@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} } @misc{HosodaMaherShinanoetal.2023, author = {Hosoda, Junko and Maher, Stephen J. and Shinano, Yuji and Villumsen, Jonas Christoffer}, title = {A parallel branch-and-bound heuristic for the integrated long-haul and local vehicle routing problem on an adaptive transportation network}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89700}, year = {2023}, abstract = {Consolidation of commodities and coordination of vehicle routes are fundamental features of supply chain management problems. While locations for consolidation and coordination are typically known a priori, in adaptive transportation networks this is not the case. The identification of such consolidation locations forms part of the decision making process. Supply chain management problems integrating the designation of consolidation locations with the coordination of long haul and local vehicle routing is not only challenging to solve, but also very difficult to formulate mathematically. In this paper, the first mathematical model integrating location clustering with long haul and local vehicle routing is proposed. This mathematical formulation is used to develop algorithms to find high quality solutions. A novel parallel framework is developed that combines exact and heuristic methods to improve the search for high quality solutions and provide valid bounds. The results demonstrate that using exact methods to guide heuristic search is an effective approach to find high quality solutions for difficult supply chain management problems.}, language = {en} } @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{MasingLindnerEbert2023, author = {Masing, Berenike and Lindner, Niels and Ebert, Patricia}, title = {Forward and Line-Based Cycle Bases for Periodic Timetabling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89731}, year = {2023}, abstract = {The optimization of periodic timetables is an indispensable planning task in public transport. Although the periodic event scheduling problem (PESP) provides an elegant mathematical formulation of the periodic timetabling problem that led to many insights for primal heuristics, it is notoriously hard to solve to optimality. One reason is that for the standard mixed-integer linear programming formulations, linear programming relaxations are weak and the integer variables are of pure technical nature and in general do not correlate with the objective value. While the first problem has been addressed by developing several families of cutting planes, we focus on the second aspect. We discuss integral forward cycle bases as a concept to compute improved dual bounds for PESP instances. To this end, we develop the theory of forward cycle bases on general digraphs. Specifically for the application of timetabling, we devise a generic procedure to construct line-based event-activity networks, and give a simple recipe for an integral forward cycle basis on such networks. Finally, we analyze the 16 railway instances of the benchmark library PESPlib, match them to the line-based structure and use forward cycle bases to compute better dual bounds for 14 out of the 16 instances.}, 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{Paskin2022, type = {Master Thesis}, author = {Paskin, Martha}, title = {Estimating 3D Shape of the Head Skeleton of Basking Sharks Using Annotated Landmarks on a 2D Image}, year = {2022}, abstract = {Basking sharks are thought to be one of the most efficient filter-feeding fish in terms of the throughput of water filtered through their gills. Details about the underlying morphology of their branchial region have not been studied due to various challenges in acquiring real-world data. The present thesis aims to facilitate this, by developing a mathematical shape model which constructs the 3D structure of the head skeleton of a basking shark using annotated landmarks on a single 2D image. This is an ill-posed problem as estimating the depth of a 3D object from a single 2D view is, in general, not possible. To reduce this ambiguity, we create a set of pre-defined training shapes in 3D from CT scans of basking sharks. First, the damaged structures of the sharks in the scans are corrected via solving a set of optimization problems, before using them as accurate 3D representations of the object. Then, two approaches are employed for the 2D-to-3D shape fitting problem-an Active Shape Model approach and a Kendall's Shape Space approach. The former represents a shape as a point on a high-dimensional Euclidean space, whereas the latter represents a shape as an equivalence class of points in this Euclidean space. Kendall's shape space approach is a novel technique that has not yet been applied in this context, and a comprehensive comparison of the two approaches suggests this approach to be superior for the problem at hand. This can be credited to an improved interpolation of the training shapes.}, language = {en} } @misc{PaskinBaumDeanetal.2022, author = {Paskin, Martha and Baum, Daniel and Dean, Mason N. and von Tycowicz, Christoph}, title = {A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks -- Source Code and Data}, doi = {10.12752/8730}, year = {2022}, abstract = {Source code and novel dataset of basking shark head skeletons facilitating the reproduction of the results presented in 'A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks' - ECCV 2022.}, language = {en} } @misc{TateiwaShinanoYasudaetal.2021, author = {Tateiwa, Nariaki and Shinano, Yuji and Yasuda, Masaya and Kaji, Shizuo and Yamamura, Keiichiro and Fujisawa, Katsuki}, title = {Massively parallel sharing lattice basis reduction}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-85209}, year = {2021}, abstract = {For cryptanalysis in lattice-based schemes, the performance evaluation of lattice basis reduction using high-performance computers is becoming increasingly important for the determination of the security level. We propose a distributed and asynchronous parallel reduction algorithm based on randomization and DeepBKZ, which is an improved variant of the block Korkine-Zolotarev (BKZ) reduction algorithm. Randomized copies of a lattice basis are distributed to up to 103,680 cores and independently reduced in parallel, while some basis vectors are shared asynchronously among all processes via MPI. There is a trade-off between randomization and information sharing; if a substantial amount of information is shared, all processes will work on the same problem, thereby diminishing the benefit of parallelization. To monitor this balance between randomness and sharing, we propose a metric to quantify the variety of lattice bases. We empirically find an optimal parameter of sharing for high-dimensional lattices. We demonstrate the efficacy of our proposed parallel algorithm and implementation with respect to both performance and scalability through our experiments.}, language = {en} } @misc{FujiiItoKimetal.2021, author = {Fujii, Koichi and Ito, Naoki and Kim, Sunyoung and Kojima, Masakazu and Shinano, Yuji and Toh, Kim-Chuan}, title = {Solving Challenging Large Scale QAPs}, issn = {1438-0064}, doi = {10.12752/8130}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81303}, year = {2021}, abstract = {We report our progress on the project for solving larger scale quadratic assignment problems (QAPs). Our main approach to solve large scale NP-hard combinatorial optimization problems such as QAPs is a parallel branch-and-bound method efficiently implemented on a powerful computer system using the Ubiquity Generator(UG) framework that can utilize more than 100,000 cores. Lower bounding procedures incorporated in the branch-and-bound method play a crucial role in solving the problems. For a strong lower bounding procedure, we employ the Lagrangian doubly nonnegative (DNN) relaxation and the Newton-bracketing method developed by the authors' group. In this report, we describe some basic tools used in the project including the lower bounding procedure and branching rules, and present some preliminary numerical results. Our next target problem is QAPs with dimension at least 50, as we have succeeded to solve tai30a and sko42 from QAPLIB for the first time.}, language = {en} }