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About 23% of the German energy demand is supplied by natural gas. Additionally, for about the same amount Germany serves as a transit country. Thereby, the German network represents a central hub in the European natural gas transport network. The transport infrastructure is operated by transmissions system operators (TSOs). The number one priority of the TSOs is to ensure the security of supply. However, the TSOs have only very limited knowledge about the intentions and planned actions of the shippers (traders). Open Grid Europe (OGE), one of Germany’s largest TSO, operates a high-pressure transport network of about 12,000 km length. With the introduction of peak-load gas power stations, it is of great importance to predict in- and out-flow of the network to ensure the necessary flexibility and security of supply for the German Energy Transition (“Energiewende”). In this paper, we introduce a novel hybrid forecast method applied to gas flows at the boundary nodes of a transport network. This method employs an optimized feature selection and minimization. We use a combination of a FAR, LSTM and mathematical programming to achieve robust high-quality forecasts on real-world data for different types of network nodes.
About 20% of the German energy demand is supplied by natural gas. Ad-
ditionally, for about twice the amount Germany serves as a transit country. Thereby, the German network represents a central hub in the European natural gas transport network. The transport infrastructure is operated by so-called transmissions system operators or TSOs. The number one priority of the TSOs is to ensure security of supply. However, the TSOs have no knowledge of the intentions and planned actions of the shippers (traders).
Open Grid Europe (OGE), one of Germany’s largest TSO, operates a high-
pressure transport network of about 12.000 km length. Since flexibility and security of supply is of utmost importance to the German Energy Transition (“Energiewende”) especially with the introduction of peak-load gas power stations, being able to predict in- and out-flow of the network is of great importance.
In this paper we introduce a new hybrid forecast method applied to gas
flows at the boundary nodes of a transport network. The new method employs optimized feature minimization and selection. We use a combination of an FAR, LSTM DNN and mathematical programming to achieve robust high quality forecasts on real world data for different types of network nodes.
Keywords: Gas Forecast, Time series, Hybrid Method, FAR, LSTM, Mathematical Optimisation
We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann libraries and for a new collection of numerically difficult instances.
We present an exact rational solver for mixed-integer linear programming that avoids the numerical inaccuracies inherent in the floating-point computations used by existing software. This allows the solver to be used for establishing theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-and-bound, using numerically-safe methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several safe dual bounding methods depending on the structure of the instance, our exact solver is only moderately slower than an inexact floating-point branch-and-bound solver. The software is incorporated into the SCIP optimization framework, using the exact LP solver QSopt_ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the MIPLIB and Mittelmann libraries and for a new collection of numerically difficult instances.
Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate. Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems. The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de
Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby assigning a central role in energy politics to the transportation and distribution of gas. These newly imposed political requirements influenced the technical processes of gas transport in such a way that the complex task of planning and operating gas networks has become even more intricate.
Mathematically, the combination of discrete decisions on the configuration of a gas transport network, the nonlinear equations describing the physics of gas, and the uncertainty in demand and supply yield large-scale and highly complex stochastic mixed-integer nonlinear optimization problems.
The Matheon project "Optimization of Gas Transport" takes the key role of making available the necessary core technology to solve the mathematical optimization problems which model the topology planning and the operation of gas networks. An important aspect of the academic impact is the free availability of our framework. As a result of several years of research and development, it is now possible to download a complete state-of-the-art framework for mixed-integer linear and nonlinear programming in source code at http://scip.zib.de
A massively parallel interior-point solver for linear energy system models with block structure
(2019)
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.
Linear energy system models are a crucial component of energy system design and operations, as well as energy policy consulting. If detailed enough, such models lead to large-scale linear programs, which can be intractable even for the best state-of-the-art solvers. This article introduces an interior-point solver that exploits common structures of 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. In order to handle the large number of linking constraints and variables commonly observed in energy system models, a distributed Schur complement preconditioner 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 solver PIPS-IPM. We evaluate the computational performance on energy system models with up to four billion nonzero entries in the constraint matrix—and up to one billion columns and one billion 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 in recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models.
In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs.
This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.
In 2005 the European Union liberalized the gas market with a disruptive change
and decoupled trading of natural gas from its transport. The gas is now trans-
ported by independent so-called transmissions system operators or TSOs. The
market model established by the European Union views the gas transmission
network as a black box, providing shippers (gas traders and consumers) the
opportunity to transport gas from any entry to any exit. TSOs are required
to offer the maximum possible capacities at each entry and exit such that any
resulting gas flow can be realized by the network. The revenue from selling these
capacities more than one billion Euro in Germany alone, but overestimating the
capacity might compromise the security of supply. Therefore, evaluating the
available transport capacities is extremely important to the TSOs.
This is a report on a large project in mathematical optimization, set out
to develop a new toolset for evaluating gas network capacities. The goals and
the challenges as they occurred in the project are described, as well as the
developments and design decisions taken to meet the requirements.
Since 2005, the gas market in the European Union is liberalized and the trading of natural gas is decoupled from its transport. The transport is done by so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer maximum independent capacities at each entry and exit such that the resulting gas flows can be realized by the network without compromising security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs.
This paper gives an overview of the toolset for evaluating gas network capacities that has been developed within the ForNe project, a joint research project of seven research partners initiated by Open Grid Europe, Germany's biggest TSO. While most of the relevant mathematics is described in the book "Evaluating Gas Network Capacities", this article sketches the system as a whole, describes some developments that have taken place recently, and gives some details about the current implementation.
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.
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.
We present an exact rational solver for mixed-integer linear programming
that avoids the numerical inaccuracies inherent in the floating-point
computations used by existing software. This allows the solver to be used
for establishing theoretical results and in applications where correct
solutions are critical due to legal and financial consequences. Our solver
is a hybrid symbolic/numeric implementation of LP-based branch-and-bound,
using numerically-safe methods for all binding computations in the search
tree. Computing provably accurate solutions by dynamically choosing the
fastest of several safe dual bounding methods depending on the structure of
the instance, our exact solver is only moderately slower than an inexact
floating-point branch-and-bound solver. The software is incorporated into
the SCIP optimization framework, using the exact LP solver QSopt_ex and the
GMP arithmetic library. Computational results are presented for a suite of
test instances taken from the MIPLIB and Mittelmann collections.
Article's Scientific Prestige: Measuring the Impact of Individual Articles in the Web of Science
(2022)
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.
Article’s scientific prestige: Measuring the impact of individual articles in the web of science
(2023)
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.
BEAM-ME: Accelerating Linear Energy Systems Models by a Massively Parallel Interior Point Method
(2020)
Die europaische Gasinfrastruktur wird disruptiv in ein zukunftiges dekarbonisiertes Energiesystem verändert; ein Prozess, der angesichts der jüngsten politischen Situation beschleunigt werden muss. Mit einem wachsenden Wasserstoffmarkt wird der pipelinebasierte Transport unter Nutzung der bestehenden Erdgasinfrastruktur wirtschaftlich sinnvoll, trägt zur Erhöhung der öffentlichen Akzeptanz bei und beschleunigt den Umstellungsprozess. In diesem Beitrag wird die maximal technisch machbare Einspeisung von Wasserstoff in das bestehende deutsche Erdgastransportnetz hinsichtlich regulatorischer Grenzwerte der Gasqualität analysiert. Die Analyse erfolgt auf Basis eines transienten Tracking-Modells, das auf dem allgemeinen Pooling-Problem einschließlich Linepack aufbaut. Es zeigt sich, dass das Gasnetz auch bei strengen Grenzwerten gen ̈ugend Kapazität bietet, um für einen großen Teil der bis 2030 geplanten Erzeugungskapazität für grünen Wasserstoff als garantierter Abnehmer zu dienen.
Die europäische Gasinfrastruktur wird disruptiv in ein zukünftiges dekarbonisiertes Energiesystem verändert; ein Prozess, der angesichts der jüngsten politischen Situation beschleunigt werden muss. Mit einem wachsenden Wasserstoffmarkt wird der pipelinebasierte Transport unter Nutzung der bestehenden Erdgasinfrastruktur wirtschaftlich sinnvoll, trägt zur Erhöhung der öffentlichen Akzeptanz bei und beschleunigt den Umstellungsprozess. In diesem Fachbeitrag wird die maximal technisch machbare Einspeisung von Wasserstoff in das bestehende deutsche Erdgastransportnetz hinsichtlich regulatorischer Grenzwerte der Gasqualität analysiert. Die Analyse erfolgt auf Basis eines transienten Tracking-Modells, das auf dem allgemeinen Pooling-Problem
einschließlich Linepack aufbaut. Es zeigt sich, dass das Gasnetz auch bei strengen Grenzwerten genügend Kapazität bietet, um für einen großen Teil der bis 2030 geplanten Erzeugungskapazität für grünen Wasserstoff als garantierter Abnehmer zu dienen.
In the transition towards a pure hydrogen infrastructure, repurposing the existing natural gas infrastructure is considered. In this study, the maximal technically feasible injection of hydrogen into the existing German natural gas transmission network is analysed with respect to regulatory limits regarding the gas quality. We propose a transient tracking model based on the general pooling problem including linepack. The analysis is conducted using real-world hourly gas flow data on a network of about 10,000 km length.
In the transition towards a pure hydrogen infrastructure, utilizing the existing natural gas infrastructure is a necessity. In this study, the maximal technically feasible injection of hydrogen into the existing German natural gas transmission network is analysed with respect to regulatory limits regarding the gas quality. We propose a transient tracking model based on the general pooling problem including linepack. The analysis is conducted using real-world hourly gas flow data on a network of about 10,000 km length.
Mixed integer programs ($MIPs$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in $SIP$, a state-of-the-art $MIP$ solver. We give computational results that show the superiority of the new strategy.
Branching rules revisited
(2004)
Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on. We present a new generalization called {\sl reliability branching} of today's state-of-the-art {\sl strong branching} and {\sl pseudocost branching} strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed newstrategy.
Branching Rules Revisited
(2005)
Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017.
Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a $4\%$ decrease in solve time, and an $8\%$ decrease in number of nodes over affected instances of MIPLIB 2017.
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 parallel 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 benchmark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been considerably 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.
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.
Im Oktober 2012 hatte die Deutsche Forschungsgemeinschaft (DFG) ein Förderprogramm zur Neuausrichtung überregionaler Informationsservices ausgeschrieben, um eine umfassende Reorganisation bestehender Infrastrukturen anzustoßen, die mit den Empfehlungen des Wissenschaftsrates zur Zukunft der bibliothekarischen Verbundsysteme in Deutschland gefordert wurde. Im Themenfeld „Bibliotheksdateninfrastruktur und Lokale Systeme“ der DFG-Ausschreibung wurde das vom Hessischen Bibliotheksinformationssystem (HeBIS), vom Bibliotheksverbund Bayern (BVB) und vom Kooperativen Bibliotheksverbund Berlin-Brandenburg (KOBV) beantragte Vorhaben „Cloudbasierte Infrastruktur für Bibliotheksdaten“ (CIB) bewilligt. Das Projekt zielt auf die Überführung bibliothekarischer Workflows und Dienste in cloudbasierte Arbeitsumgebungen und die sukzessive Ablösung traditioneller Verbund- und Lokalsysteme durch internationale Systemplattformen. Zu den Arbeitspaketen des Vorhabens gehört u. a. die Einbindung von Norm- und Fremddatenangeboten und von weiteren Services in diese Plattformen.
Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver.
The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced.
Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver. The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced.
In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.
In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.
This paper introduces an implementation for solving the single-source shortest path problem on distributed-memory machines. It is tailored to power-law graphs and scales to trillions of edges.
The new implementation reached 2nd and 10th place in the latest Graph500 benchmark in June 2022 and handled the largest and second-largest graphs among all participants.
In recent years, European gas transport has been affected by major disruptive events like political issues such as, most recently, the Russian war on Ukraine. To incorporate the impacts of such events into decision-making during the energy transition, more complex models for gas network analysis are required. However, the limited availability of consistent data presents a significant obstacle in this endeavor. We use a mathematical-modeling-based scenario generator to deal with this obstacle. The scenario generator consists of capacitated network flow models representing the gas network at different aggregation levels. In this study, we present the coarse-to-fine approach utilized in this scenario generator.
This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques.
This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the nonlinear constraints by employing constraint programming techniques.
Compressor stations are the heart of every high-pressure gas transport network.
Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network.
Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner.
As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area.
Since the desired performance of the station changes over time, the configuration of the station has to adapt.
Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario.
This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge.
By presenting extensive computational results on real world data we demonstrate the performance of our approach.
Compressor stations are the heart of every high-pressure gas transport network.
Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network.
Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner.
As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area.
Since the desired performance of the station changes over time, the configuration of the station has to adapt.
Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario.
This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge.
By presenting extensive computational results on real world data we demonstrate the performance of our approach.
In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection.
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.
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.
As the natural gas market is moving towards short-term planning, accurate and robust short-term forecasts of the demand and supply of natural gas is of fundamental importance for a stable energy supply, a natural gas control schedule, and transport operation on a daily basis. We propose a hybrid forecast model, Functional AutoRegressive and Convolutional Neural Network model, based on state-of-the-art statistical modeling and artificial neural networks. We conduct short-term forecasting of the hourly natural gas flows of 92 distribution nodes in the German high-pressure gas pipeline network, showing that the proposed model provides nice and stable accuracy for different types of nodes. It outperforms all the alternative models, with an improved relative accuracy up to twofold for plant nodes and up to fourfold for municipal nodes. For the border nodes with rather flat gas flows, it has an accuracy that is comparable to the best performing alternative model.
Deep learning for spatio-temporal supply and demand forecasting in natural gas transmission networks
(2021)
Germany is the largest market for natural gas in the European Union, with an annual consumption of approx. 95 billion cubic meters. Germany's high-pressure gas pipeline network is roughly 40,000 km long, which enables highly fluctuating quantities of gas to be transported safely over long distances. Considering that similar amounts of gas are also transshipped through Germany to other EU states, it is clear that Germany's gas transport system is essential to the European energy supply. Since the average velocity of gas in a pipeline is only 25km/h, an adequate high-precision, high-frequency forecasting of supply and demand is crucial for efficient control and operation of such a transmission network. We propose a deep learning model based on spatio-temporal convolutional neural networks (DLST) to tackle the problem of gas flow forecasting in a complex high-pressure transmission network. Experiments show that our model effectively captures comprehensive spatio-temporal correlations through modeling gas networks and consistently outperforms state-of-the-art benchmarks on real-world data sets by at least 21$\%$.
The results demonstrate that the proposed model can deal with complex nonlinear gas network flow forecasting with high accuracy and effectiveness.
Deep learning for spatio-temporal supply anddemand forecasting in natural gas transmission networks
(2021)
Germany is the largest market for natural gas in the European Union, with an annual consumption of approx. 95 billion cubic meters. Germany's high-pressure gas pipeline network is roughly 40,000 km long, which enables highly fluctuating quantities of gas to be transported safely over long distances. Considering that similar amounts of gas are also transshipped through Germany to other EU states, it is clear that Germany's gas transport system is essential to the European energy supply. Since the average velocity of gas in a pipeline is only 25km/h, an adequate high-precision, high-frequency forecasting of supply and demand is crucial for efficient control and operation of such a transmission network. We propose a deep learning model based on spatio-temporal convolutional neural networks (DLST) to tackle the problem of gas flow forecasting in a complex high-pressure transmission network. Experiments show that our model effectively captures comprehensive spatio-temporal correlations through modeling gas networks and consistently outperforms state-of-the-art benchmarks on real-world data sets by at least 21%.
The results demonstrate that the proposed model can deal with complex nonlinear gas network flow forecasting with high accuracy and effectiveness.
In Deutschland wurden 2011 wichtige Akzente für die Umsetzung des Grünen Wegs der Open-Access-Bewegung gesetzt: Mit finanzieller Unterstützung der Deutschen Forschungsgemeinschaft (DFG) haben Bibliotheken sogenannte Allianz-Lizenzen mit Verlagen verhandelt, in denen weitreichende Rechte hinsichtlich der Open-Access-Archivierung verankert sind. Autorinnen und Autoren zugriffsberechtigter Einrichtungen können ihre Artikel, die in diesen lizenzierten Zeitschriften erschienen sind, ohne oder mit nur kurzer Embargofrist in geeigneten Repositorien ihrer Wahl frei zugänglich machen.
Allerdings macht der Kreis berechtigter Autorinnen und Autoren nur sehr zögerlich von seinen Open-Access-Rechten Gebrauch. Auch die Bibliotheken – als Betreiber der Repositorien und damit Vertreter für die berechtigten Autorinnen und Autoren – nutzen dieses Recht nur unzureichend.
Mit DeepGreen verfolgen die Antragssteller das Ziel, einen Großteil jener Publikationen, die unter den speziell im DFG-geförderten Kontext verhandelten Bedingungen grün online gehen dürften, auch tatsächlich online abrufbar zu machen. Im Rahmen des Projektes wird prototypisch mit Allianzverlagen und berechtigten Bibliotheken ein möglichst stark automatisierter Workflow entwickelt, in dem rechtssichere Verlagsdaten inklusive der Volltexte abgeliefert und von Repositorien eingespielt werden. Ein technischer Baustein ist dabei ein intermediäres Repositorium, das als Datenverteiler dient.
Das nationale Projektkonsortium besteht aus den zwei Bibliotheksverbünden Kooperativer Bibliotheksverbund Berlin-Brandenburg (KOBV) und Bibliotheksverbund Bayern (BVB), den zwei Universitätsbibliotheken der Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) und der Technische Universität Berlin (TU Berlin), zusätzlich die Bayerische Staatsbibliothek (BSB) und eine außeruniversitäre Forschungseinrichtung - das Helmholtz Open Science Koordinationsbüro am Deutschen GeoForschungsZentrum (GFZ).
Das Projekt startet zum 01. Januar 2016. Hier vorliegend finden Sie den Projektantrag zum Nachlesen.
Mit dem DFG-geförderten Projekt DeepGreen soll eine automatisierte, rechtssichere Lösung entwickelt werden, um Artikeldaten von wissenschaftlichen Verlagen abzuholen und anschließend, nach Ablauf etwaiger lizenzrechtlicher Embargofristen, an berechtigte Repositorien zu verteilen und somit in den Open Access zu überführen. Dabei liegt der Fokus auf den DFG-geförderten und überregional verhandelten Allianz-Lizenzen, mit spezieller Open-Access-Komponente.
Die vorliegende Handreichung richtet sich speziell an die Betreiber institutioneller Repositorien und stellt Empfehlungen und einen Workflow bereit, um eine erfolgreiche Veröffentlichung, der durch die DeepGreen-Datendrehscheibe zugeordneten Artikel, zu ermöglichen. Die Handreichung basiert auf den bisherigen Erfahrungen der DeepGreen-Projektbeteiligten.
In 2011, important priorities were set to realize green publications in the open access movement in Germany. With financial support from the German Research Foundation (DFG), libraries negotiated Alliance licenses with publishers that guarantee extensive open access rights. Authors of institutions, that have therewith access to licensed journals, can freely publish their articles immediately or after a short embargo period in a repository of their choice. However, authors hesitantly use these open access rights. Also libraries – as managers of institutional and subject based repositories and thus legitimated representatives for the authors – only rarely make use of these rights. The aim of DeepGreen is to make the majority of those publications available online. Together with publishers of the Alliance licenses, the project consortium wants to develop a nearly fully automated workflow that covers both the delivery of data, including the full texts, of the publishers, as well as the data transformation to the necessary import formats and the loading process into the repositories. An intermediate “publication router” will serve as a distribution platform. The DeepGreen metadata schema contains metadata properties describing a wide range of deliverable bibliographic metadata from the Alliance license publishers (most common standards are JATS and CrossRef XML) as well as its compliance with technical, quality and metadata standards of the repositories. The schema includes required metadata elements and optional properties providing additional information.The metadata schema is aligned to the OCLC repository best practices (“Best Practices for CONTENTdm and other OAI-PMH compliant repositories: creating sharable metadata”, URL: http://www.oclc.org/content/dam/support/wcdigitalcollectiongateway/MetadataBestPractices.pdf). The current version of the schema is subject to changes as the functional requirements and workflow practices are evolving during the project experiences and prototype production.
Für den geforderten – und von der Deutschen Forschungsgemeinschaft (DFG) geförderten – Open-Access-Transformationsprozess der deutschen, wissenschaftlichen Publikationslandschaft braucht es neue Formen der Zusammenarbeit zwischen Wissenschaft und Verlagen. Bereits seit 2011 wurden mit Unterstützung seitens der DFG in Deutschland die sogenannten Allianz-Lizenzen zwischen Bibliotheken und Verlagen verhandelt, in denen weitreichende Rechte hinsichtlich der Open-Access-Archivierung verankert sind: Autorinnen und Autoren aber auch die sie vertretenden Einrichtungen dürfen Artikel, die in lizenzierten Zeitschriften erschienen sind, ohne oder mit nur kurzer Embargofrist in geeigneten Repositorien ihrer Wahl frei zugänglich machen. Aufbauend auf diese Open-Access-Komponenten zeigt das DFG-geförderte Projekt „DeepGreen“ ein mögliches neues Modell der Zusammenarbeit mit Verlagen auf: DeepGreen setzt auf die automatisierte Verteilung von Artikeldaten von Verlagen an Repositorien und will disziplinübergreifend einen Großteil jener wissenschaftlichen Publikationen aus Fachzeitschriften, die unter lizenzrechtlichen Kontexten frei zugänglich online gehen dürften, auch tatsächlich online abrufbar machen.
Erprobte DeepGreen von 2016 bis Ende 2017 prototypisch die Machbarkeit der Zielstellung, will das Projekt in der zweiten Projektphase (2018-2020) den (möglichst stark) automatisierten Workflow gemeinsam mit Verlagen, berechtigten Bibliotheken und anderen Einrichtungen etablieren. Technischer Baustein ist eine zentrale, intermediäre Datenverteilstation, die die automatische und rechtssichere Ablieferung von Metadaten inklusive der Volltexte aus Verlagshand direkt an dazu berechtigte institutionelle Repositorien gewährleistet. Erreicht werden soll ein bundesweiter Service, der auf verbindlichen Absprachen mit Verlagen und Bibliotheken fußt und (zunächst) die Bedingungen der Allianz-Lizenzen umsetzt. Gleichzeitig wird die Übertragbarkeit des DeepGreen-Ansatzes auf weitere Lizenzkontexte (FID-Lizenzen, Konsortiallizenzen, Gold-Open-Access-Vereinbarungen) geprüft. Eine zusätzliche Ausbaustufe stellt die Überlegung zur automatisierten Ablieferung an Fachrepositorien und Forschungsinformationssysteme dar, die ebenfalls geplant wird.
Das nationale Projektkonsortium besteht aus den zwei Bibliotheksverbünden Kooperativer Bibliotheksverbund Berlin-Brandenburg (KOBV) und Bibliotheksverbund Bayern (BVB), zwei Universitätsbibliotheken, der Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) und der Technische Universität Berlin (TU Berlin), zusätzlich der Bayerischen Staatsbibliothek (BSB) und einer außeruniversitären Forschungseinrichtung - dem Helmholtz Open Science Koordinationsbüro am Deutschen GeoForschungsZentrum (GFZ).
Das Folgeprojekt beginnt am 01. August 2018. Hier vorliegend finden Sie den Projektantrag zum Nachlesen.
DeepGreen wurde vom 01.08.2018 bis zum 30.06.2021 in einer zweiten Projektphase von der Deutschen Forschungsgemeinschaft (DFG) gefördert. DeepGreen unterstützt Bibliotheken als Dienstleister für Hochschulen, außeruniversitäre Forschungseinrichtungen und die dort tätigen Wissenschaftler:innen dabei, Publikationen auf Open-Access-Repositorien frei zugänglich zu machen und fördert das Zusammenspiel von wissenschaftlichen Einrichtungen und Verlagen. An der zweiten Projektphase waren der Kooperative Bibliotheksverbund Berlin-Brandenburg, die Bayerische Staatsbibliothek, der Bibliotheksverbund Bayern, die Universitätsbibliotheken der Friedrich-Alexander-Universität Erlangen-Nürnberg und der Technischen Universität Berlin und das Helmholtz Open Science Office beteiligt. In dem Projekt wurde erfolgreich eine technische und organisatorische Lösung zur automatisierten Verteilung von Artikeldaten wissenschaftlicher Verlage an institutionelle und fachliche Repositorien entwickelt. In der zweiten Projektphase lag der Fokus auf der Erprobung der Datendrehscheibe in der Praxis und der Ausweitung auf weitere Datenabnehmer und weitere Verlage. Im Anschluss an die DFG-geförderte Projektlaufzeit ist DeepGreen in einen zweijährigen Pilotbetrieb übergegangen. Ziel des Pilotbetriebs ist es, den Übergang in einen bundesweiten Real-Betrieb vorzubereiten.
DeepGreen ist ein Service, der es teilnehmenden institutionellen Open-Access-Repositorien,Open-Access-Fachrepositorien und Forschungsinformationssystemen erleichtert, für sie relevante Verlagspublikationen in zyklischer Abfolge mithilfe von Schnittstellen Open Access zur Verfügung zu stellen. Die entsprechende Bandbreite an Relationen zwischen den Akteuren, diverse lizenzrechtliche Rahmenbedingungen sowie technische Anforderungen gestalten das Thema komplex. Ziel dieser Handreichung ist es, neben all diesen Themen, die begleitend beleuchtet werden, im Besonderen Empfehlungen für die reibungslose Nutzung der Datenübertragung zu liefern. Außerdem werden mithilfe einer vorangestellten Workflow- Evaluierung Unterschiede und Besonderheiten in den Arbeitsschritten bei institutionellen Open-Access-Repositorien und Open-Access-Fachrepositorien aufgezeigt und ebenfalls mit Empfehlungen angereichert.
The present study investigates the stability of a tangential-velocity discontinuity in porous media during the withdrawing and injecting processes of natural gases from and into an underground gas storage. The focus is placed on analyzing the impact of inertia forces on the interface stability using the Forchheimer equations. Other publications have relied primarily on Darcy's law to describe flow stability in porous media. However, Darcy's law only adequately describes flows in which viscous forces dominate over inertia forces. As the flow rate increases, the significance of inertia forces becomes more pronounced, and Darcy's law becomes insufficient for considering such flows. Our findings indicate that even a slight consideration of the inertia effect leads to permanent destabilization of the discontinuity interface, regardless of the fluid viscosity or the Mach number. In contrast, when the inertia effect is neglected, the interface is stabilized across the entire Mach number range if the fluid viscosity is strong enough.
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.
This paper describes several experiments to explore the options for solving a class of mixed integer nonlinear programming problems that stem from a real-world mine production planning project. The only type of nonlinear constraints in these problems are bilinear equalities involving continuous variables, which enforce the ratios between elements in mixed material streams. A branch-and-bound algorithm to handle the integer variables has been tried in another project. However, this branch-and-bound algorithm is not effective for handling the nonlinear constraints. Therefore state-of-the-art nonlinear solvers are utilized to solve the resulting nonlinear subproblems in this work. The experiments were carried out using the NEOS server for optimization. After finding that current nonlinear programming solvers seem to lack suitable preprocessing capabilities, we preprocess the instances beforehand and use an heuristic approach to solve the nonlinear subproblems. In the appendix, we explain how to add a polynomial constraint handler that uses IPOPT as embedded nonlinear programming solver for the constraint programming framework SCIP. This is one of the crucial steps for implementing our algorithm in SCIP. We briefly described our approach and give an idea of the work involved.
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.
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.
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.
Forecasting natural gas demand and supply is essential for an efficient operation of the German gas distribution system and a basis for the operational decisions of the transmission system operators. The German gas market is moving towards more short-term planning, in particular, day-ahead contracts. This increases the difficulty that the operators in the dispatching centre are facing, as well as the necessity of accurate forecasts. This paper presents a novel predictive model that provides day-ahead forecasts of the high resolution gas flow by developing a Functional AutoRegressive model with eXogenous variables (FARX). The predictive model allows the dynamic patterns of hourly gas flows to be described in a wide range of historical profiles, while also taking the relevant determinants data into account. By taking into account a richer set of information, FARX provides stronger performance in real data analysis, with both accuracy and high computational efficiency. Compared to several alternative models in out-of-sample forecasts, the proposed model can improve forecast accuracy by at least 12% and up to 5-fold for one node, 3% to 2-fold and 2-fold to 4-fold for the other two nodes. The results show that lagged 1-day gas flow and nominations are important predictors, and with their presence in the forecast model, temperature becomes insignificant for short-term predictions.
Natural gas is the cleanest fossil fuel since it emits the lowest amount of other remains after being burned. Over the years, natural gas usage has increased significantly. Accurate forecasting is crucial for maintaining gas supplies, transportation and network stability. This paper presents two methodologies to identify the optimal configuration o parameters of a Neural Network (NN) to forecast the next 24 h of gas flow for each node of a large gas network.
In particular the first one applies a Design Of Experiments (DOE) to obtain a quick initial solution. An orthogonal design, consisting of 18 experiments selected among a total of 4.374 combinations of seven parameters (training algorithm, transfer function, regularization, learning rate, lags, and epochs), is used. The best result is selected as initial solution of an extended experiment for which the Simulated Annealing is run to find the optimal design among 89.100 possible combinations of parameters.
The second technique is based on the application of Genetic Algorithm for the selection of the optimal parameters of a recurrent neural network for time series forecast. GA was applied with binary representation of potential solutions, where subsets of bits in the bit string represent different values for several parameters of the recurrent neural network.
We tested these methods on three municipal nodes, using one year and half of hourly gas flow to train the network and 60 days for testing. Our results clearly show that the presented methodologies bring promising results in terms of optimal configuration of parameters and forecast error.
Modern mixed-integer programming (MIP) solvers employ dozens of auxiliary algorithmic components to support the branch-and-bound search in finding and improving primal solutions and in strengthening the dual bound. Typically, all components are tuned to minimize the average running time to prove optimality. In this article, we take a different look at the run of a MIP solver. We argue that the solution process consists of three distinct phases, namely achieving feasibility, improving the incumbent solution, and proving optimality. We first show that the entire solving process can be improved by adapting the search strategy with respect to the phase-specific aims using different control tunings. Afterwards, we provide criteria to predict the transition between the individual phases and evaluate the performance impact of altering the algorithmic behaviour of the non-commercial MIP solver Scip at the predicted phase transition points.
This study examines the usability of a real-world, large-scale natural gas transport infrastructure for hydrogen transport. We investigate whether a converted network can transport the amounts of hydrogen necessary to satisfy current energy demands. After introducing an optimization model for the robust transient control of hydrogen networks, we conduct computational experiments based on real-world demand scenarios. Using a representative network, we demonstrate that replacing each turbo compressor unit by four parallel hydrogen compressors, each of them comprising multiple serial compression stages, and imposing stricter rules regarding the balancing of in- and outflow suffices to realize transport in a majority of scenarios. However, due to the reduced linepack there is an increased need for technical and non-technical measures leading to a more dynamic network control. Furthermore, the amount of energy needed for compression increases by 364% on average.
Gas distribution networks are complex structures that consist of
passive pipes, and active, controllable elements such as valves and
compressors. Controlling such network means to find a suitable setting
for all active components such that a nominated amount of gas can be
transmitted from entries to exits through the network, without
violating physical or operational constraints. The control of a
large-scale gas network is a challenging task from a practical point
of view. In most companies the actual controlling process is supported
by means of computer software that is able to simulate the flow of the
gas. However, the active settings have to be set manually within such
simulation software. The solution quality thus depends on the
experience of a human planner.
When the gas network is insufficient for the transport then topology
extensions come into play. Here a set of new pipes or active elements
is determined such that the extended network admits a feasible control
again. The question again is how to select these extensions and where
to place them such that the total extension costs are
minimal. Industrial practice is again to use the same simulation
software, determine extensions by experience, add them to the virtual
network, and then try to find a feasible control of the active
elements. The validity of this approach now depends even more on the
human planner.
Another weakness of this manual simulation-based approach is that it
cannot establish infeasibility of a certain gas nomination, unless all
settings of the active elements are tried. Moreover, it is impossible
to find a cost-optimal network extension in this way.
In order to overcome these shortcomings of the manual planning
approach we present a new approach, rigorously based on mathematical
optimization. Hereto we describe a model for finding feasible
controls and then extend this model such that topology extensions can
additionally and simultaneously be covered. Numerical results for real-world instances are presented and
discussed.
Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed.
Generalized preprocessing techniques for Steiner tree and maximum-weight connected subgraph problems
(2017)
This article introduces new preprocessing techniques for the Steiner tree problem in graphs and one of its most popular relatives, the maximum-weight connected subgraph problem. Several of the techniques generalize previous results from the literature. The correctness of the new methods is shown, but also their NP-hardness is demonstrated. Despite this pessimistic worst-case complexity, several relaxations are discussed that are expected to allow for a strong practical efficiency of these techniques in strengthening both exact and heuristic solving approaches.
A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%.
A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%.
In this article, strategical infrastructure planning problems in the design of large-scale telecommunication networks are discussed based on experiences from three projects with industrial partners: The access network planning of the German Gigabit-Wissenschaftsnetz (G-WiN) for DFN (Verein zur Förderung eines Deutschen Forschungsnetzes e.V.), the mobile network switching center location planning project for E-Plus Mobilfunk, and the fixed network switching center location planning project for TELEKOM AUSTRIA. We introduce a mathematical model for a hierarchical multi-commodity capacitated facility location problem, present adaptions of this basic model to the specific requirements within the different projects and discuss the individual peculiarities and model decisions made. Eventually, we present and discuss computational results of three associated case studies, illustrating '"how we did the job`` with mathematical methods.
It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.
It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.
Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful approaches to many relevant variants, from both a theoretical and a computational point of view. This article illustrates the theoretical and algorithmic progress on Steiner tree type problems on two examples, the Steiner connectivity and the Steiner tree packing problem.
Compressible flows appear in many natural and technological processes, for instance, the flow of natural gases in a pipe system. Thus, a detailed study of the stability of tangential velocity discontinuity in compressible media is relevant and necessary. The first early investigation in two-dimensional (2D) media was given more than 70 years ago. In this article, we continue investigating the stability in three-dimensional (3D) media. The idealized statement of this problem in an infinite spatial space was studied by Syrovatskii in 1954. However, the omission of the absolute sign of cos θ with θ being the angle between vectors of velocity and wave number in a certain inequality produced the inaccurate conclusion that the flow is always unstable for entire values of the Mach number M. First, we revisit this case to arrive at the correct conclusion, namely that the discontinuity surface is stabilized for a large Mach number with a given value of the angle θ. Next, we introduce a real finite spatial system such that it is bounded by solid walls along the flow direction. We show that the discontinuity surface is stable if and only if the dispersion relation equation has only real roots, with a large value of the Mach number; otherwise, the surface is always unstable. In particular, we show that a smaller critical value of the Mach number is required to make the flow in a narrow channel stable.
In this article we study the problem of designing a nation-wide communication network. Such networks usually consist of an access layer, a backbone layer, and maybe several intermediate layers. The nodes of each layer must be connected to those of the next layer in a tree-like fashion. The backbone layer has to satisfy certain survivability and routing constraints. Given the node locations, the demands between them, the possible connections and hardware configurations, and various other technical and administrational constraints, the goal is to decide, which node is assigned to which network level, how the nodes are connected, what hardware must be installed, and how traffic is routed in the backbone. Mixed integer linear programming models and solution methods are presented for both the access and the backbone network design problem. The focus is on the design of IP-over-SDH networks, but the access network design model and large parts of the backbone network design models are general and also applicable for other types of communication networks. Results obtained with these methods in the planning of the German research network are presented.
The stability of flows in porous media plays a vital role in transiting energy supply from natural gas to hydrogen, especially for estimating the usability of existing underground gas storage infrastructures. Thus, this research aims to analyze the interface stability of the tangential-velocity discontinuity between two compressible gases by using Darcy's model to include the porosity effect. The results shown in this research will be a basis for considering whether underground gas storages in porous material can be used to store hydrogen. We show the relation between the Mach number M, the viscosity \mu, and the porosity \epsilon on the stability of the interface. This interface stability affects gases' withdrawal and injection processes, thus will help us to determine the velocity which with gas can be extracted and injected into the storage effectively. By imposing solid walls along the flow direction, the critical values of these parameters regarding the stability of the interface are smaller than when considering no walls. The consideration of bounded flows approaches the problem more realistically. In particular, this analysis plays a vital role when considering two-dimensional gas flows in storages and pipes.
Introduction
(2015)
Jack-III Ein Branch & Cut-Verfahren zur Lösung des gewichteten Steinerbaumproblems in Graphen
(1995)
In der vorliegenden Arbeit werden die grundlegenden Gedanken und die Implementierung eines Branch & Cut-Algorithmus zur Lösung des gewichteten Steinerbaumproblems in Graphen beschrieben. Der Algorithmus basiert auf der linearen Relaxierung einer bidirektionalen ganzzahligen Formulierung des Problems. Wir werden das Problem einführen, drei ganzzahlige Modellierungen vorstellen, auf Reduktionsverfahren und Heuristiken eingehen sowie das Verfahren und seine Implementierung darstellen. Am Ende werden wir die Implementierung an 191 bekannten Probleminstanzen testen und auch optimale Lösungen fur zwei nach Wissen des Autors bis zu diesem Zeitpunkt ungelöste Instanzen liefern.
KOBV Jahresbericht 2013-2014
(2015)
KOBV Jahresbericht 2015-2016
(2017)
KOBV Jahresbericht 2019-2020
(2021)
Der aktuelle KOBV-Jahresbericht informiert darüber, was in den Mitgliedsbibliotheken und Partnerprojekten in den letzten beiden Jahren passiert ist und was sich in der Verbundzentrale und in der Bibliothekslandschaft ändert. Die Ausgabe 2019/2020 enthält den Schwerpunktteil »Digitalisierung« mit verschiedenen Perspektiven auf die digitale Arbeitswelt.