Theses - Computation for Design and Optimization
http://hdl.handle.net/1721.1/39113
2016-12-11T04:10:10ZTensor decomposition and parallelization of Markov Decision Processes
http://hdl.handle.net/1721.1/105018
Tensor decomposition and parallelization of Markov Decision Processes
Smart, David P. (David Paul)
Markov Decision Processes (MDPs) with large state spaces arise frequently when applied to real world problems. Optimal solutions to such problems exist, but may not be computationally tractable, as the required processing scales exponentially with the number of states. Unsurprisingly, investigating methods for efficiently determining optimal or near-optimal policies has generated substantial interest and remains an active area of research. A recent paper introduced an MDP representation as a tensor composition of a set of smaller component MDPs, and suggested a method for solving an MDP by decomposition into its tensor components and solving the smaller problems in parallel, combining their solutions into one for the original problem. Such an approach promises an increase in solution efficiency, since each smaller problem could be solved exponentially faster than the original. This paper develops this MDP tensor decomposition and parallelization algorithm, and analyzes both its computational performance and the optimality of its resultant solutions.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 85-81).
2016-01-01T00:00:00ZComplex systems and a computational social science perspective on the labor market
http://hdl.handle.net/1721.1/104577
Complex systems and a computational social science perspective on the labor market
Almaatouq, Abdullah
Labor market institutions are central for modern economies, and their polices can directly affect unemployment rates and economic growth. At the individual level, unemployment often has a detrimental impact on people's well-being and health. At the national level, high employment is one of the central goals of any economic policy, due to its close association with national prosperity. The main goal of this thesis is to highlight the need for frameworks that take into account the complex structure of labor market interactions. In particular, we explore the benefits of leveraging tools from computational social science, network science, and data-driven theories to measure the flow of opportunities and information in the context of the labor market. First, we investigate our key hypothesis, which is that opportunity/information flow through weak ties, and this is a key determinant of the length of unemployment. We then extend the idea of opportunity/information flow to clusters of other economic activities, where we expect the flow within clusters of related activities to be higher than within isolated activities. This captures the intuition that within related activities there are more "capitals" involved and that such activities require similar "capabilities." Therefore, more extensive clusters of economic activities should generate greater growth through exploiting the greater flow of opportunities and information. We quantify the opportunity/information flow using a complexity measure of two economic activities (i.e. jobs and exports).
Thesis: S.M., Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 99-109).; Thesis: S.M.. Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.
2016-01-01T00:00:00ZNumerical approaches to optimize dispatch on microgrids with energy storage
http://hdl.handle.net/1721.1/104567
Numerical approaches to optimize dispatch on microgrids with energy storage
Xie, Lutao
Microgrids and distributed generation are predicted to become extremely dominant in developing nations, and will be largely beneficial to both electricity suppliers and consumers. With the penetration of renewable energy into the electricity supply, to maintain a balance between power supply and demand is becoming more difficult. Nevertheless, it is quite feasible that large electrical storage systems such as batteries can efficiently mitigate problems caused by the intermittency of renewables, and thus enable stable adoption of such power sources. In order to understand how the energy capacity and power characteristics of batteries should be specified to optimize economic or socioeconomic benefits, an optimizing strategy for battery usage in microgrids energy scheduling was constructed. This strategy is based on the past power consumption, predictions of day-ahead power consumption, and historical trends of seasonal and daily trends, which gives a nonlinear, discontinuous and high dimensional objective function. Optimizing such an objective function is found to be very computational intensive and complex. In this paper, the nature of this large-scale optimization problem is studied. For real time dispatch, four optimization methods including active-set, interior-point method, sequential quadratic programming (SQP) and trust-region-reflective are discussed and compared to find the relatively fast and robust optimization algorithm. The computation was implemented by using the MATLAB nonlinear programming solver 'fmincon'. Three main objectives are carried out to improve the efficiency of solving this optimization problem: (1) determination of the mathematical& physical definitions of tolerances and discussion on convergence criteria with the corresponding tolerances; (2) Study and comparison on influences of the initial condition and the behavior of the objective function (highly related to peak demand charge); and (3) suggestions on modification of the model to achieve reduction of the computation time whilst maintain acceptable accuracy.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 49-50).
2016-01-01T00:00:00ZReduced-space Gaussian process regression forecast for nonlinear dynamical systems
http://hdl.handle.net/1721.1/104565
Reduced-space Gaussian process regression forecast for nonlinear dynamical systems
Wan, Zhong Yi, S.M. Massachusetts Institute of Technology
In this thesis work, we formulate a reduced-order data-driven strategy for the efficient probabilistic forecast of complex high-dimensional dynamical systems for which data-streams are available. The first step of this method consists of the reconstruction of the vector field in a reduced-order subspace of interest using Gaussian Process Regression (GPR). GPR simultaneously allows for the reconstruction of the vector field, as well as the estimation of the local uncertainty. The latter is due to i) the local interpolation error and ii) due to the truncation of the high-dimensional phase space and it analytically quantified in terms of the GPR hyperparameters. The second step involves the formulation of stochastic models that explicitly take into account the reconstructed dynamics and their uncertainty. For regions of the attractor where the training data points are not sufficiently dense for GPR to be effective an adaptive blended scheme is formulated that guarantees correct statistical steady state properties. We examine the effectiveness of the proposed method to complex systems including the Lorenz 63, Lorenz 96, the Kuramoto-Sivashinsky, as well as a prototype climate model. We also study the performance of the proposed approach as the intrinsic dimensionality of the system attractor increases in highly turbulent regimes.
Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 93-97).
2016-01-01T00:00:00Z