Hybrid Advanced Optimization Methods with Evolutionary Computation Techniques in Energy Forecasting

More accurate and precise energy demand forecasts are required when energy decisions are made in a competitive environment. Particularly in the Big Data era, forecasting models are always based on a complex function combination, and energy data are always complicated. Examples include seasonality, cyclicity, fluctuation, dynamic nonlinearity, and so on. These forecasting models have resulted in an over-reliance on the use of informal judgment and higher expenses when lacking the ability to determine data characteristics and patterns. The hybridization of optimization methods and superior evolutionary algorithms can provide important improvements via good parameter determinations in the optimization process, which is of great assistance to actions taken by energy decision-makers. This book aimed to attract researchers with an interest in the research areas described above. Specifically, it sought contributions to the development of any hybrid optimization methods (e.g., quadratic programming techniques, chaotic mapping, fuzzy inference theory, quantum computing, etc.) with advanced algorithms (e.g., genetic algorithms, ant colony optimization, particle swarm optimization algorithm, etc.) that have superior capabilities over the traditional optimization approaches to overcome some embedded drawbacks, and the application of these advanced hybrid approaches to significantly improve forecasting accuracy

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Regularized approximate policy iteration using kernel for on-line reinforcement learning

By using Reinforcement Learning (RL), an autonomous agent interacting with the environment can learn how to take adequate actions for every situation in order to optimally achieve its own goal. RL provides a general methodology able to solve uncertain and complex decision problems which may be present in many real-world applications. RL problems are usually modeled as a Markov Decision Processes (MDPs) deeply studied in the literature. The main peculiarity of a RL algorithm is that the RL agent is assumed to learn the optimal policies from its experiences without knowing the parameters of the MDP. The key element in solving the MDP is learning a value function which gives the expectation of total reward an agent might expect at its current state taking a given action. This value function allows to obtain the optimal policy. In this thesis we study the capacity of SVR using kernel methods to adapt and solve complex RL problems in large or continuous state space. SVR can be studied using a geometrical interpretation in terms of optimal margin or can be seen as a regularization problem given in a Reproducing Kernel Hilbert Space (RKHS) SVR have good properties over the generalization ability and as they are based a on convex optimization problem, they do not suffer from sub-optimality. SVR are non-parametric showing the ability to automatically adapt to the complexity of the problem. Accordingly, applying SVR to approximate value functions sounds to be a good approach. SVR can be solved both in batch mode when the whole set of training sample are at disposal of the learning agents or incrementally which enables the addition or removal of training samples very effectively. Incremental SVR finds the appropriate KKT conditions for new or updated data by modifying their influences into the regression function maintaining consistence in the KKT conditions for the rest of data used for learning. In RL problems an incremental SVR should be able to approximate the action value function leading to the optimal policy. Accordingly, computation load should be lower, learning speed faster and generalization more effective than other existing method The overall contribution coming from of our work is to develop, formalize, implement and study a new RL technique for generalization in discrete and continuous state spaces with finite actions. Our method uses the Approximate Policy Iteration (API) framework with the BRM criterion which allows to represent the action value function using SVR. This approach for RL is the first one we know using SVR compatible to the agent interaction- with-the-environment framework of RL which shows his power by solving a large number of benchmark problems, including very difficult ones, like the bicycle driving and riding control problem. In addition, unlike most RL approaches to generalization, we develop a proof finding theoretical bounds for the convergence of the method to the optimal solution under given conditions.Mediante el uso de aprendizaje por refuerzo (RL), un agente autónomo interactuando con el medio ambiente puede aprender a tomar adecuada acciones para cada situación con el fin de lograr de manera óptima su propia meta. RL proporciona una metodología general capaz de resolver problemas de decisión complejos que pueden estar presentes en muchas aplicaciones del mundo real. Problemas RL usualmente se modelan como una Procesos de Decisión de Markov (MDP) estudiados profundamente en la literatura. La principal peculiaridad de un algoritmo de RL es que el agente es asumido para aprender las políticas óptimas de sus experiencias sin saber los parámetros de la MDP. El elemento clave en resolver el MDP está en el aprender una función de valor que da la expectativa de recompensa total que un agente puede esperar en su estado actual para tomar una acción determinada. Esta función de valor permite obtener la política óptima. En esta tesis se estudia la capacidad del SVR utilizando núcleo métodos para adaptarse y resolver problemas RL complejas en el espacio estado grande o continua. RVS puede ser estudiado mediante un interpretación geométrica en términos de margen óptimo o puede ser visto como un problema de regularización dado en un Reproducing Kernel Hilbert Space (RKHS). SVR tiene buenas propiedades sobre la capacidad de generalización y ya que se basan en una optimización convexa problema, ellos no sufren de sub-optimalidad. SVR son no paramétrico que muestra la capacidad de adaptarse automáticamente a la complejidad del problema. En consecuencia, la aplicación de RVS para aproximar funciones de valor suena para ser un buen enfoque. SVR puede resolver tanto en modo batch cuando todo el conjunto de muestra de entrenamiento están a disposición de los agentes de aprendizaje o incrementalmente que permite la adición o eliminación de muestras de entrenamiento muy eficaz. Incremental SVR encuentra las condiciones adecuadas para KKT nuevas o actualizadas de datos modificando sus influencias en la función de regresión mantener consistencia en las condiciones KKT para el resto de los datos utilizados para el aprendizaje. En los problemas de RL una RVS elemental será capaz de aproximar la función de valor de acción que conduce a la política óptima. En consecuencia, la carga de cálculo debería ser menor, la velocidad de aprendizaje más rápido y generalización más efectivo que el otro método existente La contribución general que viene de nuestro trabajo es desarrollar, formalizar, ejecutar y estudiar una nueva técnica de RL para la generalización en espacio de estados discretos y continuos con acciones finitas. Nuestro método utiliza el marco de la Approximate Policy Iteration (API) con el criterio de BRM que permite representar la función de valor de acción utilizando SVR. Este enfoque de RL es el primero que conocemos usando SVR compatible con el marco de RL con agentes interaccionado con el ambiente que muestra su poder mediante la resolución de un gran número de problemas de referencia, incluyendo los muy difíciles, como la conducción de bicicletas y problema de control de conducción. Además, a diferencia de la mayoría RL se acerca a la generalización, desarrollamos un hallazgo prueba límites teóricos para la convergencia del método a la solución óptima en condiciones dadas.Postprint (published version

Robust and Optimal Methods for Geometric Sensor Data Alignment

Geometric sensor data alignment - the problem of finding the rigid transformation that correctly aligns two sets of sensor data without prior knowledge of how the data correspond - is a fundamental task in computer vision and robotics. It is inconvenient then that outliers and non-convexity are inherent to the problem and present significant challenges for alignment algorithms. Outliers are highly prevalent in sets of sensor data, particularly when the sets overlap incompletely. Despite this, many alignment objective functions are not robust to outliers, leading to erroneous alignments. In addition, alignment problems are highly non-convex, a property arising from the objective function and the transformation. While finding a local optimum may not be difficult, finding the global optimum is a hard optimisation problem. These key challenges have not been fully and jointly resolved in the existing literature, and so there is a need for robust and optimal solutions to alignment problems. Hence the objective of this thesis is to develop tractable algorithms for geometric sensor data alignment that are robust to outliers and not susceptible to spurious local optima. This thesis makes several significant contributions to the geometric alignment literature, founded on new insights into robust alignment and the geometry of transformations. Firstly, a novel discriminative sensor data representation is proposed that has better viewpoint invariance than generative models and is time and memory efficient without sacrificing model fidelity. Secondly, a novel local optimisation algorithm is developed for nD-nD geometric alignment under a robust distance measure. It manifests a wider region of convergence and a greater robustness to outliers and sampling artefacts than other local optimisation algorithms. Thirdly, the first optimal solution for 3D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms other geometric alignment algorithms on challenging datasets due to its guaranteed optimality and outlier robustness, and has an efficient parallel implementation. Fourthly, the first optimal solution for 2D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms existing approaches on challenging datasets, reliably finding the global optimum, and has an efficient parallel implementation. Finally, another optimal solution is developed for 2D-3D geometric alignment, using a robust surface alignment measure. Ultimately, robust and optimal methods, such as those in this thesis, are necessary to reliably find accurate solutions to geometric sensor data alignment problems

Review of Low Voltage Load Forecasting: Methods, Applications, and Recommendations

The increased digitalisation and monitoring of the energy system opens up numerous opportunities to decarbonise the energy system. Applications on low voltage, local networks, such as community energy markets and smart storage will facilitate decarbonisation, but they will require advanced control and management. Reliable forecasting will be a necessary component of many of these systems to anticipate key features and uncertainties. Despite this urgent need, there has not yet been an extensive investigation into the current state-of-the-art of low voltage level forecasts, other than at the smart meter level. This paper aims to provide a comprehensive overview of the landscape, current approaches, core applications, challenges and recommendations. Another aim of this paper is to facilitate the continued improvement and advancement in this area. To this end, the paper also surveys some of the most relevant and promising trends. It establishes an open, community-driven list of the known low voltage level open datasets to encourage further research and development.Comment: 37 pages, 6 figures, 2 tables, review pape

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics

Regularized approximate policy iteration using kernel for on-line reinforcement learning

By using Reinforcement Learning (RL), an autonomous agent interacting with the environment can learn how to take adequate actions for every situation in order to optimally achieve its own goal. RL provides a general methodology able to solve uncertain and complex decision problems which may be present in many real-world applications. RL problems are usually modeled as a Markov Decision Processes (MDPs) deeply studied in the literature. The main peculiarity of a RL algorithm is that the RL agent is assumed to learn the optimal policies from its experiences without knowing the parameters of the MDP. The key element in solving the MDP is learning a value function which gives the expectation of total reward an agent might expect at its current state taking a given action. This value function allows to obtain the optimal policy. In this thesis we study the capacity of SVR using kernel methods to adapt and solve complex RL problems in large or continuous state space. SVR can be studied using a geometrical interpretation in terms of optimal margin or can be seen as a regularization problem given in a Reproducing Kernel Hilbert Space (RKHS) SVR have good properties over the generalization ability and as they are based a on convex optimization problem, they do not suffer from sub-optimality. SVR are non-parametric showing the ability to automatically adapt to the complexity of the problem. Accordingly, applying SVR to approximate value functions sounds to be a good approach. SVR can be solved both in batch mode when the whole set of training sample are at disposal of the learning agents or incrementally which enables the addition or removal of training samples very effectively. Incremental SVR finds the appropriate KKT conditions for new or updated data by modifying their influences into the regression function maintaining consistence in the KKT conditions for the rest of data used for learning. In RL problems an incremental SVR should be able to approximate the action value function leading to the optimal policy. Accordingly, computation load should be lower, learning speed faster and generalization more effective than other existing method The overall contribution coming from of our work is to develop, formalize, implement and study a new RL technique for generalization in discrete and continuous state spaces with finite actions. Our method uses the Approximate Policy Iteration (API) framework with the BRM criterion which allows to represent the action value function using SVR. This approach for RL is the first one we know using SVR compatible to the agent interaction- with-the-environment framework of RL which shows his power by solving a large number of benchmark problems, including very difficult ones, like the bicycle driving and riding control problem. In addition, unlike most RL approaches to generalization, we develop a proof finding theoretical bounds for the convergence of the method to the optimal solution under given conditions.Mediante el uso de aprendizaje por refuerzo (RL), un agente autónomo interactuando con el medio ambiente puede aprender a tomar adecuada acciones para cada situación con el fin de lograr de manera óptima su propia meta. RL proporciona una metodología general capaz de resolver problemas de decisión complejos que pueden estar presentes en muchas aplicaciones del mundo real. Problemas RL usualmente se modelan como una Procesos de Decisión de Markov (MDP) estudiados profundamente en la literatura. La principal peculiaridad de un algoritmo de RL es que el agente es asumido para aprender las políticas óptimas de sus experiencias sin saber los parámetros de la MDP. El elemento clave en resolver el MDP está en el aprender una función de valor que da la expectativa de recompensa total que un agente puede esperar en su estado actual para tomar una acción determinada. Esta función de valor permite obtener la política óptima. En esta tesis se estudia la capacidad del SVR utilizando núcleo métodos para adaptarse y resolver problemas RL complejas en el espacio estado grande o continua. RVS puede ser estudiado mediante un interpretación geométrica en términos de margen óptimo o puede ser visto como un problema de regularización dado en un Reproducing Kernel Hilbert Space (RKHS). SVR tiene buenas propiedades sobre la capacidad de generalización y ya que se basan en una optimización convexa problema, ellos no sufren de sub-optimalidad. SVR son no paramétrico que muestra la capacidad de adaptarse automáticamente a la complejidad del problema. En consecuencia, la aplicación de RVS para aproximar funciones de valor suena para ser un buen enfoque. SVR puede resolver tanto en modo batch cuando todo el conjunto de muestra de entrenamiento están a disposición de los agentes de aprendizaje o incrementalmente que permite la adición o eliminación de muestras de entrenamiento muy eficaz. Incremental SVR encuentra las condiciones adecuadas para KKT nuevas o actualizadas de datos modificando sus influencias en la función de regresión mantener consistencia en las condiciones KKT para el resto de los datos utilizados para el aprendizaje. En los problemas de RL una RVS elemental será capaz de aproximar la función de valor de acción que conduce a la política óptima. En consecuencia, la carga de cálculo debería ser menor, la velocidad de aprendizaje más rápido y generalización más efectivo que el otro método existente La contribución general que viene de nuestro trabajo es desarrollar, formalizar, ejecutar y estudiar una nueva técnica de RL para la generalización en espacio de estados discretos y continuos con acciones finitas. Nuestro método utiliza el marco de la Approximate Policy Iteration (API) con el criterio de BRM que permite representar la función de valor de acción utilizando SVR. Este enfoque de RL es el primero que conocemos usando SVR compatible con el marco de RL con agentes interaccionado con el ambiente que muestra su poder mediante la resolución de un gran número de problemas de referencia, incluyendo los muy difíciles, como la conducción de bicicletas y problema de control de conducción. Además, a diferencia de la mayoría RL se acerca a la generalización, desarrollamos un hallazgo prueba límites teóricos para la convergencia del método a la solución óptima en condiciones dadas