TY - GEN A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Miltenberger, Matthias A1 - Weninger, Dieter T1 - Progress in Presolving for Mixed Integer Programming N2 - Presolving attempts to eliminate redundant information from the problem formulation and simultaneously tries to strengthen the formulation. It can be very effective and is often essential for solving instances. Especially for mixed integer programming problems, fast and effective presolving algorithms are very important. In this paper, we report on three new presolving techniques. The first method searches for singleton continuous columns and tries to fix the corresponding variables. Then we present a presolving technique which exploits a partial order of the variables to induce fixings. Finally, we show an approach based on connected components in graphs. Our computational results confirm the profitable use of the algorithms in practice. T3 - ZIB-Report - 13-48 KW - mixed-integer programming KW - presolving KW - preprocessing Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42530 SN - 1438-0064 ER - TY - GEN A1 - Clarner, Jan-Patrick A1 - Tawfik, Christine A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Network-induced Unit Commitment - A model class for investment and production portfolio planning for multi-energy systems N2 - In light of the energy transition production planning of future decarbonized energy systems lead to very large and complex optimization problems. A widely used modeling paradigm for modeling and solving such problems is mathematical programming. While there are various scientific energy system models and modeling tools, most of them do not provide the necessary level of detail or the modeling flexibility to be applicable for industrial usage. Industrial modeling tools, on the other hand, provide a high level of detail and modeling flexibility. However, those models often exhibit a size and complexity that restricts their scope to a time horizon of several months, severely complicating long-term planning. As a remedy, we propose a model class that is detailed enough for real-world usage but still compact enough for long-term planning. The model class is based on a generalized unit commitment problem on a network with investment decisions. The focus lies on the topological dependency of different energy production and transportation units. T3 - ZIB-Report - 22-16 KW - Multi-energy systems KW - Unit commitment KW - Investment planning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87607 SN - 1438-0064 ER - TY - GEN A1 - Pedersen, Jaap A1 - Le, Thi Thai A1 - Koch, Thorsten A1 - Zittel, Janina T1 - Optimal discrete pipe sizing for tree-shaped CO2 networks N2 - While energy-intensive industries like the steel industry plan to switch to renewable energy sources, other industries, such as the cement industry, have to rely on carbon capture storage and utilization technologies to reduce the inevitable carbon dioxide (CO2) emissions of their production processes. In this context, we investigate the problem of finding optimal pipeline diameters from a discrete set of diameters for a tree-shaped network transporting captured CO2 from multiple sources to a single sink. The general problem of optimizing arc capacities in potential-based fluid networks is a challenging mixed-integer nonlinear program. Additionally, the behaviour of CO2 is highly sensitive and nonlinear regarding temperature and pressure changes. We propose an iterative algorithm splitting the problem into two parts: a) the pipe-sizing problem under a fixed supply scenario and temperature distribution and b) the thermophysical modelling including mixing effects, the Joule-Thomson effect, and heat exchange with the surrounding environment. We show the effectiveness of our approach by applying our algorithm to a real-world network planning problem for a CO2 network in Western Germany. T3 - ZIB-Report - 22-15 KW - CO2 Transport KW - Network Design KW - Pipeline Sizing Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-87574 SN - 1438-0064 ER - TY - JOUR A1 - Le, Thi Thai A1 - Koch, Thorsten T1 - Viscosity and porosity effects on tangential-discontinuity surface stability in 3D Compressible Media JF - Physics of Fluids N2 - The stability of a flow in porous media relates to the velocity rate of injecting and withdrawing natural gases inside porous storage. We thus aim to analyze the stability of flows in porous media to accelerate the energy transition process. This research examines a flow model of a tangential--velocity discontinuity with porosity and viscosity changes in a three-dimensional (3D) compressible medium because of a co-existence of different gases in a storage. The fluids are assumed to move in a relative motion where the plane y=0 is a tangential-velocity discontinuity surface. We obtain that the critical value of the Mach number to stabilize a tangential discontinuity surface of flows via porous media is smaller than the one of flows in a plane. The critical value of the Mach number M to stabilize a discontinuity surface of the 3D flow is different by a factor |cosθ| compared to the two-dimensional (2D) flow. Here, θ is the angle between velocity and wavenumber vectors. Our results also show that the flow model with viscosity and porosity effects is stable faster than those without these terms. Our analysis is done for both infinite and finite flows. The effect of solid walls along the flow direction could suppress the instability, i.e., the tangential-discontinuity surface is stabilized faster Y1 - 2022 U6 - https://doi.org/10.1063/5.0095970 VL - 34 IS - 7 PB - AIP Publishing ER - TY - JOUR A1 - Chen, Ying A1 - Koch, Thorsten A1 - Zakiyeva, Nazgul A1 - Liu, Kailiang A1 - Xu, Zhitong A1 - Chen, Chun-houh A1 - Nakano, Junji A1 - Honda, Keisuke T1 - Article's Scientific Prestige: Measuring the Impact of Individual Articles in the Web of Science N2 - We performed a citation analysis on the Web of Science publications consisting of more than 63 million articles and 1.45 billion citations on 254 subjects from 1981 to 2020. We proposed the Article’s Scientific Prestige (ASP) metric and compared this metric to number of citations (#Cit) and journal grade in measuring the scientific impact of individual articles in the large-scale hierarchical and multi-disciplined citation network. In contrast to #Cit, ASP, that is computed based on the eigenvector centrality, considers both direct and indirect citations, and provides steady-state evaluation cross different disciplines. We found that ASP and #Cit are not aligned for most articles, with a growing mismatch amongst the less cited articles. While both metrics are reliable for evaluating the prestige of articles such as Nobel Prize winning articles, ASP tends to provide more persuasive rankings than #Cit when the articles are not highly cited. The journal grade, that is eventually determined by a few highly cited articles, is unable to properly reflect the scientific impact of individual articles. The number of references and coauthors are less relevant to scientific impact, but subjects do make a difference. T3 - ZIB-Report - 22-07 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86380 VL - 17 IS - 1 SP - 101379 ER - TY - GEN A1 - Turner, Mark A1 - Koch, Thorsten A1 - Serrano, Felipe A1 - Winkler, Michael T1 - Adaptive Cut Selection in Mixed-Integer Linear Programming N2 - Cut selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP. T3 - ZIB-Report - 22-04 KW - cut selection KW - mixed-integer linear programming KW - reinforcement learning Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86055 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten A1 - Shinano, Yuji T1 - Faster exact solution of sparse MaxCut and QUBO problems T3 - ZIB-Report - 22-02 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85715 SN - 1438-0064 ER - TY - JOUR A1 - Hoppmann-Baum, Kai A1 - Burdakov, Oleg A1 - Mexi, Gioni A1 - Casselgren, Carl Johan A1 - Koch, Thorsten T1 - Length-Constrained Cycle Partition with an Application to UAV Routing JF - Optimization Methods and Software N2 - This article discusses the Length-Constrained Cycle Partition Problem (LCCP), which constitutes a new generalization of the Travelling Salesperson Problem (TSP). Apart from nonnegative edge weights, the undirected graph in LCCP features a nonnegative critical length parameter for each vertex. A cycle partition, i.e., a vertex-disjoint cycle cover, is a feasible solution for LCCP if the length of each cycle is not greater than the critical length of each vertex contained in it. The goal is to find a feasible partition having a minimum number of cycles. Besides analyzing theoretical properties and developing preprocessing techniques, we propose an elaborate heuristic algorithm that produces solutions of good quality even for large-size instances. Moreover, we present two exact mixed-integer programming formulations (MIPs) for LCCP, which are inspired by well-known modeling approaches for TSP. Further, we introduce the concept of conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a discussion on computational experiments that we conducted using (A)TSPLIB-based problem instances. As a motivating example application, we describe a routing problem where a fleet of uncrewed aerial vehicles (UAVs) must patrol a given set of areas. Y1 - 2022 U6 - https://doi.org/10.1080/10556788.2022.2053972 ER - TY - JOUR A1 - Turner, Mark A1 - Koch, Thorsten A1 - Serrano, Felipe A1 - Winkler, Michael T1 - Adaptive Cut Selection in Mixed-Integer Linear Programming JF - Open Journal of Mathematical Optimization N2 - Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP. Y1 - 2023 U6 - https://doi.org/10.5802/ojmo.25 VL - 4 SP - 5 ER - TY - GEN A1 - Charousset-Brignol, Sandrine A1 - van Ackooij, Wim A1 - Oudjane, Nadia A1 - Daniel, Dominique A1 - Noceir, Slimane A1 - Haus, Utz-Uwe A1 - Lazzaro, Alfio A1 - Frangioni, Antonio A1 - Lobato, Rafael A1 - Ghezelsoflu, Ali A1 - Iardella, Niccolò A1 - Galli, Laura A1 - Gorgone, Enrico A1 - dell’Amico, Mauro A1 - Giannelos, Spyros A1 - Moreira, Alex A1 - Strbac, Goran A1 - Borozan, Stefan A1 - Falugi, Paula A1 - Pudjianto, Danny A1 - Wyrwoll, Lothar A1 - Schmitt, Carlo A1 - Franken, Marco A1 - Beulertz, Daniel A1 - Schwaeppe, Henrik A1 - Most, Dieter A1 - Yüksel-Ergün, Inci A1 - Zittel, Janina A1 - Koch, Thorsten T1 - Synergistic approach of multi-energy models for a European optimal energy system management tool T2 - The Project Repository Journal Y1 - 2021 VL - 9 SP - 113 EP - 116 ER -