To integrate large volumes of renewables and use electricity more efficiently, many industrial trials are on-going around the world that aim to realize decentralized or hierarchical control of renewable and distributed energy resources, flexible loads and monitoring devices. As the cost and complexity involved in the centralized communications and control infrastructure may be prohibitive in controlling millions of these distributed energy resources and devices, distributed optimization methods are expected to become much more prevalent in the operation of future electric power systems, as they have the potential to address this challenge and can be applied to various applications such as optimal power ow, state estimation, voltage control, and many others. While many distributed optimization algorithms are developed mathematically, little effort has been reported so far on how these methods should actually be implemented in real-world large-scale systems. The challenges associated with this include identifying how to decompose the overall optimization problem, what communication infrastructures can support the information exchange among subproblems, and whether to coordinate the updates of the subproblems in a synchronous or asynchronous manner. This research is dedicated to developing mathematical tools to address these issues, particularly for solving the non-convex optimal power flow problem. As the first part of this thesis, we develop a partitioning method that defines the boundaries of regions when applying distributed algorithms to a power system. This partitioning method quantifies the computational couplings among the buses and groups the buses with large couplings into one region. Through numerical experiments, we show that the developed spectral partitioning approach is the key to achieving fast convergence of distributed optimization algorithms on large-scale systems. After the partitioning of the system is defined, one needs to determine whether the communications among neighboring regions are supported. Therefore, as the second part of this thesis, we propose models for centralized and distributed communications infrastructures and study the impact of communication delays on the efficiency of distributed optimization algorithms through network simulations. Our findings suggest that the centralized communications infrastructure can be prohibitive for distributed optimization and cost-effective migration paths to a more distributed communications infrastructure are necessary. As the sizes and complexities of subproblems and communication delays are generally heterogeneous, synchronous distributed algorithms can be inefficient as they require waiting for the slowest region in the system. Hence, as the third part of this thesis, we develop an asynchronous distributed optimization method and show its convergence for the considered optimal power flow problem. We further study the impact of parameter tuning, system partitioning and communication delays on the proposed asynchronous method and compare its practical performance with its synchronous counterpart. Simulation results indicate that the asynchronous approach can be more efficient with proper partitioning and parameter settings on large-scale systems. The outcome of this research provides important insights into how existing hardware and software solutions for Energy Management Systems in the power grid can be used or need to be extended for deploying distributed optimization methods, which establishes the interconnection between theoretical studies of distributed algorithms and their practical implementation. As the evolution towards a more distributed control architecture is already taking place in many utility networks, the approaches proposed in this thesis provide important tools and a methodology for adopting distributed optimization in power systems.

Rapid advances of computer modeling and simulation tools and computing hardware have turned Model Based Design (MBD) a more viable technology. However, using a computationally intensive, “black-box” form MBD software tool to carry out design optimization leads to a number of key challenges. The non-unimodal objective function and/or non-convex feasible search region of the implicit numerical simulations in the optimization problems are beyond the capability of conventional optimization algorithms. In addition, the computationally intensive simulations used to evaluate the objective and/or constraint functions during the MBD process also make conventional stochastic global optimization algorithms unusable due to their requirement of a huge number of objective and constraint function evaluations. Surrogate model, or metamodeling-based global optimization techniques have been introduced to address these issues. Various surrogate models, including kriging, radial basis functions (RBF), multivariate adaptive regression splines (MARS), and polynomial regression (PR), are built using limited samplings on the original objective/constraint functions to reduce needed computation in the search of global optimum. In many real-world design optimization applications, computationally expensive numerical simulation models are used as objective and/or constraint functions. To solve these problems, enormous fitness function evaluations are required during the evolution based search process when advanced Global Optimization algorithms, such as DIRECT search, Differential Evolution (DE), and Bat Algorithm (BA) are used. In this work, improvements have been made to three widely used global optimization algorithms, Divided Rectangles (DIRECT), Differential Evolution (DE), and Bat Algorithm (BA) by integrating appropriate surrogate modeling methods to increase the computation efficiency of these algorithms to support MBD. The superior performance of these new algorithms in comparison with their original counterparts are shown using commonly used optimization algorithm testing benchmark problems. Integration of the surrogate modeling methods have considerably improved the search efficiency of the DIRECT, DE, and BA algorithms with significant reduction on the Number of Function Evaluations (NFEs). The newly introduced algorithms are then applied to a complex engineering design optimization problem, the design optimization of floating wind turbine platform, to test its effectiveness in real-world applications. These newly improved algorithms were able to identify better design solutions using considerably lower NFEs on the computationally expensive performance simulation model of the design. The methods of integrating surrogate modeling to improve DIRECT, DE and BA global optimization searches and the resulting algorithms proved to be effective for solving complex and computationally intensive global optimization problems, and formed a foundation for future research in this area. / Graduate

The initial question addressed in this thesis is how to take into account the multi-objective aspect of decision problems in inverse optimization. The most straightforward extension consists of finding a minimal adjustment of the objective functions coefficients such that a given feasible solution becomes efficient. However, there is not only a single question raised by inverse multi-objective optimization, because there is usually not a single efficient solution. The way we define inverse multi-objective<p>optimization takes into account this important aspect. This gives rise to many questions which are identified by a precise notation that highlights a large collection of inverse problems that could be investigated. In this thesis, a selection of inverse problems are presented and solved. This selection is motivated by their possible applications and the interesting theoretical questions they can rise in practice. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

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Cette thèse montre des contributions à l'analyse d'algorithmes pour l'optimisation de fonctions bruitées. Les taux de convergences (regret simple et regret cumulatif) sont analysés pour les algorithmes de recherche linéaire ainsi que pour les algorithmes de recherche aléatoires. Nous prouvons que les algorithmes basé sur la matrice hessienne peuvent atteindre le même résultat que certaines algorithmes optimaux, lorsque les paramètres sont bien choisis. De plus, nous analysons l'ordre de convergence des stratégies évolutionnistes pour des fonctions bruitées. Nous déduisons une convergence log-log. Nous prouvons aussi une borne basse pour le taux de convergence de stratégies évolutionnistes. Nous étendons le travail effectué sur les mécanismes de réévaluations en les appliquant au cas discret. Finalement, nous analysons la mesure de performance en elle-même et prouvons que l'utilisation d'une mauvaise mesure de performance peut mener à des résultats trompeurs lorsque différentes méthodes d'optimisation sont évaluées. / This thesis exposes contributions to the analysis of algorithms for noisy functions. It exposes convergence rates for linesearch algorithms as well as for random search algorithms. We prove in terms of Simple Regret and Cumulative Regret that a Hessian based algorithm can reach the same results as some optimal algorithms in the literature, when parameters are tuned correctly. On the other hand we analyse the convergence order of Evolution Strategies when solving noisy functions. We deduce log-log convergence. We also give a lower bound for the convergence rate of the Evolution Strategies. We extend the work on revaluation by applying it to a discrete settings. Finally we analyse the performance measure itself and prove that the use of an erroneus performance measure can lead to misleading results on the evaluation of different methods.

Indiana University-Purdue University Indianapolis (IUPUI) / An increase in the awareness of environmental conservation is leading the automotive industry into the adaptation of alternatively fueled vehicles. Electric, Fuel-Cell as well as Hybrid-Electric vehicles focus on this research area with the aim to efficiently utilize vehicle powertrain as the first step. Energy and Power Management System control strategies play a vital role in improving the efficiency of any hybrid propulsion system. However, these control strategies are sensitive to the dynamics of the powertrain components used in the given system. A kinematic mathematical model for Plug-in Hybrid Electric Vehicle (PHEV) has been developed in this study and is further optimized by determining optimal power management strategy for minimal fuel consumption as well as NOx emissions while executing a set drive cycle. A multi-objective optimization using weighted sum formulation is needed in order to observe the trade-off between the optimized objectives. Particle Swarm Optimization (PSO) algorithm has been used in this research, to determine the trade-off curve between fuel and NOx. In performing these optimizations, the control signal consisting of engine speed and reference battery SOC trajectory for a 2-hour cycle is used as the controllable decision parameter input directly from the optimizer. Each element of the control signal was split into 50 distinct points representing the full 2 hours, giving slightly less than 2.5 minutes per point, noting that the values used in the model are interpolated between the points for each time step. With the control signal consisting of 2 distinct signals, speed, and SOC trajectory, as 50 element time-variant signals, a multidimensional problem was formulated for the optimizer. Novel approaches to balance the optimizer exploration and convergence, as well as seeding techniques are suggested to solve the optimal control problem. The optimization of each involved individual runs at 5 different weight levels with the resulting cost populations being compiled together to visually represent with the help of Pareto front development. The obtained results of simulations and optimization are presented involving performances of individual components of the PHEV powertrain as well as the optimized PMS strategy to follow for a given drive cycle. Observations of the trade-off are discussed in the case of Multi-Objective Optimizations.

In this thesis, the theory and application of black-box optimization methods are explored. More specifically, we looked at two families of algorithms, descent methods andresponse surface methods (closely related to trust region methods). We also looked at possibilities in using a dimension reduction technique called active subspace which utilizes sampled gradients. This dimension reduction technique can make the descent methods more suitable to high-dimensional problems, which turned out to be most effective when the data have a ridge-like structure. Finally, the optimization methods were used on a real-world problem in the context of pre-hospital care where the objective is to minimize the ambulance response times in the municipality of Umea by changing the positions of the ambulances. Before applying the methods on the real-world ambulance problem, a simulation study was performed on synthetic data, aiming at finding the strengths and weaknesses of the different models when applied to different test functions, at different levels of noise. The results showed that we could improve the ambulance response times across several different performance metrics compared to the response times of the current ambulancepositions. This indicates that there exist adjustments that can benefit the pre-hospitalcare in the municipality of Umea. However, since the models in this thesis work find local and not global optimums, there might still exist even better ambulance positions that can improve the response time further. / I denna rapport undersöks teorin och tillämpningarna av diverse blackbox optimeringsmetoder. Mer specifikt så har vi tittat på två familjer av algoritmer, descentmetoder och responsytmetoder (nära besläktade med tillitsregionmetoder). Vi tittar också på möjligheterna att använda en dimensionreduktionsteknik som kallas active subspace som använder samplade gradienter för att göra descentmetoderna mer lämpade för högdimensionella problem, vilket visade sig vara mest effektivt när datat har en struktur där ändringar i endast en riktning har effekt på responsvärdet. Slutligen användes optimeringsmetoderna på ett verkligt problem från sjukhusvården, där målet var att minimera svarstiderna för ambulansutryckningar i Umeå kommun genom att ändra ambulanspositionerna. Innan metoderna tillämpades på det verkliga ambulansproblemet genomfördes också en simuleringsstudie på syntetiskt data. Detta för att hitta styrkorna och svagheterna hos de olika modellerna genom att undersöka hur dem hanterar ett flertal testfunktioner under olika nivåer av brus. Resultaten visade att vi kunde förbättra ambulansernas responstider över flera olika prestandamått jämfört med responstiderna för de nuvarande ambulanspositionerna. Detta indikerar att det finns förändringar av positioneringen av ambulanser som kan gynna den pre-hospitala vården inom Umeå kommun. Dock, eftersom modellerna i denna rapport hittar lokala och inte globala optimala punkter kan det fortfarande finnas ännu bättre ambulanspositioner som kan förbättra responstiden ytterligare.

This work proposes a new method for using reduced order models in lieu of high fidelity analysis during the sensitivity analysis step of gradient based design optimization. The method offers a reduction in the computational cost of finite difference based sensitivity analysis in that context. The method relies on interpolating reduced order models which are based on proper orthogonal decomposition. The interpolation process is performed using radial basis functions and Grassmann manifold projection. It does not require additional high fidelity analyses to interpolate a reduced order model for new points in the design space. The interpolated models are used specifically for points in the finite difference stencil during sensitivity analysis. The proposed method is applied to an airfoil shape optimization (ASO) problem and a transport wing optimization (TWO) problem. The errors associated with the reduced order models themselves as well as the gradients calculated from them are evaluated. The effects of the method on the overall optimization path, computation times, and function counts are also examined. The ASO results indicate that the proposed scheme is a viable method for reducing the computational cost of these optimizations. They also indicate that the adaptive step is an effective method of improving interpolated gradient accuracy. The TWO results indicate that the interpolation accuracy can have a strong impact on optimization search direction.

Constant-force mechanisms are mechanical devices that provide a near-constant output force over a prescribed deflection range. This thesis develops various optimization-based methods for designing robust constant-force mechanisms. The configuration of the mechanisms that are the focus of this research comprises a cam and a compliant spring fixed at one end while making contact with the cam at the other end. This configuration has proven to be an innovative solution in several applications because of its simplicity in manufacturing and operation. In this work, several methods are introduced to design these mechanisms, and reduce the sensitivity of these mechanisms to manufacturing uncertainties and frictional effects. The mechanism's sensitivity to these factors is critical in small scale applications where manufacturing variations can be large relative to overall dimensions, and frictional forces can be large relative to the output force. The methods in this work are demonstrated on a small scale electrical contact on the order of millimeters in size. The method identifies a design whose output force is 98.20% constant over its operational deflection range. When this design is analyzed using a Monte Carlo simulation the standard deviation in constant force performance is 0.76%. When compared to a benchmark design from earlier research, this represents a 34% increase in constant-force performance, and a reduction from 1.68% in the standard deviation of performance. When this new optimal design is evaluated to reduce frictional effects a design is identifed that shows a 36% reduction in frictional energy loss while giving up, however, 18.63% in constant force.

The concept of portfolio optimization has been widely studied in the academy and implemented in the financial markets since its introduction by Markowitz 70 years ago. The problem of the mean-variance optimization framework caused by input uncertainty has been one of the foci in the previous research. In this study, several models (linear shrinkage and Black-Litterman) based on Bayesian approaches are studied to improve the estimation of inputs. Moreover, a new framework based on robust optimization is presented to mitigate the input uncertainty further.  An out-of-sample test is specially designed, and the results show that Bayesian models in this study can improve the optimization results in terms of higher Sharpe ratios (the quotient between portfolio returns and their risks). Both covariance matrix estimators based on the linear shrinkage method contain less error and provide better optimization results, i.e. higher Sharpe ratios. The Black-Litterman model with a proper choice of inputs can significantly improve the portfolio return. The new framework based on the combination of shrinkage estimators, Black-Litterman, and robust optimization presents a better way for portfolio optimization than the classical framework of mean-variance optimization.