Validation of nominations in gas networks and properties of technical capacities

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Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics

The second MFO Oberwolfach Workshop on Mixed-Integer Nonlinear Programming (MINLP) took place between 2nd and 8th June 2019. MINLP refers to one of the hardest Mathematical Programming (MP) problem classes, involving both nonlinear functions as well as continuous and integer decision variables. MP is a formal language for describing optimization problems, and is traditionally part of Operations Research (OR), which is itself at the intersection of mathematics, computer science, engineering and econometrics. The scientific program has covered the three announced areas (hierarchies of approximation, mixed-integer nonlinear optimal control, and dealing with uncertainties) with a variety of tutorials, talks, short research announcements, and a special "open problems'' session

Kinetic Intersections as a Source of Information on Rate Coefficients

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Challenges in Optimization with Complex PDE-Systems (hybrid meeting)

The workshop concentrated on various aspects of optimization problems with systems of nonlinear partial differential equations (PDEs) or variational inequalities (VIs) as constraints. In particular, discussions around several keynote presentations in the areas of optimal control of nonlinear or non-smooth systems, optimization problems with functional and discrete or switching variables leading to mixed integer nonlinear PDE constrained optimization, shape and topology optimization, feedback control and stabilization, multi-criteria problems and multiple optimization problems with equilibrium constraints as well as versions of these problems under uncertainty or stochastic influences, and the respectively associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, aspects of optimal control of data-driven PDE constraints (e.g. related to machine learning) were addressed

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Model compendium, data, and optimization benchmarks for sector-coupled energy systems

Decarbonization and defossilization of energy supply as well as increasing decentralization of energy gen- eration necessitate the development of efficient strategies for design and operation of sector-coupled energy systems. Today, design and operation of process and energy systems rely on powerful numeri- cal methods, in particular, optimization methods. The development of such methods benefits from re- producible benchmarks including transparent model equations and complete input data sets. However, to the authors’ best knowledge and with respect to design and optimal control of sector-coupled en- ergy systems, there is a lack of available benchmarks. Hence, this article provides a model compendium, exemplary realistic data sets, as well as two case studies (i.e., optimization benchmarks) for an in- dustrial/research campus in an open-source description. The compendium includes stationary, quasi- stationary, and dynamic models for typical components as well as linearization schemes relevant for optimization of design, operation, and control of sector-coupled energy systems

GasLib — A Library of Gas Network Instances

The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML (extensible markup language) format. In this paper, we explain this format and present the instances that are available in the library

Probabilistic Optimization Techniques in Smart Power System

Uncertainties are the most significant challenges in the smart power system, necessitating the use of precise techniques to deal with them properly. Such problems could be effectively solved using a probabilistic optimization strategy. It is further divided into stochastic, robust, distributionally robust, and chance-constrained optimizations. The topics of probabilistic optimization in smart power systems are covered in this review paper. In order to account for uncertainty in optimization processes, stochastic optimization is essential. Robust optimization is the most advanced approach to optimize a system under uncertainty, in which a deterministic, set-based uncertainty model is used instead of a stochastic one. The computational complexity of stochastic programming and the conservativeness of robust optimization are both reduced by distributionally robust optimization.Chance constrained algorithms help in solving the constraints optimization problems, where finite probability get violated. This review paper discusses microgrid and home energy management, demand-side management, unit commitment, microgrid integration, and economic dispatch as examples of applications of these techniques in smart power systems. Probabilistic mathematical models of different scenarios, for which deterministic approaches have been used in the literature, are also presented. Future research directions in a variety of smart power system domains are also presented.publishedVersio

Optimization based energy-efficient control inmobile communication networks

In this work we consider how best to control mobility and transmission for the purpose of datatransfer and aggregation in a network of mobile autonomous agents. In particular we considernetworks containing unmanned aerial vehicles (UAVs). We first consider a single link betweena mobile transmitter-receiver pair, and show that the total amount of transmittable data isbounded. For certain special, but not overly restrictive cases, we can determine closed-formexpressions for this bound, as a function of relevant mobility and communication parameters.We then use nonlinear model predictive control (NMPC) to jointly optimize mobility and trans-mission schemes of all networked nodes for the purpose of minimizing the energy expenditureof the network. This yields a novel nonlinear optimal control problem for arbitrary networksof autonomous agents, which we solve with state-of-the-art nonlinear solvers. Numerical re-sults demonstrate increased network capacity and significant communication energy savingscompared to more na ̈ıve policies. All energy expenditure of an autonomous agent is due tocommunication, computation, or mobility and the actual computation of the NMPC solutionmay be a significant cost in both time and computational resources. Furthermore, frequentbroadcasting of control policies throughout the network can require significant transmit andreceive energies. Motivated by this, we develop an event-triggering scheme which accounts forthe accuracy of the optimal control solution, and provides guarantees of the minimum timebetween successive control updates. Solution accuracy should be accounted for in any triggeredNMPC scheme where the system may be run in open loop for extended times based on pos-sibly inaccurate state predictions. We use this analysis to trade-off the cost of updating ourtransmission and locomotion policies, with the frequency by which they must be updated. Thisgives a method to trade-off the computation, communication and mobility related energies ofthe mobile autonomous network.Open Acces