On parallel computing for stochastic optimization models and algorithms

167 p.Esta tesis tiene como objetivo principal la resolución de problemas de optimización bajo incertidumbre a gran escala, mediante la interconexión entre las disciplinas de Optimización estocástica y Computación en paralelo. Se describen algoritmos de descomposición desde la perspectivas de programación matemática y del aprovechamiento de recursos computacionales con el fin de resolver problemas de manera más rápida, de mayores dimensiones o/y obtener mejores resultados que sus técnicas homónimas en serie. Se han desarrollado dos estrategias de paralelización, denotadas como inner y outer. La primera de las cuales, realiza tareas en paralelo dentro de un esquema algorítmico en serie, mientras que la segunda ejecuta de manera simultánea y coordinada varios algoritmos secuenciales. La mayor descomposición del problema original, compartiendo el área de factibilidad, creando fases de sincronización y comunicación entre ejecuciones paralelas o definiendo condiciones iniciales divergentes, han sido claves en la eficacia de los diseños de los algoritmos propuestos. Como resultado, se presentan tanto algoritmos exactos como matheurísticos, que combinan metodologías metaheurísticas y técnicas de programación matemática. Se analiza la escalabilidad de cada algoritmo propuesto, y se consideran varios bancos de problemas de diferentes dimensiones, hasta un máximo de 58 millones de restricciones y 54 millones de variables (de las cuales 15 millones son binarias). La experiencia computacional ha sido principalmente realizada en el cluster ARINA de SGI/IZO-SGIker de la UPV/EHU

Transmission Expansion Planning : computational challenges toward real-size networks

The importance of the transmission network for supplying electricity demand is undeniable, and Transmission Expansion Planning (TEP) studies is key for a reliable power system. Due to increasing sources of uncertainty such as more intermittent energy resources, mobile and controllable demands, and fast technology improvements for PVs and energy storage devices, the need for using systematic ways for solving this complex problem is increased. One of the main barriers for deploying optimization-based TEP studies is computationally intractability, which is the main motivation for this research. The aim of this work is to investigate the computational challenges associated with systematic TEP studies for large-scale problems, and develop algorithms to improve computational performance. In the first step, we investigate the impact of adding security constraints (as NERC standard requirement) into TEP optimization problem, and develop the Variable Contingency List (VCL) algorithm to pre-screen security constraints to only add those that may affect the feasible region. It significantly decreases the size of the problem compared to considering all security constraints. Then, we evaluate the impact of the size of candidate lines list (number of binary variables) on TEP, and developed a heuristic algorithm to decrease the size of this list. In the next step, we integrate uncertainties into the TEP optimization problem and formulate the problem as a two-stage stochastic program. Adding uncertainties increases the size of the problem significantly. It leads us to develop a three-level filter that introduces important scenario identification index (ISII) and similar scenario elimination (SSE) technique to decrease the number of security constraints in stochastic TEP in a systematic and tractable way. We then investigate the scalability of the stochastic TEP formulation. We develop a configurable decomposition framework that allows us to decompose the original problem into subproblems that can be solved independently and in parallel. This framework can benefit from using both progressive hedging (PH) and Benders decomposition (BD) algorithms to decompose and parallelize a large-scale problem both vertically and horizontally. We have also developed a bundling algorithm that improves the performance of PH algorithm and the overall performance of the framework. We have implemented our work on a reduced ERCOT network with more than 3000 buses to demonstrate the practicality of the proposed method in this work for large-scale problems.Electrical and Computer Engineerin