This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to ε-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms.In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem.
We present an algorithm for shape-optimization under stochastic loading, and representative numerical results. Our strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-based shape optimization. In particular, usage of linear elasticity and quadratic objective functions permits to obtain a computational cost which scales linearly in the number of linearly independent applied forces, which often is much smaller than the number of different realizations of the stochastic forces. Numerical computations are performed using a level-set method with composite finite elements both in two and in three spatial dimensions.
We describe and compare heuristic solution methods for a multi-stage stochastic network interdiction problem. The problem is to maximize the probability of sufficient disruption of the flow of information or goods in a network whose characteristics are not certain. In this formulation, interdiction subject to a budget constraint is followed by operation of the network, which is then followed by a second interdiction subject to a second budget constraint. Computational results demonstrate and compare the effectiveness of heuristic algorithms. This problem is interesting in that computing an objective function value requires tremendous effort. We exhibit classes of instances in our computational experiments where local search based on a transformation neighborhood is dominated by a constructive neighborhood.
Abstract:We describe the application of a decomposition based solution method to a class of network interdiction problems. The problem of maximizing the probability of sufficient disruption of the flow of information or goods in a network whose characteristics are not certain is shown to be solved effectively by applying a scenario decomposition method developed by Riis and Schultz [Comput Optim Appl 24 (2003), 267-287]. Computational results demonstrate the effectiveness of the algorithm and design decisions that result in speed improvements.
Risk-averse optimization has attracted much attention in nite-dimensional stochastic programming. In this paper, we propose a risk-averse approach in the in nite dimensional context of shape optimization. We consider elastic materials under stochastic loading. As measures of risk awareness we investigate the expected excess and the excess probability. The developed numerical algorithm is based on a regularized gradient ow acting on an implicit description of the shapes based on level sets. We incorporate topological derivatives to allow for topological changes in the shape optimization procedure. Numerical results in 2D demonstrate the impact of the risk-averse modeling on the optimal shapes and on the cost distribution over the set of scenarios.
Kurzfassung
Dieser Beitrag stellt das Konzept eines betriebsbegleitenden Assistenzsystems für die Produktionsinfrastruktur vor, welches im Rahmen des Kopernikus-Vorhabens SynErgie zur Erschließung der Energieflexibilitätspotenziale der Produktionsinfrastruktur entstanden ist. Zunächst wird das dabei in das Themengebiet der energieflexiblen Produktionsinfrastruktur eingeführt sowie deren betrachteten Komponenten vorgestellt. Im Anschluss werden das Assistenzsystem inklusive des Optimierungsproblems sowie dessen technische Infrastruktur erläutert.
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