Global Deterministic Optimization with Artificial Neural Networks Embedded

Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and concave envelopes of the nonlinear activation function of ANNs. The optimization problem is solved using our in-house global deterministic solver MAiNGO. The performance of the proposed method is shown in four optimization examples: an illustrative function, a fermentation process, a compressor plant and a chemical process optimization. The results show that computational solution time is favorable compared to the global general-purpose optimization solver BARON.Comment: J Optim Theory Appl (2018

Exposición "El Quijote en las Bibliotecas Universitarias Españolas", Ciudad Real-Albacete, Octubre-Diciembre 2005

Sección: Noticias. Noticias externasEl cuatrocientos aniversario de la publicación de El Quijote de D. Miguel de Cervantes Saavedra se está conmemorando con numerosas y variadas actividades, que intentan acercar, refrescar, o dar a conocer, además de la genial obra de nuestra literatura, el entorno social, cultural y económico de la época en la que transcurre la novela, o que vivió su autor Cervantes.N

Man-portable power generation devices : product design and supporting algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 351-380).A methodology for the optimal design and operation of microfabricated fuel cell systems is proposed and algorithms for relevant optimization problems are developed. The methodology relies on modeling, simulation and optimization at three levels of modeling detail. The first class of optimization problems considered are parametric mixed-integer linear programs and the second class are bilevel programs with nonconvex inner and outer programs; no algorithms exist currently in the open literature for the global solution of either problem in the form considered here. Microfabricated fuel cell systems are a promising alternative to batteries for manportable power generation. These devices are potential consumer products that comprise a more or less complex chemical process, and can therefore be considered chemical products. With current computational possibilities and available algorithms it is impossible to solve for the optimal design and operation in one step since the devices considered involve complex geometries, multiple scales, time-dependence and parametric uncertainty. Therefore, a methodology is presented based on decomposition into three levels of modeling detail, namely system-level models for process synthesis,(cont.) intermediate fidelity models for optimization of sizes and operation, and detailed, computational fluid dynamics models for geometry improvement. Process synthesis, heat integration and layout considerations are addressed through the use of lumped algebraic models, general enough to be independent of detailed design choices, such as reactor configuration and catalyst choice. Through the use of simulation and parametric mixed-integer optimization the most promising process structures along with idealized layouts are selected among thousands of alternatives. At the intermediate fidelity level space-distributed models are used, which allow optimization of unit sizes and operation for a given process structure without the need to specify a detailed geometry. The resulting models involve partial differential-algebraic equations and dynamic optimization is employed as the solution technique. Finally, the use of detailed two- and three-dimensional computational fluid dynamics facilitates geometrical improvements as well as the derivation and validation of modeling assumptions that are employed in the system-level and intermediate fidelity models. Steady-state case studies are presented assuming a constant power demand;(cont.) the methodology can be also applied to transient considerations and the case of variable power demand. Parametric programming provides the solution of an optimization problem, the data of which depend on one or many unknown real-valued parameters, for each possible value of the parameter(s). In this thesis mixed-integer linear programs are considered, i.e., optimization programs with affine functions involving real- and integervalued variables. In the first part the multiparametric cost-vector case is considered, i.e., an arbitrary finite number of parameters is allowed, that influence only the coefficients of the objective function. The extension of a well-known algorithm for the single-parameter case is presented, and the algorithm behavior is illustrated on simple examples with two parameters. The optimality region of a given basis is a polyhedron in the parameter space, and the algorithm relies on progressively constructing these polyhedra and solving mixed-integer linear programs at their vertices. Subsequently, two algorithmic alternatives are developed, one based on the identification of optimality regions, and one on branch-and-bound. In the second part the single-parameter general case is considered,(cont.) i.e., a single parameter is allowed that can simultaneously influence the coefficients of the objective function, the right-hand side of the constraints, and also the coefficients of the matrix. Two algorithms for mixed-integer linear programs are proposed. The first is based on branch-and-bound on the integer variables, solving a parametric linear program at each node, and the second is based on decomposition of the parametric optimization problem into a series of mixed-integer linear and mixed-integer nonlinear optimization problems. For the parametric linear programs an improvement of a literature algorithm for the solution of linear programs based on rational operations is presented and an alternative based on predictor-continuation is proposed. A set of test problems is introduced and numerical results for these test problems are discussed. The algorithms are then applied to case studies from the man-portable power generation. Finally extensions to the nonlinear case are discussed and an example from chemical equilibrium is analyzed. Bilevel programs are hierarchical programs where an outer program is constrained by an embedded inner program.(cont.) Here the co-operative formulation of inequality constrained bilevel programs involving real-valued variables and nonconvex functions in both the inner and outer programs is considered. It is shown that previous literature proposals for the global solution of such programs are not generally valid for nonconvex inner programs and several consequences of nonconvexity in the inner program are identified. Subsequently, a bounding algorithm for the global solution is presented. The algorithm is rigorous and terminates finitely to a solution that satisfies e-optimality in the inner and outer programs. For the lower bounding problem, a relaxed program, containing the constraints of the inner and outer programs augmented by a parametric upper bound on the optimal solution function of the inner program, is solved to global optimality. For the case that the inner program satisfies a constraint qualification, a heuristic for tighter lower bounds is presented based on the KKT necessary conditions of the inner program. The upper bounding problem is based on probing the solution obtained in the lower bounding procedure. Branching and probing are not required for convergence but both have potential advantages.(cont.) Three branching heuristics are described and analyzed. A set of test problems is introduced and numerical results for these test problems and for literature examples are presented.by Alexander Mitsos.Ph.D

Cost-Optimal Power-to-Methanol: Flexible Operation or Intermediate Storage?

The synthesis of methanol from captured carbon dioxide and green hydrogen could be a promising replacement for the current fossil-based production. The major energy input and cost driver for such a process is the electricity for hydrogen production. Time-variable electricity cost or availability thus motivates flexible operation. However, it is unclear if each unit of the process should be operated flexibly, and if storage of electricity or hydrogen reduces the methanol production cost. To answer these questions, we modeled a Power-to-Methanol plant with batteries and hydrogen storage. Using this model, we solved a combined design and scheduling optimization problem, which provides the optimal size of the units of the plant and their optimal (quasi-stationary) operation. The annualized cost of methanol was minimized for a grid-connected and a stand-alone case study. The optimization results confirm that storage, especially hydrogen storage, is particularly beneficial when the electricity price is high and highly fluctuating. Irrespective of the presence of storage, the whole Power-to-Methanol plant should be operated flexibly: even moderate flexibility of the methanol synthesis unit significantly reduces the production cost

Normalizing Flow-based Day-Ahead Wind Power Scenario Generation for Profitable and Reliable Delivery Commitments by Wind Farm Operators

We present a specialized scenario generation method that utilizes forecast information to generate scenarios for the particular usage in day-ahead scheduling problems. In particular, we use normalizing flows to generate wind power generation scenarios by sampling from a conditional distribution that uses day-ahead wind speed forecasts to tailor the scenarios to the specific day. We apply the generated scenarios in a simple stochastic day-ahead bidding problem of a wind electricity producer and run a statistical analysis focusing on whether the scenarios yield profitable and reliable decisions. Compared to conditional scenarios generated from Gaussian copulas and Wasserstein-generative adversarial networks, the normalizing flow scenarios identify the daily trends more accurately and with a lower spread while maintaining a diverse variety. In the stochastic day-ahead bidding problem, the conditional scenarios from all methods lead to significantly more profitable and reliable results compared to an unconditional selection of historical scenarios. The obtained profits using the normalizing flow scenarios are consistently closest to the perfect foresight solution, in particular, for small sets of only five scenarios.Comment: manuscript (17 pages, 7 figures, 5 tables), supporting information (2 pages, 1 figure, 1 table

Perlindungan Konsumen di Indonesia

Law No. 8 of 1999 on Consumer Protection must be upheld in business and trade relations in general for the creation of a justice. Criminal provisions should be placed as Primum remedium About Consumer Protection Act so that it really works with its criminal sanctions as special and general prevention of corporate crime

Data-Driven Model Reduction and Nonlinear Model Predictive Control of an Air Separation Unit by Applied Koopman Theory

Achieving real-time capability is an essential prerequisite for the industrial implementation of nonlinear model predictive control (NMPC). Data-driven model reduction offers a way to obtain low-order control models from complex digital twins. In particular, data-driven approaches require little expert knowledge of the particular process and its model, and provide reduced models of a well-defined generic structure. Herein, we apply our recently proposed data-driven reduction strategy based on Koopman theory [Schulze et al. (2022), Comput. Chem. Eng.] to generate a low-order control model of an air separation unit (ASU). The reduced Koopman model combines autoencoders and linear latent dynamics and is constructed using machine learning. Further, we present an NMPC implementation that uses derivative computation tailored to the fixed block structure of reduced Koopman models. Our reduction approach with tailored NMPC implementation enables real-time NMPC of an ASU at an average CPU time decrease by 98 %

Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction

We propose Gibbs-Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. That is, we include the Gibbs-Duhem equation explicitly in the loss function for training neural networks, which is straightforward in standard machine learning (ML) frameworks enabling automatic differentiation. In contrast to recent hybrid ML approaches, our approach does not rely on embedding a specific thermodynamic model inside the neural network and corresponding prediction limitations. Rather, Gibbs-Duhem consistency serves as regularization, with the flexibility of ML models being preserved. Our results show increased thermodynamic consistency and generalization capabilities for activity coefficient predictions by Gibbs-Duhem-informed graph neural networks and matrix completion methods. We also find that the model architecture, particularly the activation function, can have a strong influence on the prediction quality. The approach can be easily extended to account for other thermodynamic consistency conditions

Optimization of multi-pressure himidification-dehumidification desalination using thermal vapor compression and hybridization

Conference site: http://www.ishmt2011.iitm.ac.in/Humidification-dehumidification (HD or HDH) desalination, and specifically HD driven by a thermal vapor compressor (TVC), is a thermal desalination method that has the potential to produce potable water efficiently in order to address the growing demand for water. This article presents a numerical study and optimization of two HD-TVC cycle configurations in order to determine the best achievable thermal performance. Through the use of nonlinear programming, it is found that the simplest configuration of HD-TVC has performance comparable to a traditional single-stage, single-pressure HD cycle (GOR 0.8–2.0), while the hybridized HD-TVC cycle with reverse osmosis (RO) has thermal performance that is competitive with existing large scale desalination systems (GOR 11.8–28.3).Center for Clean Water and Clean Energy at MIT and KFUPMNumerica TechnologyKing Fahd University of Petroleum and Mineral