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Mon, 29 Nov 2021 11:58:52 +0100Mon, 29 Nov 2021 11:58:52 +0100Robust DC Optimal Power Flow with Modeling of Solar Power Supply Uncertainty via R-Vine Copulas
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/480
We present a robust approximation of joint chance constrained DC Optimal Power Flow in combination with a model-based prediction of uncertain power supply via R-vine copulas.
It is applied to optimize the discrete curtailment of solar feed-in in an electrical distribution network and guarantees network stability under fluctuating feed-in.
This is modeled by a two-stage mixed-integer stochastic optimization problem proposed by Aigner et al. (European Journal of Operational Research, (2021)).
The solution approach is based on the approximation of chance constraints via robust constraints using suitable uncertainty sets.
The resulting robust optimization problem has a known equivalent tractable reformulation.
To compute uncertainty sets that lead to an inner approximation of the stochastic problem, an R-vine copula model is fitted to the distribution of the multi-dimensional power forecast error, i.e., the difference between the forecasted solar power and the measured feed-in at several network nodes.
The uncertainty sets are determined by encompassing a sufficient number of samples drawn from the R-vine copula model.
Furthermore, an enhanced algorithm is proposed to fit R-vine copulas which can be used to draw conditional samples for given solar radiation forecasts.
The experimental results obtained for real-world weather and network data demonstrate the effectiveness of the combination of stochastic programming and model-based prediction of uncertainty via copulas.
We improve the outcomes of previous work by showing that the resulting uncertainty sets are much smaller and lead to less conservative solutions while maintaining the same probabilistic guarantees.Kevin-Martin Aigner; Peter Schaumann; Freimut von Loeper; Alexander Martin; Volker Schmidt; Frauke Lierspreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/480Mon, 29 Nov 2021 11:58:52 +0100Nodal Stabilization of the Flow in a Network with a Cycle
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/479
In this paper we discuss an approach to the stability analysis for classical
solutions of closed loop systems that is based upon the tracing of the evolution of the Riemann invariants along the characteristics. We consider a network where several edges are coupled through node conditions that govern the evolution of the Riemann invariants through the nodes of the network. The analysis of the decay of the Riemann invariants requires to follow backwards all the characteristics that enter such a node and contribute
to the evolution. This means that with each nodal reflection/crossing the number of characteristics that contribute to the evolution increases.
We show how for simple networks with a suffcient number of damping nodal controlers it is possible to keep track of this family of characteristics and use this approach to analyze the exponential stability of the system. The analysis is based on an adapted version of
Gronwall's lemma that allows us to take into account the possible increase of the Riemann invariants when the characteristic curves cross a node of the network.
Our example is motivated by applications in the control of gas pipeline flow, where the
graphs of the networks often contain many cycles.Martin Gugat; Sven Weilandarticlehttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/479Tue, 16 Nov 2021 15:10:30 +0100Least squares collocation for the simulation of gas network DAEs
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/478
Henning Sauter; Caren Tischendorfpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/478Sun, 14 Nov 2021 18:04:26 +0100Optimal control of gas network DAEs
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/477
Henning Sauter; Caren Tischendorfpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/477Sun, 14 Nov 2021 18:04:14 +0100Computing optimality certificates for convex mixed-integer nonlinear problems
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/476
Every optimization problem has a corresponding verification problem which verifies whether a given optimal solution is in fact optimal. In the literature there are a lot of such ways to verify optimality for a given solution, e.g., the branch-and-bound tree. To simplify this task, Baes et al. introduced optimality certificates for convex mixed-integer nonlinear programs and proved that these are bounded in the number of integer variables. We introduce an algorithm to compute the certificates and conduct computational experiments. Through the experiments we show that the optimality certificates can be surprisingly small.Katrin Halbig; Lukas Hümbs; Florian Rösel; Lars Schewe; Dieter Weningerpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/476Fri, 12 Nov 2021 20:27:48 +0100An active signature method for constrained abs-linear minimization
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/474
In this paper we consider the solution of optimization tasks with a piecewise linear objective function and piecewise linear constraints. First, we state optimality conditions for that class of problems using the abs-linearization approach and prove that they can be verified in polynomial time. Subsequently, we propose an algorithm called Constrained Active Signature Method that explicitly exploits the piecewise linear structure to solve such optimization problems. Convergence of the algorithm within a finite number of iterations is proven. Numerical results for various testcases including linear complementarity conditions and a bi-level problem illustrate the performance of the new algorithm.Timo Kreimeier; Andrea Walther; Andreas Griewankpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/474Fri, 12 Nov 2021 13:32:08 +0100A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Markets with Transport
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/458
We analyze Generalized Nash Equilibrium Problems (GNEPs) for which the objectives of the individuals are interdependent and shared constraints are governed by a system of partial differential equations (PDEs). This allows us to model the strategic interaction of competing firms, which explicitly take into account the dynamics of transporting a commodity, such as natural gas, through a network. We establish existence of a variational equilibrium, which solves the considered GNEP. We identify a reformulation of the original equilibrium problem that is suited to derive and establish a solution algorithm. Based on the solutions for a test instance, we finally illustrate how our results can be used to analyze dynamic aspects such as linepack in the context of liberalized gas markets.Veronika Grimm; Michael Hintermüller; Olivier Huber; Lars Schewe; Martin Schmidt; Gregor Zöttlpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/458Fri, 12 Nov 2021 10:30:21 +0100Solving Least-Squares Collocated Differential Algebraic Equations by Successive Abs-Linear Minimization - A Case Study on Gas Network Simulation
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/473
This paper studies the numerical simulation of gas networks with regulating elements using differential algebraic equations (DAEs) in combination with least-squares collocation. In contrast to classical collocation methods, more collocation points than degrees of freedom for the collocation polynomials are used. Recently, it has been shown that such a least-squares collocation has a regularizing effect for DAEs, in particular for DAEs with higher index. In each time step of the numerical integration, one has to solve a system of nonlinear equations that is nonsmooth due to the regulating elements in the gas networks. We consider four solvers one of which explicitly exploits the inherent nonsmooth nature. Numerical results are given for three different test cases with increasing complexity illustrating the feasibility of the proposed approach to approximate a solution of the DAE and the advantageous performance of the nonsmooth solver that is based on the concept of abs-linearization.Timo Kreimeier; Henning Sauter; Tom Streubel; Caren Tischendorf; Andrea Waltherpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/473Fri, 12 Nov 2021 10:24:07 +0100On M-stationarity conditions for probabilistic MPECs
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/472
We consider Mathematical Programs with Equilibrium Constraints with proba-
bilistic constraints (PMPECs). Such models have proven to be useful in modeling
electricity or gas markets subject to random parameters. Our main interest is the
derivation of Mordukhovich (M-) stationarity conditions under suitable constraint
quali...cations ensuring the calmness of the canonically perturbed generalized equation.
Applying recent results from deterministic MPECs, we identify the needed properties
of the probability function in order to derive explicit M-stationarity conditions. The
results are applied to a simple stochastic bilevel problem in an economic context.Rene Henrionarticlehttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/472Thu, 11 Nov 2021 18:19:33 +0100Exact Methods for Discrete Γ-Robust Min-Max Problems
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/471
Developing solution methods for mixed-integer bilevel problems is known to be a challenging task - even if all parameters of the problem are exactly known. Many real-world applications of bilevel optimization, however, involve data uncertainty due to some kind of bounded rationality. We study mixed-integer min-max problems with a follower who faces uncertainties regarding the parameters of the lower-level problem. Adopting a Γ-robust approach, we present an extended formulation and a multi-scenario formulation to model this type of problem. For both settings, we provide a generic branch-and-cut framework. Specifically, we investigate interdiction problems with a monotone Γ-robust follower and we derive problem-tailored cuts, which extend existing techniques that have been proposed for the deterministic case. For the Γ-robust knapsack interdiction problem, we computationally evaluate and compare the performance of the proposed algorithms for both modeling approaches.Yasmine Beck; Ivana Ljubic; Martin Schmidtpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/471Wed, 10 Nov 2021 16:08:32 +0100Numerical methods for optimal switching control of PDE-dynamical systems
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/469
This article provides a review on certain computational approaches to solve optimal control problems for evolution-type partial differential equations, where some control functions are limited to switching. The mechanism that enforces switching is modeled as integer restrictions. This brings a combinatorial aspect into the apart from switching already computationally very demanding optimization problems. Recently, great advances have been made to tackle such problems rigorously using relaxation and combinatorial integral approximation. An overview of these methods and the known theoretical results concerning convergence and error estimates are provided in a consistent manner. Further, we point to applications with benchmark character as well as to open problems.Falk Hantepreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/469Wed, 10 Nov 2021 09:06:44 +0100Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/467
We consider mixed-integer linear quantile minimization problems that yield large-scale problems that are very hard to solve for real-world instances. We motivate the study of this problem class by two important real-world problems: a maintenance planning problem for electricity networks and a variant of the classic portfolio optimization problem. For these problems, we develop valid inequalities and present an overlapping alternating direction method. Moreover, we discuss an adaptive scenario clustering method for which we prove that it terminates after a finite number of iterations with a global optimal solution. We study the computational impact of all presented techniques and finally show that their combination leads to an overall method that can solve the maintenance planning problem on large-scale real-world instances provided by the ROADEF challenge 2020.Diego Cattaruzza; Martine Labbé; Matteo Petris; Marius Roland; Martin Schmidtpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/467Tue, 09 Nov 2021 14:11:28 +0100Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/465
We present a new balancing-based structure-preserving model reduc-
tion technique for linear port-Hamiltonian descriptor systems. The pro-
posed method relies on a modification of a set of two dual generalized
algebraic Riccati equations that arise in the context of linear quadratic
Gaussian balanced truncation for differential algebraic systems. We de-
rive an a priori error bound with respect to a right coprime factorization
of the underlying transfer function thereby allowing for an estimate with
respect to the gap metric. We further theoretically and numerically ana-
lyze the influence of the Hamiltonian and a change thereof, respectively.
With regard to this change of the Hamiltonian, we provide a novel proce-
dure that is based on a recently introduced Kalman–Yakubovich–Popov
inequality for descriptor systems. Numerical examples demonstrate how
the quality of reduced-order models can significantly be improved by first
computing an extremal solution to this inequality.Tobias Breiten; Philipp Schulzepreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/465Fri, 05 Nov 2021 16:41:31 +0100Reduction of Potential-Based Flow Networks
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/463
We consider potential-based flow networks with terminal nodes at which flow can enter or leave the network and physical properties such as voltages or pressures are measured and controlled. We study conditions under which such a network can be reduced to a smaller, equivalent network with the same behavior at the terminal nodes. Potential-based flow networks are widely used to model infrastructure networks such as electricity, gas, or water networks. In contrast to Kron's reduction for electrical networks, we prove that, in general, potential-based flow networks with at least three terminals cannot be reduced to smaller networks whose size only depends on the number of terminals. On the other hand, we show that it is possible to represent a special class of potential-based flow networks by a complete graph on the terminals, and we establish a characterization of networks that can be reduced to a path network. Our results build on fundamental properties of effective resistances proved in this paper, including explicit formulae for their dependence on edge resistances of the network and their metric properties.Max Klimm; Marc Pfetsch; Rico Raber; Martin Skutellapreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/463Thu, 04 Nov 2021 13:59:23 +0100Approximation of Binary Second Order Cone Programs of Packing Type
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/461
This paper considers binary second order cone programs of packing type where a linear objective is optimized under m second order cone packing constraints and all decision variables are binary. We show that when m is part of the input, these problems cannot be approximated within a factor of 1/(m + 1)^(1−ε) for any ε > 0, unless P = NP. We then propose approximation algorithms based on different algorithmic principles that almost match this approximation factor: a pipage rounding technique that solves fractional relaxations of the problems and modifies the solutions so that few fractional variables remain, a greedy approach, and a randomized rounding technique. While all algorithms have similar theoretical approximation guarantees in the order of 1/m, we also test the algorithms on realistic instances that arise in the context of gas transportation networks. This empirical study reveals in particular that taking the best of the proposed algorithms produces highly competitive solutions that yield on average 96 % of the value of an optimal
solution.Max Klimm; Marc Pfetsch; Rico Raber; Martin Skutellapreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/461Thu, 04 Nov 2021 11:52:35 +0100Parametric computation of minimum cost flows with piecewise quadratic costs
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/462
We develop algorithms solving parametric flow problems with separable, continuous, piecewise quadratic, and strictly convex cost functions. The parameter to be considered is a common multiplier on the demand of all nodes. Our algorithms compute a family of flows that are each feasible for the respective demand and minimize the costs among the feasible flows for that demand. For single commodity networks with homogenous cost functions, our algorithm requires one matrix multiplication for the initialization, a rank 1 update for each nondegenerate step and the solution of a convex quadratic program for each degenerate step. For nonhomogeneous cost functions, the initialization requires the solution of a convex quadratic program instead. For multi-commodity networks, both the initialization and every step of the algorithm require the solution of a convex program. As each step is mirrored by a breakpoint in the output this yields output-polynomial algorithms in every case.Max Klimm; Philipp Warodearticlehttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/462Thu, 04 Nov 2021 11:52:01 +0100CSG: A stochastic gradient method for a wide class of optimization problems appearing in a machine learning or data-driven context
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/460
In a recent article the so called continuous stochastic gradient method (CSG) for the eﬃcient solution of a class of stochastic optimization problems was introduced. While the applicability of known stochastic gradient type methods is typically limited to so called expected risk functions, no such limitation exists for CSG. The key to this lies in the computation of design dependent integration weights, which allows for an optimal usage of available information leading to stronger convergence properties. However, due to the nature of the formula for these integration weights, the practical applicability was essentially limited to problems, in which stochasticity enters via a low-dimensional and suﬁciently simple probability distribution. In this paper the scope of the CSG method is signiﬁcantly extended presenting new ways of calculating the integration weights. A full convergence analysis for this new variant of the CSG method is presented and its eﬃciency is demonstrated in comparison to more classical stochastic gradient methods by means of a number of problem classes, relevant in stochastic optimization and machine learning.Lukas Pflug; Max Grieshammer; Andrian Uihlein; Michael Stinglpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/460Wed, 03 Nov 2021 09:44:33 +0100Dynamic optimal transport on networks
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/457
In this paper we study a dynamical optimal transport problem on a network that allows
for transport of mass between different edges if a penalty κ is paid. We show existence
of minimisers using duality and discuss the relationships of the distance-functional to
other metrics such as the Fisher-Rao and the classical Wasserstein metric and analyse the
resulting distance functional in the limiting case κ → ∞.Martin Burger; Ina Humpert; Jan Pietschmannpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/457Tue, 02 Nov 2021 22:04:08 +0100Interpolation and approximation via Momentum ResNets and Neural ODEs
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/447
In this article, we explore the effects of memory terms in continuous-layer Deep Residual Networks by studying Neural ODEs (NODEs). We investigate two types of models. On one side, we consider the case of Residual Neural Networks with dependence on multiple layers, more precisely Momentum ResNets. On the other side, we analyse a Neural ODE with auxiliary states playing the role of memory states. We examine the interpolation and universal approximation properties for both architectures through a simultaneous control perspective. We also prove the ability of the second model to represent sophisticated maps, such as parametrizations of time-dependent functions. Numerical simulations complement our study.Domènec Ruiz-Balet; Elisa Affili; Enrique Zuazuapreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/447Tue, 02 Nov 2021 09:00:48 +0100Retailer Competition
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/455
We consider strategic retail pricing in markets where retailers buy commodities at fluctuating wholesale prices and resell them by applying dynamic retail tariff, such as real--time pricing, to final consumers. These tariffs are defined in such a way that they can reflect, to some extent, the wholesale price fluctuations and might increase market efficiency and retailers'profits. This paper provides important modelling approaches and insights regarding dynamic retail tariffs. This is of especially large relevance in the light of current efforts to implement dynamic retail pricing schemes in liberalized energy markets worldwide.
From a modelling point of view, we propose a multi-leader-follower problem to investigate the implications of strategic retail pricing and we compare the impacts of the implementation of both fixed price tariffs and dynamic tariffs on final consumers. Moreover, we develop algorithms which solve the multi- leader-follower problems for general setups and allow us to characterize the resulting market equilibria. In addition, for specific symmetric setups we are able to provide explicit analytical solutions.
The analytical and numerical results obtained for our framework show that, in those cases where strategic competition among retailers plays little role, dynamic real-time pricing increases market efficiency and retailer profits as compared to fixed-tariff pricing. This confirms the existing results which do not explicitly model strategic retail competition. However, if strategic competition among retailers plays an important role, the application of real-time pricing can reduce market efficiency and retailer profits with respect to fixed-tariff pricing, as our detailed strategic analysis highlights.Giorgia Oggioni; Alexandra Schwartz; Gregor Zöttl; Ann-Kathrin Wiertzworkingpaperhttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/455Fri, 22 Oct 2021 20:36:28 +0200Modeling Hydrogen Networks for Future Energy Systems: A Comparison of Linear and Nonlinear Approaches
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/453
Common energy system models that integrate hydrogen transport in pipelines typically simplify fluid flow models and reduce the network size in order to achieve solutions quickly. This contribution analyzes two different types of pipeline network topologies (namely, star and tree networks) and two different fluid flow models (linear and nonlinear) for a given hydrogen capacity scenario of electrical reconversion in Germany to analyze the impact of these simplifications. For each network topology, robust demand and supply scenarios are generated. The results show that a simplified topology, as well as the consideration of detailed fluid flow, could heavily influence the total pipeline investment costs. For the given capacity scenario, an overall cost reduction of the pipeline costs of 37% is observed for the star network with linear cost compared to the tree network with nonlinear fluid flow. The impact of these improvements regarding the total electricity reconversion costs has led to a cost reduction of 1.4%, which is fairly small. Therefore, the integration of nonlinearities into energy system optimization models is not recommended due to their high computational burden. However, the applied method for generating robust demand and supply scenarios improved the credibility and robustness of the network topology, while the simplified fluid flow consideration can lead to infeasibilities. Thus, we suggest the utilization of the nonlinear model for post- processing to prove the feasibility of the results and strengthen their credibility, while retaining the computational performance of linear modeling.Markus Reuß; Lara Welder; Johannes Thürauf; Jochen Linßen; Thomas Grube; Lars Schewe; Martin Schmidt; Detlef Stolten; Martin Robiniusarticlehttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/453Tue, 19 Oct 2021 14:17:40 +0200A turnpike property for optimal control problems with dynamic probabilistic constraints
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/452
In this paper we consider systems that are governed by linear time-discrete dynamics with an initial condition and a terminal condition for the expected values. We study optimal control problems where in the objective function a term of tracking type for the expected values and a control cost appear. In addition, the feasible states have to satisfy a conservative probabilistic constraint that requires that the probability that the trajectories remain in a given set F is greater than or equal to a given lower bound. An application are
optimal control problems related to storage management systems with uncertain in- and output. We give suffcient conditions that imply that the optimal expected trajectories remain close to a certain state that can be characterized as the solution of an optimal control problem without prescribed initial- and terminal condition. Hence we contribute to the study of the turnpike phenomenon that is well-known in mathematical economics.Martin Gugat; René Henrion; Holger Heitschpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/452Mon, 18 Oct 2021 16:44:44 +0200Optimality conditions and Moreau–Yosida regularization for almost sure state constraints
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/450
We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable. We obtain strong forms of necessary and sufficient optimality conditions for problems subject to equality and conical constraints. We propose a Moreau–Yosida regularization for the conical constraint and show consistency of the optimality conditions for the regularized problem as the regularization parameter is taken to infinity.Caroline Geiersbach; Michael Hintermüllerpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/450Mon, 18 Oct 2021 15:15:59 +0200Risk-Neutral PDE-Constrained Generalized Nash Equilibrium Problems
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/449
A class of risk-neutral PDE-constrained generalized Nash equilibrium problems is introduced in which the feasible strategy set of each player is subject to a common linear elliptic partial differential equation with random inputs. In addition, each player’s actions are taken from a bounded, closed, and convex set on the individual strategies and a bound constraint on the common state variable. Existence of Nash equilibria and first-order optimality conditions are derived by exploiting higher integrability and regularity of the random field state variables and a specially tailored constraint qualification for GNEPs with the assumed structure. A relaxation scheme based on the Moreau-Yosida approximation of the bound constraint is proposed, which ultimately leads to numerical algorithms for the individual player problems as well as the GNEP as a whole. The relaxation scheme is related to probability constraints and the viability of the proposed numerical algorithms are demonstrated via several examples.Deborah Gahururu; Michael Hintermüller; Thomas Surowiecpreprinthttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/449Mon, 18 Oct 2021 15:10:18 +0200Towards the Solution of Robust Gas Network Optimization Problems Using the Constrained Active Signature Method
https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/448
This work studies robust gas network optimization under uncertainties in demand and in the physical parameters. The corresponding optimization problems are nonconvex in node pressures and flows along the pipes. They are thus very difficult to solve for realistic instance sizes. In recent approaches, an adaptive bundle method has been developed, where one solves the occurring adversarial problems via iteratively refined piecewise linear relaxations. These subproblems need to be solved always from scratch using mixed-integer linear programming (MIP). As alternative to the MIP solver, we employ here a nonsmooth optimization approach that allows a warm start strategy such that it can profit from the results obtained for coarser relaxations. We evaluate the approach for realistic gas network topologies and outline possibilities for future research.Timo Kreimeier; Martina Kuchlbauer; Frauke Liers; Michael Stingl; Andrea Waltherarticlehttps://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/448Sun, 17 Oct 2021 09:03:59 +0200