@misc{FujiiKimKojimaetal.2023, author = {Fujii, Koichi and Kim, Sunyoung and Kojima, Masakazu and Mittelmann, Hans D. and Shinano, Yuji}, title = {An Exceptionally Difficult Binary Quadratic Optimization Problem with Symmetry: a Challenge for The Largest Unsolved QAP Instance Tai256c}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-93072}, year = {2023}, abstract = {Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB. It is known that QAP tai256c can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92. As the BQOP is much simpler than the original QAP, the conversion increases the possibility to solve the QAP. Solving exactly the BQOP, however, is still very difficult. Indeed, a 1.48\% gap remains between the best known upper bound (UB) and lower bound (LB) of the unknown optimal value. This paper shows that the BQOP admits a nontrivial symmetry, a property that makes the BQOP very hard to solve. The symmetry induces equivalent subproblems in branch and bound (BB) methods. To effectively improve the LB, we propose an efficient BB method that incorporates a doubly nonnegative relaxation, the standard orbit branching and a technique to prune equivalent subproblems. With this BB method, a new LB with 1.25\% gap is successfully obtained, and computing an LB with 1.0\% gap is shown to be still quite difficult.}, language = {en} } @misc{FujiiItoKimetal.2022, author = {Fujii, Koichi and Ito, Naoki and Kim, Sunyoung and Kojima, Masakazu and Shinano, Yuji and Toh, Kim-Chuan}, title = {大規模二次割当問題への挑戦}, journal = {統計数理研究所共同研究リポート 453 最適化:モデリングとアルゴリズム33 2022年3月 「大規模二次割当問題への挑戦」 p.84-p.92}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-86779}, year = {2022}, abstract = {二次割当問題は線形緩和が弱いことが知られ,強化のため多様な緩和手法が考案されているが,その一つである二重非負値計画緩和( DNN 緩和)及びその解法として近年研究が進んでいるニュートン・ブラケット法を紹介し,それらに基づく分枝限定法の実装及び数値実験結果について報告する.}, language = {ja} } @misc{Shinano2021, author = {Shinano, Yuji}, title = {UG - Ubiquity Generator Framework v1.0.0beta}, doi = {10.12752/8521}, year = {2021}, abstract = {UG is a generic framework to parallelize branch-and-bound based solvers (e.g., MIP, MINLP, ExactIP) in a distributed or shared memory computing environment. It exploits the powerful performance of state-of-the-art "base solvers", such as SCIP, CPLEX, etc. without the need for base solver parallelization. UG framework, ParaSCIP(ug[SCIP,MPI]) and FiberSCIP (ug[SCIP,Pthreads]) are available as a beta version. v1.0.0: new documentation and cmake, generalization of ug framework, implementation of selfsplitrampup for fiber- and parascip, better memory and time limit handling.}, language = {en} } @misc{TateiwaShinanoYamamuraetal.2021, author = {Tateiwa, Nariaki and Shinano, Yuji and Yamamura, Keiichiro and Yoshida, Akihiro and Kaji, Shizuo and Yasuda, Masaya and Fujisawa, Katsuki}, title = {CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-82802}, year = {2021}, abstract = {Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments.}, 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} } @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{BeckerHiller2020, author = {Becker, Kai-Helge and Hiller, Benjamin}, title = {Efficient Enumeration of Acyclic Graph Orientations with Sources or Sinks Revisited}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-77684}, year = {2020}, abstract = {In a recent paper, Conte et al. [CGMR2017] presented an algorithm for enumerating all acyclic orientations of a graph G=(V,E) with a single source (and related orientations) with delay O(|V||E|). In this paper we revisit the problem by going back to an early paper by de Fraysseix et al. [FMR1995], who proposed an algorithm for enumerating all bipolar orientations of a graph based on a recursion formula. We first formalize de Fraysseix et al.'s algorithm for bipolar orientations and determine that its delay is also O(|V||E|). We then apply their recursion formula to the case of Conte et al.'s enumeration problem and show that this yields a more efficient enumeration algorithm with delay O(\sqrt(|V|)|E|). Finally, a way to further streamline the algorithm that leads to a particularly simple implementation is suggested.}, language = {en} } @misc{ShinanoVigerske2025, author = {Shinano, Yuji and Vigerske, Stefan}, title = {Smoothie: Mixing the strongest MIP solvers to solve hard MIP instances on supercomputers - Phase I development}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-101906}, year = {2025}, abstract = {Mixed-Integer Linear Programming (MIP) is applicable to such a wide range of real-world decision problems that the competition for the best code to solve such problems has lead to tremendous progress over the last decades. While current solvers can solve some of the problems that seemed completely out-of-reach just 10 years ago, there are always relevant MIP problems that currently cannot be solved. With the Smoothie solver we intend to solve extremely hard MIP problems by building on the many years that went into the development of several state-of-the-art MIP solvers and by utilizing some of the largest computing resources available. The high-level task parallelization framework UG (Ubiquity Generator) is used and extended by Smoothie to build a solver that uses large-scale parallelization to distribute the solution of a single MIP on a shared- or distributed-memory computing infrastructure, thereby employing several established MIP solvers simultaneously. For the first development phase, which is the topic of this report, both FICO Xpress and Gurobi are used in concurrent mode on a single machine, while information on incumbent solutions and explored branch-and-bound subtrees is exchanged. A dynamic restarting mechanism ensures that solver configurations are selected that promise most suitable for the MIP to be solved. We report on initial findings using this early version of Smoothie on unsolved problems from MIPLIB 2017.}, language = {en} } @misc{KempkeKuntKatamishetal.2025, author = {Kempke, Nils-Christian and Kunt, Tim and Katamish, Bassel and Vanaret, Charlie and Sasanpour, Shima and Clarner, Jan-Patrick and Koch, Thorsten}, title = {Developing heuristic solution techniques for large-scale unit commitment models}, issn = {1438-0064}, arxiv = {http://arxiv.org/abs/2502.19012}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-99555}, year = {2025}, abstract = {Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and operational decision-making. ESOMs are frequently formulated as linear (LPs) and mixed-integer linear (MIP) problems. MIPs allow continuous and discrete decision variables. Consequently, they are substantially more expressive than LPs but also more challenging to solve. The ever-growing size and complexity of ESOMs take a toll on the computational time of state-of-the-art commercial solvers. Indeed, for large-scale ESOMs, solving the LP relaxation -- the basis of modern MIP solution algorithms -- can be very costly. These time requirements can render ESOM MIPs impractical for real-world applications. This article considers a set of large-scale decarbonization-focused unit commitment models with expansion decisions based on the REMix framework (up to 83 million variables and 900,000 discrete decision variables). For these particular instances, the solution to the LP relaxation and the MIP optimum lie close. Based on this observation, we investigate the application of relaxation-enforced neighborhood search (RENS), machine learning guided rounding, and a fix-and-propagate (FP) heuristic as a standalone solution method. Our approach generated feasible solutions 20 to 100 times faster than GUROBI, achieving comparable solution quality with primal-dual gaps as low as 1\% and up to 35\%. This enabled us to solve numerous scenarios without lowering the quality of our models. For some instances that Gurobi could not solve within two days, our FP method provided feasible solutions in under one hour.}, language = {en} }