@misc{GleixnerBertholdMuelleretal.2016, author = {Gleixner, Ambros and Berthold, Timo and M{\"u}ller, Benjamin and Weltge, Stefan}, title = {Three Enhancements for Optimization-Based Bound Tightening}, issn = {1438-0064}, doi = {10.1007/s10898-016-0450-4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57803}, year = {2016}, abstract = {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.}, language = {en} } @misc{VigerskeGleixner2016, author = {Vigerske, Stefan and Gleixner, Ambros}, title = {SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework}, issn = {1438-0064}, doi = {10.1080/10556788.2017.1335312}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59377}, year = {2016}, abstract = {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.}, language = {en} } @misc{RehfeldtHobbieSchoenheitetal.2019, author = {Rehfeldt, Daniel and Hobbie, Hannes and Sch{\"o}nheit, David and Gleixner, Ambros and Koch, Thorsten and M{\"o}st, Dominik}, title = {A massively parallel interior-point solver for linear energy system models with block structure}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74321}, year = {2019}, abstract = {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.}, language = {en} } @misc{D'AndreagiovanniGleixner2016, author = {D'Andreagiovanni, Fabio and Gleixner, Ambros}, title = {Towards an accurate solution of wireless network design problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59010}, year = {2016}, abstract = {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.}, language = {en} } @misc{GleixnerKempkeKochetal.2019, author = {Gleixner, Ambros and Kempke, Nils-Christian and Koch, Thorsten and Rehfeldt, Daniel and Uslu, Svenja}, title = {First Experiments with Structure-Aware Presolving for a Parallel Interior-Point Method}, issn = {1438-0064}, doi = {10.1007/978-3-030-48439-2_13}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74084}, year = {2019}, abstract = {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.}, language = {en} } @inproceedings{SofranacGleixnerPokutta2020, author = {Sofranac, Boro and Gleixner, Ambros and Pokutta, Sebastian}, title = {Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices}, booktitle = {2020 IEEE/ACM 10th Workshop on Irregular Applications: Architectures and Algorithms (IA3)}, arxiv = {http://arxiv.org/abs/2009.07785}, doi = {10.1109/IA351965.2020.00007}, pages = {1 -- 11}, year = {2020}, abstract = {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.}, language = {en} } @phdthesis{Gleixner2015, author = {Gleixner, Ambros}, title = {Exact and Fast Algorithms for Mixed-Integer Nonlinear Programming}, publisher = {Logos Verlag Berlin}, isbn = {978-3-8325-4190-3}, pages = {341}, year = {2015}, abstract = {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.}, language = {en} } @article{ŠofranacGleixnerPokutta2022, author = {Šofranac, Boro and Gleixner, Ambros and Pokutta, Sebastian}, title = {Accelerating domain propagation: An efficient GPU-parallel algorithm over sparse matrices}, volume = {109}, journal = {Parallel Computing}, doi = {10.1016/j.parco.2021.102874}, pages = {102874}, year = {2022}, abstract = {• 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.}, language = {en} } @article{RehfeldtFranzKoch2022, author = {Rehfeldt, Daniel and Franz, Henriette and Koch, Thorsten}, title = {Optimal Connected Subgraphs: Integer Programming Formulations and Polyhedra}, volume = {80}, journal = {Networks}, number = {3}, publisher = {Wiley}, doi = {10.1002/net.22101}, pages = {314 -- 332}, year = {2022}, language = {en} } @misc{GleixnerEiflerGallyetal.2017, author = {Gleixner, Ambros and Eifler, Leon and Gally, Tristan and Gamrath, Gerald and Gemander, Patrick and Gottwald, Robert Lion and Hendel, Gregor and Hojny, Christopher and Koch, Thorsten and Miltenberger, Matthias and M{\"u}ller, Benjamin and Pfetsch, Marc and Puchert, Christian and Rehfeldt, Daniel and Schl{\"o}sser, Franziska and Serrano, Felipe and Shinano, Yuji and Viernickel, Jan Merlin and Vigerske, Stefan and Weninger, Dieter and Witt, Jonas T. and Witzig, Jakob}, title = {The SCIP Optimization Suite 5.0}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66297}, year = {2017}, abstract = {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.}, language = {en} } @article{Hendel2018, author = {Hendel, Gregor}, title = {Adaptive Large Neighborhood Search for Mixed Integer Programming}, journal = {Mathematical Programming Computation}, year = {2018}, abstract = {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.}, language = {en} } @inproceedings{WitzigBertholdHeinz2019, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming}, volume = {11494}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-19212-9_6}, pages = {84 -- 94}, year = {2019}, abstract = {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.}, language = {en} } @inproceedings{YokoyamaShinanoWakayamaaetal.2018, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayamaa, Yuji and Wakui, Tetsuya}, title = {Optimal Design of a Gas Turbine Cogeneration Plant by a Hierarchical Optimization Method With Parallel Computing}, volume = {3}, booktitle = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition}, year = {2018}, abstract = {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.}, language = {en} } @inproceedings{YokoyamaShinanoWakayamaetal.2018, author = {Yokoyama, Ryohei and Shinano, Yuji and Wakayama, Yuki and Wakui, Tetsuya}, title = {Model Reduction by Time Aggregation for Optimal Design of Energy Supply Systems by an MILP Hierarchical Branch and Bound Method}, booktitle = {Proceedings of the 31st International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems (ECOS 2018)}, year = {2018}, abstract = {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.}, language = {en} } @inproceedings{BertholdStuckeyWitzig2019, author = {Berthold, Timo and Stuckey, Peter and Witzig, Jakob}, title = {Local Rapid Learning for Integer Programs}, volume = {11494}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2019}, publisher = {Springer}, doi = {10.1007/978-3-030-19212-9_5}, pages = {67 -- 83}, year = {2019}, abstract = {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.}, language = {en} } @article{BestuzhevaHijaziCoffrin2019, author = {Bestuzheva, Ksenia and Hijazi, Hassan and Coffrin, Carleton}, title = {Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching}, volume = {32}, journal = {INFORMS Journal on Computing}, number = {3}, publisher = {INFORMS Institute for Operations Research and the Management Sciences}, address = {5521 Research Park Drive, Suite 200, Catonsville, MD 21228 USA}, doi = {https://doi.org/10.1287/ijoc.2019.0900}, pages = {682 -- 696}, year = {2019}, abstract = {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.}, language = {en} } @inproceedings{AndersonHendelLeBodicetal.2018, author = {Anderson, Daniel and Hendel, Gregor and Le Bodic, Pierre and Viernickel, Jan Merlin}, title = {Clairvoyant Restarts in Branch-and-Bound Search Using Online Tree-Size Estimation}, booktitle = {AAAI-19: Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence}, year = {2018}, abstract = {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.}, language = {de} } @inproceedings{GleixnerSteffy2019, author = {Gleixner, Ambros and Steffy, Daniel}, title = {Linear Programming using Limited-Precision Oracles}, booktitle = {A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019}, doi = {10.1007/978-3-030-17953-3_30}, pages = {399 -- 412}, year = {2019}, abstract = {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.}, language = {en} } @inproceedings{Serrano2019, author = {Serrano, Felipe}, title = {Intersection cuts for factorable MINLP}, volume = {11480}, booktitle = {A. Lodi, V. Nagarajan (eds), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO 2019}, doi = {10.1007/978-3-030-17953-3_29}, pages = {385 -- 398}, year = {2019}, abstract = {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.}, language = {en} } @misc{ShinanoAchterbergBertholdetal.2015, author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Winkler, Michael}, title = {Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores}, issn = {1438-0064}, doi = {10.1109/IPDPS.2016.56}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56404}, year = {2015}, abstract = {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.}, language = {en} } @misc{MunguiaOxberryRajanetal.2017, author = {Munguia, Lluis-Miquel and Oxberry, Geoffrey and Rajan, Deepak and Shinano, Yuji}, title = {Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs}, number = {ZIB-Report 17-58}, issn = {1438-0064}, doi = {10.1007/s10589-019-00074-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65517}, year = {2017}, abstract = {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.}, language = {en} } @article{GamrathBertholdHeinzetal.2019, author = {Gamrath, Gerald and Berthold, Timo and Heinz, Stefan and Winkler, Michael}, title = {Structure-driven fix-and-propagate heuristics for mixed integer programming}, volume = {11}, journal = {Mathematical Programming Computation}, number = {4}, publisher = {Springer}, address = {Berlin Heidelberg}, doi = {10.1007/s12532-019-00159-1}, pages = {675 -- 702}, year = {2019}, abstract = {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.}, language = {en} } @misc{Wyczik2018, type = {Master Thesis}, author = {Wyczik, Christopher}, title = {Optimierung von Deployment- und Umgebungs-Integrit{\"a}t durch ein dezentrales Konfigurationsrepository auf Basis einer Blockchain}, pages = {44}, year = {2018}, abstract = {Viele Firmen nutzen f{\"u}r 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 f{\"u}r den Endnutzer. Hierbei ist es wichtig, dass die Konfiguration der Server regelm{\"a}ßig {\"u}berpr{\"u}ft wird. Eine solche Sicherstellung der Deployment- und Umgebungs-Integrit{\"a}t wird meistens durch eine Mitarbeiter der Firma oder durch einen externen Dienstleister erbracht. D.h. die Firma muss sich auf die Zuverl{\"a}ssigkeit eines Mitarbeiters oder einer externen Dienstleistung verlassen, bie zunehmender Komplexit{\"a}t ist sie sogar abh{\"a}ngig. Das Ziel dieser Masterarbeit ist es, zu untersuchen, ob die Sicherstellung der Deployment- und Umgebungs-Integrit{\"a}t durch automatisierte kryptografische Beweise, anstelle externer Dienstleistungen oder anderer Mitarbeiter, gew{\"a}hrleistet werden kann. Als Anwendungsfall dient die Toll Collect GmbH. Im ersten Teil dieser Arbeit wird das Matheamtische Modell einer Blockchain erl{\"a}utert. die Blockchain wurde erstmals in einem Dokument, welches unter dem Pseudonym Satoshi Nakamoto ver{\"o}ffentlicht 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-Integrit{\"a}t durch eine heirf{\"u}hr entwickelte Blockchainl{\"o}sung dezentralisiert werden. Es wird außerdem der {\"U}bergang vom Mathematischen Modell zur Implementierung gezeigt.}, language = {de} } @misc{BertholdStuckeyWitzig2018, author = {Berthold, Timo and Stuckey, Peter and Witzig, Jakob}, title = {Local Rapid Learning for Integer Programs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71190}, year = {2018}, abstract = {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.}, language = {en} } @misc{Hendel2018, author = {Hendel, Gregor}, title = {Adaptive Large Neighborhood Search for Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71167}, year = {2018}, abstract = {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.}, language = {en} } @misc{WitzigBertholdHeinz2018, author = {Witzig, Jakob and Berthold, Timo and Heinz, Stefan}, title = {A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71170}, year = {2018}, abstract = {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.}, language = {en} } @misc{RehfeldtKoch2018, author = {Rehfeldt, Daniel and Koch, Thorsten}, title = {Reduction-based exact solution of prize-collecting Steiner tree problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70958}, year = {2018}, language = {en} } @misc{ShinanoRehfeldtKoch2018, author = {Shinano, Yuji and Rehfeldt, Daniel and Koch, Thorsten}, title = {Building Optimal Steiner Trees on Supercomputers by using up to 43,000 Cores}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71118}, year = {2018}, abstract = {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.}, language = {en} } @misc{Serrano2018, author = {Serrano, Felipe}, title = {Intersection cuts for factorable MINLP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71105}, year = {2018}, abstract = {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.}, language = {en} } @misc{Wegscheider2019, type = {Master Thesis}, author = {Wegscheider, Fabian}, title = {Exploiting Symmetry in Mixed-Integer Nonlinear Programming}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77055}, year = {2019}, language = {en} } @article{WitzigGleixner2020, author = {Witzig, Jakob and Gleixner, Ambros}, title = {Conflict-Driven Heuristics for Mixed Integer Programming}, volume = {33}, journal = {INFORMS Journal on Computing}, number = {2}, doi = {10.1287/ijoc.2020.0973}, pages = {706 -- 720}, year = {2020}, abstract = {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.}, language = {en} } @article{GleixnerHendelGamrathetal.2021, author = {Gleixner, Ambros and Hendel, Gregor and Gamrath, Gerald and Achterberg, Tobias and Bastubbe, Michael and Berthold, Timo and Christophel, Philipp M. and Jarck, Kati and Koch, Thorsten and Linderoth, Jeff and L{\"u}bbecke, Marco and Mittelmann, Hans and Ozyurt, Derya and Ralphs, Ted and Salvagnin, Domenico and Shinano, Yuji}, title = {MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library}, volume = {13}, journal = {Mathematical Programming Computation}, number = {3}, doi = {10.1007/s12532-020-00194-3}, pages = {443 -- 490}, year = {2021}, abstract = {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.}, language = {en} } @inproceedings{SerranoMuñoz2020, author = {Serrano, Felipe and Muñoz, Gonzalo}, title = {Maximal Quadratic-Free Sets}, booktitle = {Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020}, doi = {10.1007/978-3-030-45771-6_24}, pages = {307 -- 321}, year = {2020}, abstract = {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.}, language = {en} } @article{SunRehfeldtBraziletal.2020, author = {Sun, Yahui and Rehfeldt, Daniel and Brazil, Marcus and Thomas, Doreen and Halgamuge, Saman}, title = {A Physarum-Inspired Algorithm for Minimum-Cost Relay Node Placement in Wireless Sensor Networks}, journal = {IEEE/ACM Transactions on Networking}, doi = {10.1109/TNET.2020.2971770}, year = {2020}, language = {en} } @misc{MuellerMuñozGasseetal.2019, author = {M{\"u}ller, Benjamin and Muñoz, Gonzalo and Gasse, Maxime and Gleixner, Ambros and Lodi, Andrea and Serrano, Felipe}, title = {On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75179}, year = {2019}, abstract = {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.}, language = {en} } @misc{GleixnerSteffy2019, author = {Gleixner, Ambros and Steffy, Daniel}, title = {Linear Programming using Limited-Precision Oracles}, issn = {1438-0064}, doi = {10.1007/s10107-019-01444-6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-75316}, year = {2019}, abstract = {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.}, language = {en} } @misc{GeorgesGleixnerGojicetal.2018, author = {Georges, Alexander and Gleixner, Ambros and Gojic, Gorana and Gottwald, Robert Lion and Haley, David and Hendel, Gregor and Matejczyk, Bartlomiej}, title = {Feature-Based Algorithm Selection for Mixed Integer Programming}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68362}, year = {2018}, abstract = {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.}, language = {en} } @article{ShinanoAchterbergBertholdetal.2013, author = {Shinano, Yuji and Achterberg, Tobias and Berthold, Timo and Heinz, Stefan and Koch, Thorsten and Vigerske, Stefan and Winkler, Michael}, title = {制約整数計画ソルバ SCIP の並列化}, volume = {61}, journal = {統計数理}, number = {1}, pages = {47 -- 78}, year = {2013}, abstract = {制約整数計画(CIP: Constraint Integer Programs)は,制約プログラミング(CP: Constraint Programming),混合整数計画(MIP: Mixed Integer Programming),充足可能性問題(SAT: Satisfability Problem)の研究分野におけるモデリング技術と解法を統合している.その結果,制約整数計画は,広いクラスの最適化問題を扱うことができる.SCIP(Solving Constraint Integer Programs)は,CIP を解くソルバとして実装され,Zuse Institute Berlin(ZIB)の研究者を中心として継続的に拡張が続けられている.本論文では,著者らによって開発された SCIP に対する2 種類の並列化拡張を紹介する.一つは,複数計算ノード間で大規模に並列動作する ParaSCIPである.もう一つは,複数コアと共有メモリを持つ 1 台の計算機上で(スレッド)並列で動作する FiberSCIP である.ParaSCIP は,HLRN II スーパーコンピュータ上で,一つのインスタンスを解くために最大 7,168 コアを利用した動作実績がある.また,統計数理研究所の Fujitsu PRIMERGY RX200S5 上でも,最大 512 コアを利用した動作実績がある.統計数理研究所のFujitsu PRIMERGY RX200S5 上では,これまでに最適解が得られていなかった MIPLIB2010のインスタンスである dg012142 に最適解を与えた.}, language = {ja} } @inproceedings{CaoGleixnerMiltenberger2016, author = {Cao, Karl-Ki{\^e}n and Gleixner, Ambros and Miltenberger, Matthias}, title = {Methoden zur Reduktion der Rechenzeit linearer Optimierungsmodelle in der Energiewirtschaft - Eine Performance-Analyse}, booktitle = {EnInnov 2016: 14. Symposium Energieinnovation 2016}, year = {2016}, abstract = {Dieser Beitrag stellt m{\"o}gliche Ans{\"a}tze zur Reduktion der Rechenzeit von linearen Optimierungsproblemen mit energiewirtschaftlichem Anwendungshintergrund vor. Diese Ans{\"a}tze bilden im Allgemeinen die Grundlage f{\"u}r konzeptionelle Strategien zur Beschleunigung von Energiesystemmodellen. Zu den einfachsten Beschleunigungsstrategien z{\"a}hlt die Verkleinerung der Modelldimensionen, was beispielsweise durch {\"A}ndern der zeitlichen, r{\"a}umlichen oder technologischen Aufl{\"o}sung eines Energiesystemmodells erreicht werden kann. Diese Strategien sind zwar h{\"a}ufig ein Teil der Methodik in der Energiesystemanalyse, systematische Benchmarks zur Bewertung ihrer Effektivit{\"a}t werden jedoch meist nicht durchgef{\"u}hrt. Die vorliegende Arbeit adressiert genau diesen Sachverhalt. Hierzu werden Modellinstanzen des Modells REMix in verschiedenen Gr{\"o}ßenordnungen mittels einer Performance-Benchmark-Analyse untersucht. Die Ergebnisse legen zum einen den Schluss nahe, dass verk{\"u}rzte Betrachtungszeitr{\"a}ume das gr{\"o}ßte Potential unter den hier analysierten Strategien zur Reduktion von Rechenzeit bieten. Zum anderen empfiehlt sich die Verwendung des Barrier-L{\"o}sungsverfahrens mit multiplen Threads unter Vernachl{\"a}ssigung des Cross-Over.}, language = {de} } @inproceedings{D'AndreagiovanniGleixner2016, author = {D'Andreagiovanni, Fabio and Gleixner, Ambros}, title = {Towards an accurate solution of wireless network design problems}, booktitle = {Cerulli R., Fujishige S., Mahjoub A. (eds) Combinatorial Optimization. ISCO 2016}, doi = {10.1007/978-3-319-45587-7_12}, pages = {135 -- 147}, year = {2016}, abstract = {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.}, language = {en} } @inproceedings{DevriendtGleixnerNordstroem2020, author = {Devriendt, Jo and Gleixner, Ambros and Nordstr{\"o}m, Jakob}, title = {Learn to Relax: Integrating 0-1 Integer Linear Programming with Pseudo-Boolean Conflict-Driven Search}, volume = {12296}, booktitle = {Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2020}, publisher = {Springer}, pages = {xxiv -- xxvi}, year = {2020}, abstract = {Conflict-driven Pseudo-Boolean (PB) solvers optimize 0-1 integer linear programs by extending the conflict-driven clause learning (CDCL) paradigm from SAT solving. Though PB solvers have the potential to be exponentially more efficient than CDCL solvers in theory, in practice they can sometimes get hopelessly stuck even when the linear program (LP) relaxation is infeasible over the reals. Inspired by mixed integer programming (MIP), we address this problem by interleaving incremental LP solving with cut generation within the conflict-driven PB search. This hybrid approach, which for the first time combines MIP techniques with full-blown conflict analysis over linear inequalities using the cutting planes method, significantly improves performance on a wide range of benchmarks, approaching a "best of two worlds" scenario between SAT-style conflict-driven search and MIP-style branch-and-cut.}, language = {en} } @article{品野2014, author = {品野, 勇治}, title = {最適化研究における数値実験を中心とした アプリケーション駆動研究サイクル}, volume = {59}, journal = {機関誌「オペレーションズ・リサーチ」}, number = {5}, pages = {247 -- 253}, year = {2014}, abstract = {最適化研究におけるアプリケーション駆動研究サイクルを紹介する.アプリケーション駆動研究サイクルは,学術機関での研究と企業における研究成果の利用とのつながりを良くする点では優れている.一方で,ソフトウェア開発・維持に多大な労力を要するため,日本の大学や研究機関における実施には困難さが伴う.ZIBにおいてアプリケーション駆動研究サイクルが,比較的うまく機能している背景を説明する.また,日本においてアプリケーション駆動研究サイクルを活性化するための第一歩として,論文投稿時に,論文中の数値実験に利用した全データ提出の義務化を提案したい.}, language = {ja} } @article{藤澤品野2014, author = {藤澤, 克樹 and 品野, 勇治}, title = {最適化と計算の今後 ―大規模問題をどこまで解決できるのか?―}, volume = {59}, journal = {機関誌「オペレーションズ・リサーチ」}, number = {1}, pages = {11 -- 19}, year = {2014}, abstract = {近年,大規模かつ複雑な最適化問題を高速に解く需要はさまざまな産業界や学術分野において急速に高まりつつある.これからの研究においては最先端理論 (Theory)+超大規模実データ (Practice)+最新計算技術(Computation) の三つを有機的に組み合わせることによって,実用に耐えうる解決策の提示と大規模最適化問題を扱う際の先例となることが求められている.本稿では最適化と計算に関する最新の傾向に触れるとともに,最適化の計算の今後についても考えていきたい.}, language = {ja} } @article{RehfeldtKochShinano2023, author = {Rehfeldt, Daniel and Koch, Thorsten and Shinano, Yuji}, title = {Faster exact solution of sparse MaxCut and QUBO problems}, volume = {15}, journal = {Mathematical Programming Computation}, doi = {10.1007/s12532-023-00236-6}, pages = {445 -- 470}, year = {2023}, abstract = {The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years. This article aims to advance the state of the art in the exact solution of both problems—by using mathematical programming techniques. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse maximum-cut and quadratic unconstrained binary optimization instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.}, language = {en} } @misc{BestuzhevaVoelkerGleixner2023, author = {Bestuzheva, Ksenia and V{\"o}lker, Helena and Gleixner, Ambros}, title = {Strengthening SONC Relaxations with Constraints Derived from Variable Bounds}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89510}, year = {2023}, abstract = {Nonnegativity certificates can be used to obtain tight dual bounds for polynomial optimization problems. Hierarchies of certificate-based relaxations ensure convergence to the global optimum, but higher levels of such hierarchies can become very computationally expensive, and the well-known sums of squares hierarchies scale poorly with the degree of the polynomials. This has motivated research into alternative certificates and approaches to global optimization. We consider sums of nonnegative circuit polynomials (SONC) certificates, which are well-suited for sparse problems since the computational cost depends on the number of terms in the polynomials and does not depend on the degrees of the polynomials. We propose a method that guarantees that given finite variable domains, a SONC relaxation will yield a finite dual bound. This method opens up a new approach to utilizing variable bounds in SONC-based methods, which is particularly crucial for integrating SONC relaxations into branch-and-bound algorithms. We report on computational experiments with incorporating SONC relaxations into the spatial branch-and-bound algorithm of the mixed-integer nonlinear programming framework SCIP. Applying our strengthening method increases the number of instances where the SONC relaxation of the root node yielded a finite dual bound from 9 to 330 out of 349 instances in the test set.}, language = {en} } @misc{MuellerKuhlmannVigerske2017, author = {M{\"u}ller, Benjamin and Kuhlmann, Renke and Vigerske, Stefan}, title = {On the performance of NLP solvers within global MINLP solvers}, issn = {1438-0064}, doi = {10.1007/978-3-319-89920-6_84}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64504}, year = {2017}, abstract = {Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies.}, language = {en} } @inproceedings{HendelMiltenbergerWitzig2018, author = {Hendel, Gregor and Miltenberger, Matthias and Witzig, Jakob}, title = {Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms}, booktitle = {OR 2018: International Conference on Operations Research}, year = {2018}, abstract = {State-of-the-art solvers for mixed integer programs (MIP) govern a variety of algorithmic components. Ideally, the solver adaptively learns to concentrate its computational budget on those components that perform well on a particular problem, especially if they are time consuming. We focus on three such algorithms, namely the classes of large neighborhood search and diving heuristics as well as Simplex pricing strategies. For each class we propose a selection strategy that is updated based on the observed runtime behavior, aiming to ultimately select only the best algorithms for a given instance. We review several common strategies for such a selection scenario under uncertainty, also known as Multi Armed Bandit Problem. In order to apply those bandit strategies, we carefully design reward functions to rank and compare each individual heuristic or pricing algorithm within its respective class. Finally, we discuss the computational benefits of using the proposed adaptive selection within the SCIP Optimization Suite on publicly available MIP instances.}, language = {en} } @misc{OPUS4-8937, title = {データ格付けサービス実現のための数理基盤の構築}, volume = {91}, editor = {Fujisawa, Katsuki and Kaji, Shizuo and Ishihara, Toru and Kondo, Masaaki and Shinano, Yuji and Tanigawa, Takuji and Nakayama, Naoko}, publisher = {Institute of Mathematics for Industry, Kyushu University}, address = {Graduate School of Mathematics, Kyushu University Motooka 744, Nishi-ku, Fukuoka, 819-0395, JAPAN}, issn = {2188-1200}, year = {2022}, language = {ja} } @misc{OPUS4-8935, title = {Construction of Mathematical Basis for Realizing Data Rating Service}, volume = {90}, editor = {Fujisawa, Katsuki and Kaji, Shizuo and Ishihara, Toru and Kondo, Masaaki and Shinano, Yuji and Tanigawa, Takuji and Nakayama, Naoko}, publisher = {Institute of Mathematics for Industry, Kyushu University}, address = {Graduate School of Mathematics, Kyushu University Motooka 744, Nishi-ku, Fukuoka, 819-0395, JAPAN}, issn = {2188-1200}, year = {2022}, language = {en} } @inproceedings{Rehfeldt2022, author = {Rehfeldt, Daniel}, title = {Faster Algorithms for Steiner Tree and related Problems: From Theory to Practice}, booktitle = {Operations Research Proceedings 2022}, year = {2022}, language = {en} } @misc{TurnerBertholdBesanconetal.2022, author = {Turner, Mark and Berthold, Timo and Besan{\c{c}}on, Mathieu and Koch, Thorsten}, title = {Cutting Plane Selection with Analytic Centers and Multiregression}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89065}, year = {2022}, abstract = {Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.}, language = {en} } @misc{BertholdMexiSalvagnin2022, author = {Berthold, Timo and Mexi, Gioni and Salvagnin, Domenico}, title = {Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-88513}, year = {2022}, abstract = {The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate the usage of multiple reference vectors in all stages of the FP algorithm. In particular, we use LP-feasible vectors obtained during the main loop to tighten the variable domains before entering the computationally expensive enumeration stage. Moreover, we consider multiple integer reference vectors to explore further optimizing directions and introduce alternative objective scaling terms to balance the contributions of the distance functions and the original MIP objective. Our computational experiments demonstrate that the new method can improve performance on general MIP test sets. In detail, our modifications provide a 29.3\% solution quality improvement and 4.0\% running time improvement in an embedded setting, needing 16.0\% fewer iterations over a large test set of MIP instances. In addition, the method's success rate increases considerably within the first few iterations. In a standalone setting, we also observe a moderate performance improvement, which makes our version of FP suitable for the two main use-cases of the algorithm.}, language = {en} }