (UG) is a general framework for the external parallelization of mixed integer programming (MIP) solvers. In this paper, we present ParaXpress, a distributed memory parallelization of the powerful commercial MIP solver FICO Xpress. Besides sheer performance, an important feature of Xpress is that it provides an internal parallelization for shared memory systems. When aiming for a best possible performance of ParaXpress on a supercomputer, the question arises how to balance the internal Xpress parallelization and the external parallelization by UG against each other. We provide computational experiments to address this question and we show computational results for running ParaXpress on a Top500 supercomputer, using up to 43,344 cores in parallel. Y1 - 2018 U6 - https://doi.org/10.1080/10556788.2018.1428602 VL - 33 IS - 3 SP - 530 EP - 539 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Steffy, Daniel A1 - Wolter, Kati T1 - Iterative Refinement for Linear Programming JF - INFORMS Journal on Computing N2 - We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the objective function, right-hand side, and variable bounds. Exact computation is used to compute and store the exact representation of the transformed problems, while numeric computation is used for solving LPs. At all steps of the algorithm the LP bases encountered in the transformed problems correspond directly to LP bases in the original problem description. We show that this algorithm is effective in practice for computing extended precision solutions and that it leads to a direct improvement of the best known methods for solving LPs exactly over the rational numbers. Our implementation is publically available as an extension of the academic LP solver SoPlex. Y1 - 2016 U6 - https://doi.org/10.1287/ijoc.2016.0692 VL - 28 IS - 3 SP - 449 EP - 464 ER - TY - JOUR A1 - Witzig, Jakob A1 - Beckenbach, Isabel A1 - Eifler, Leon A1 - Fackeldey, Konstantin A1 - Gleixner, Ambros A1 - Grever, Andreas A1 - Weber, Marcus T1 - Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes JF - Multiscale Modeling and Simulation N2 - In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst. KW - Markov State Models KW - NESS KW - Non-reversible Markov Processes KW - Mixed-Integer Programming Y1 - 2018 U6 - https://doi.org/10.1137/16M1091162 SN - 1438-0064 VL - 16 IS - 1 SP - 248 EP - 265 ER - TY - JOUR A1 - Maher, Stephen J. T1 - A novel passenger recovery approach for the integrated airline recovery problem JF - Computers & Operations Research N2 - Schedule disruptions require airlines to intervene through the process of recovery; this involves modifications to the planned schedule, aircraft routings, crew pairings and passenger itineraries. Passenger recovery is generally considered as the final stage in this process, and hence passengers experience unnecessarily large impacts resulting from flight delays and cancellations. Most recovery approaches considering passengers involve a separately defined module within the problem formulation. However, this approach may be overly complex for recovery in many aviation and general transportation applications. This paper presents a unique description of the cancellation variables that models passenger recovery by prescribing the alternative travel arrangements for passengers in the event of flight cancellations. The results will demonstrate that this simple, but effective, passenger recovery approach significantly reduces the operational costs of the airline and increases passenger flow through the network. The integrated airline recovery problem with passenger reallocation is solved using column-and-row generation to achieve high quality solutions in short runtimes. An analysis of the column-and-row generation solution approach is performed, identifying a number of enhancement techniques to further improve the solution runtimes. Y1 - 2015 U6 - https://doi.org/10.1016/j.cor.2014.11.005 VL - 57 SP - 123 EP - 137 ER - TY - JOUR A1 - Gleixner, Ambros A1 - Maher, Stephen A1 - Müller, Benjamin A1 - Pedroso, João Pedro T1 - Price-and-verify: a new algorithm for recursive circle packing using Dantzig–Wolfe decomposition JF - Annals of Operations Research N2 - Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig–Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a “price-and-verify” algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature. Y1 - 2018 U6 - https://doi.org/10.1007/s10479-018-3115-5 VL - 284 IS - 2 SP - 527 EP - 555 PB - Springer US ER - TY - JOUR A1 - Humpola, Jesco A1 - Serrano, Felipe T1 - Sufficient pruning conditions for MINLP in gas network design JF - EURO Journal on Computational Optimization N2 - One-quarter of Europe’s energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi-billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology optimization problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. We offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex continuous nonlinear program (NLP) can be certified by solving an MILP. This result provides an efficient pruning procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speedup for the necessary computations. Y1 - 2017 U6 - https://doi.org/10.1007/s13675-016-0077-8 VL - 5 IS - 1-2 SP - 239 EP - 261 PB - Springer Berlin Heidelberg ER - TY - JOUR A1 - Berthold, Timo A1 - Hendel, Gregor A1 - Koch, Thorsten T1 - From feasibility to improvement to proof: three phases of solving mixed-integer programs JF - Optimization Methods and Software N2 - Modern mixed-integer programming (MIP) solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three distinct phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behaviour of the non-commercial MIP solver Scip at the predicted phase transition points. Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2017.1392519 VL - 33 IS - 3 SP - 499 EP - 517 PB - Taylor & Francis ER - TY - JOUR A1 - Koch, Thorsten T1 - The ZIMPL modeling language JF - Optima Y1 - 2017 UR - http://www.mathopt.org/Optima-Issues/optima103.pdf VL - 103 SP - 8 EP - 9 ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten A1 - Maher, Stephen J. T1 - Reduction Techniques for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem JF - Networks N2 - The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this paper we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem, the rooted prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90 percent of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state-of-the-art Steiner problem solver SCIP-Jack. Y1 - 2019 U6 - https://doi.org/10.1002/net.21857 VL - 73 SP - 206 EP - 233 PB - Wiley ET - 2 ER - TY - JOUR A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Transformations for the Prize-Collecting Steiner Tree Problem and the Maximum-Weight Connected Subgraph Problem to SAP JF - Journal of Computational Mathematics N2 - Transformations of Steiner tree problem variants have been frequently discussed in the literature. Besides allowing to easily transfer complexity results, they constitute a central pillar of exact state-of-the-art solvers for well-known variants such as the Steiner tree problem in graphs. In this paper transformations for both the prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem to the Steiner arborescence problem are introduced for the first time. Furthermore, we demonstrate the considerable implications for practical solving approaches, including the computation of strong upper and lower bounds. Y1 - 2018 U6 - https://doi.org/10.4208/jcm.1709-m2017-0002 VL - 36 IS - 3 SP - 459 EP - 468 ER - TY - JOUR A1 - Berthold, Timo A1 - Hendel, Gregor T1 - Shift-and-Propagate JF - Journal of Heuristics N2 - In recent years, there has been a growing interest in the design of general purpose primal heuristics for use inside complete mixed integer programming solvers. Many of these heuristics rely on an optimal LP solution, which may take a significant amount of time to find. In this paper, we address this issue by introducing a pre-root primal heuristic that does not require a previously found LP solution. This heuristic, named Shift-and-Propagate , applies domain propagation techniques to quickly drive a variable assignment towards feasibility. Computational experiments indicate that this heuristic is a powerful supplement to existing rounding and propagation heuristics. Y1 - 2014 U6 - https://doi.org/10.1007/s10732-014-9271-0 VL - 21 IS - 1 SP - 73 EP - 106 ER - TY - JOUR A1 - Humpola, Jesco A1 - Lehmann, Thomas A1 - Fügenschuh, Armin T1 - A primal heuristic for optimizing the topology of gas networks based on dual information JF - EURO Journal on Computational Optimization N2 - We present a novel heuristic to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point of a nonlinear relaxation. Based on the information from the KKT point we alter some of the binary variables in a locally promising way exploiting our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP. Y1 - 2015 U6 - https://doi.org/10.1007/s13675-014-0029-0 VL - 3 IS - 1 SP - 53 EP - 78 ER - TY - JOUR A1 - Maher, Stephen J. T1 - Solving the integrated airline recovery problem using column-and-row generation JF - Transportation Science N2 - Airline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, the complete airline recovery problem is generally formulated as a series of sequential stages. While the sequential approach greatly simplifies the complete recovery problem, there is no guarantee of global optimality or solution quality. To address this, there has been increasing interest in the development of efficient solution techniques to solve an integrated recovery problem. In this paper, an integrated airline recovery problem is proposed by integrating the schedule, crew and aircraft recovery stages. To achieve short runtimes and high quality solutions, this problem is solved using column-and-row generation. Column-and-row generation achieves an improvement in solution runtimes by reducing the problem size and thereby achieving a faster execution of each LP solve. Further, the results demonstrate that a good upper bound achieved early in the solution process, indicating an improved solution quality with the early termination of the algorithm. This paper also details the integration of the row generation procedure with branch-and-price, which is used to achieve integral optimal solutions. The benefits of applying column-and-row generation to solve the integrated recovery problem are demonstrated with a comparison to a standard column generation technique. Y1 - 2015 U6 - https://doi.org/10.1287/trsc.2014.0552 VL - 50 IS - 1 SP - 216 EP - 239 ER - TY - JOUR A1 - Cook, William A1 - Koch, Thorsten A1 - Steffy, Daniel A1 - Wolter, Kati T1 - A hybrid branch-and-bound approach for exact rational mixed-integer programming JF - Mathematical Programming Computation N2 - We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann libraries and for a new collection of numerically difficult instances. Y1 - 2013 U6 - https://doi.org/10.1007/s12532-013-0055-6 VL - 5 IS - 3 SP - 305 EP - 344 ER - TY - JOUR A1 - Vigerske, Stefan A1 - Gleixner, Ambros T1 - SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework JF - Optimization Methods & Software 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. Y1 - 2018 U6 - https://doi.org/10.1080/10556788.2017.1335312 VL - 33 IS - 3 SP - 563 EP - 593 ER - TY - JOUR A1 - Shinano, Yuji A1 - Inui, Nobuo A1 - Fukagawa, Youzou A1 - Takakura, Noburu T1 - Optimizing Movement Sequences for Step-and-Scan Lithography Equipment JF - Journal of Advanced Mechanical Design, Systems, and Manufacturing N2 - The purpose of this work is to improve the throughput of step-and-scan lithography equipment to shorten the production time of a wafer. For this purpose, we propose a method for solving the MSOP (Movement Sequence Optimization Problem), which is the problem of computing the fastest schedule for visiting all shots on a wafer. It is well-known that the MSOP on step-and-repeat lithography equipment can be modeled as a traveling salesman problem. In contrast to step-and-repeat lithography equipment, a schedule for step-and-scan lithography equipment must also indicate the scanning direction of each shot, in addition to the sequence of the shots. For this reason, the traveling salesman problem formulation for step-and-repeat lithography equipment cannot be applied to solve the MSOP on step-and-scan lithography equipment directly. We overcame this difficulty by introducing auxiliary vertices to model the scanning directions in the traveling salesman problem formulation. By this method, we were able to compute exact optimal sequences considering the scanning directions of shots for several MSOP instances. Our numerical experiments demonstrated that our proposed method was capable of computing exact optimal solutions for real-world MSOP instances having up to 232 shots on a wafer. These optimal solutions gave a 0.25% to 4.66% improvement in productivity over solutions computed by previously known methods. Y1 - 2013 U6 - https://doi.org/10.1299/jamdsm.7.608 VL - 7 IS - 4 SP - 608 EP - 618 ER - TY - JOUR A1 - Maher, Stephen J. A1 - Murray, John M. T1 - The unrooted set covering connected subgraph problem differentiating between HIV envelope sequences JF - European Journal of Operational Research N2 - This paper presents a novel application of operations research techniques to the analysis of HIV Env gene sequences, aiming to identify key features that are possible vaccine targets. These targets are identified as being critical to the transmission of HIV by being present in early transmitted (founder) sequences and absent in later chronic sequences. Identifying the key features of Env involves two steps: first, calculating the covariance of amino acid combinations and positions to form a network of related and compensatory mutations; and second, developing an integer program to identify the smallest connected subgraph of the constructed covariance network that exhibits a set covering property. The integer program developed for this analysis, labelled the unrooted set covering connected subgraph problem (USCCSP), integrates a set covering problem and connectivity evaluation, the latter formulated as a network flow problem. The resulting integer program is very large and complex, requiring the use of Benders' decomposition to develop an efficient solution approach. The results will demonstrate the necessity of applying acceleration techniques to the Benders' decomposition solution approach and the effectiveness of these techniques and heuristic approaches for solving the USCCSP. Y1 - 2016 U6 - https://doi.org/doi:10.1016/j.ejor.2015.07.011 VL - 248 IS - 2 SP - 668 EP - 680 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Miltenberger, Matthias A1 - Weninger, Dieter T1 - Progress in presolving for mixed integer programming JF - Mathematical Programming Computation N2 - This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 % on affected instances while not degrading the performance on the remaining problems. Y1 - 2015 U6 - https://doi.org/10.1007/s12532-015-0083-5 VL - 7 IS - 4 SP - 367 EP - 398 ER -