Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, September, 2019 / Manuscript. / Includes bibliographical references (pages 93-94). / This thesis follows and extends the discussion of Özer et al. (2011) on trust in forecast information sharing. We propose a method for belief learning and for updating. The effects of production cost (which indicate the risk) and market uncertainty (which indicates the accuracy of the private information) are analyzed quantitatively. Since complicated Nash equilibria from traditional game theory analysis often fail in real-life scenarios, we formulate simpler assumptions so that the strategies of both sides are not complicated. We compare the similarities and differences between the structure of our model and the structure of other behavioral models related to bounded rationality or cheap talk. We characterize how the supply chain environment changes trust and decisions. We find out that initial beliefs do not matter because they will be quickly adjusted by the market: the limiting behavior, as t --> [infinity], depends only on the retailers' trustworthiness and supply chain environment. Since the retailer's trustworthiness and belief is un-observable, we perform latent profile analysis to fit the model on the experiment conducted by Özer et al. (2011), and test the end game effect and out-of-sample fit. / by Pengbo Zhang. / S.M. / S.M. Massachusetts Institute of Technology, Computation for Design and Optimization Program

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2019 / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 83-85). / The food safety problem has been challenging the traditional operating model of Chinese agricultural supply chain. In the recent decades, more and more agribusinesses and cooperatives in China have adopted contract farming to strengthen food safety control during the sourcing process. Meanwhile, several pricing schemes are applied to incentivize the quality-improving effort from producers of different risk attitudes and defaulting likelihoods. In this paper, we consider a producer-agribusiness supply chain with stochastic wholesale market price and random production yield. We model the three commonly-observed pricing schemes of contract farming in China: 1. Markup contract, 2. Fixed-price contract and 3. Protective-price contract. We characterize the equilibrium of the contracting game under each pricing scheme with risk-neutral and/or risk-averse producer. Furthermore, we investigate the optimal contract selections under different producer characteristics. We find that compared to the most frequently-used markup contract, the fixed-price and protective-price contract better incentivize the risk-averse producer to exert higher levels of quality-improving effort; In addition, switching from a markup contract to a protective-price contract or a fixed-price contract (under a certain threshold of defaulting rate) will achieve a win-win outcome where both the expected profit of the company and the utility of the risk-averse producer increase. Finally, we offer insights on the selection between the protective-price contract and fixed-price contract under different market price and production yield conditions. / by Yilin Yang. / S.M. / S.M. Massachusetts Institute of Technology, Computation for Design and Optimization Program

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2019 / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 93-94). / In this thesis we present a reduced-dimension model for the density-driven hydrodynamic Rayleigh-Taylor instability. We motivate the project with experimental findings of a little-understood stabilizing effect of geometry and deviations of measured instability wavelength from theoretical predictions. We present novel methods of data analysis for the experimental data. We then present a reduced-dimension model for the governing equations of the system, Stoke's equations and Fick's law, using polynomial trial functions. We discuss the results and conduct a linear stability analysis of the reduced system. We compare the model to a finite element simulation of the full governing equations using COMSOL, and propose an optimization framework for the basis functions of the reduced model. The reduced model helps in developing physical intuition for the behavior of the instability in this confined geometry, and understanding the effects of certain parameters that are difficult to study experimentally or by simulating the full equations. / by Samar Alqatari. / S.M. / S.M. Massachusetts Institute of Technology, Computation for Design and Optimization Program

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2018 / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 79-81). / Solving convex optimization problems has become extremely efficient and reliable after the recent development of polynomial-time algorithms and advancement in computing power. Geometric Programming (GP) and Signomial Programming (SP) has been proven successful in optimizing multidisciplinary designs due to exploiting the speed of convergence and the ability to model non-linear designs. However, an optimal solution of GPs and SPs can be sensitive to uncertainties in the parameters involved in the problem. In fact, robust optimization can incorporate the uncertainties in an optimization problem and solves for the worst-case scenario. Yet, robust geometric programs (RGPs) and robust signomial programs (RSPs) are not known to have a tractable formulation that current solvers can efficiently solve. In this thesis, approximate formulations of RGPs and RSPs are proposed. Recently, the curiosity regarding the deployment of GPs and SPs in model complex engineering systems has been growing. This awareness has motivated modeling the uncertainties that are fundamental to engineering design optimization. Consequently, RGPs and RSPs provide a framework for modeling and solving GPs and SPs while representing their ambiguities as belonging to an uncertainty set. The RGP methodologies presented here are based on reformulating the GP as a convex program and then robustifying it with methods from robust linear programming. The RSP methodology is based on solving sequential local RGP approximations. These new methodologies, along with previous ones from the literature, are used to robustify aircraft design problems, and the results of these different methodologies are compared and discussed. / by Ali Saab. / S.M. / S.M. Massachusetts Institute of Technology, Computation for Design and Optimization Program

Thesis: S.M., Massachusetts Institute of Technology, School of Engineering, Center for Computational Engineering, Computation for Design and Optimization Program, 2015. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 52-54). / We consider the problem of estimating individual and social value of information in routing games. We propose a Bayesian congestion game that accounts for the heterogeneity in the commuters' access to information about traffic incidents. The model divides the population of commuters into two sub-populations or types based on their information about incidents. Types-H and L have high and low information about incidents, respectively. Each population routes its demand on an incident-prone, parallel route network. The cost function for each route depends is affine in its usage level and its slope increases with the route's incident state. Both populations (player types) know the demand of each type, route cost functions, and the incident probability. In addition, in our model, the commuters in type-H population receive private information on the true realization of incident state. We analyze both individual cost for each population and the aggregate (social) cost as the type-H population size increases. We observe that, in equilibrium, both these costs are non-monotonic and non-linear as the fraction of the total demand that is type-H increases. Our main results are as follows: First, the information improves individual welfare (i.e., when a commuter shifts from being in the type-L population to the type-H population), but the value of information is zero after a certain threshold fraction. Second, there exist another threshold (lower than the first threshold) after which increasing the relative fraction of type-H commuters does not reduce the aggregate social cost. / by Jeffrey Liu. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2014. / Cataloged from PDF version of thesis. / Includes bibliographical references (page 47). / This thesis presents a new simple lightweight C++ thread based parallelization library, intended for use in numerical algorithms. It provides simple multitasking and task synchronization functions. The library hides all internal system calls from the developer and utilizes thread pooling to provide better performance and utilization of system time and resources. The library is lightweight and platform independent, and has been tested on Linux, and Windows. Experiments were conducted to verify the proper functionality of the library and to show that parallelized algorithms on a single machine are more efficient than using the Message Passing Interface (MPI) using shared memory. In the opinion of several researchers who have used this library, the parallelized code is more easily understood and debugged than MPI. The results of initial experiments show that algorithms are as efficient or better than those using MPI. / by Maitham Makki Alhubail. / S.M.

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). / 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. / by Zhong Yi Wan. / S.M.

This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2019 / Cataloged from student-submitted PDF version of thesis. / Includes bibliographical references (pages 123-128). / This thesis considers the task of learning efficient low-dimensional models for dynamical systems. To be effective in an engineering setting, these models must be predictive -- that is, they must yield reliable predictions for conditions outside the data used to train them. These models must also be able to make predictions that enforce physical constraints. Achieving these tasks is particularly challenging for the case of systems governed by partial differential equations, where generating data (either from high-fidelity simulations or from physical experiments) is expensive. We address this challenge by developing learning approaches that embed physical constraints. We propose two physics-based approaches for generating low-dimensional predictive models. The first leverages the proper orthogonal decomposition (POD) to represent high-dimensional simulation data with a low-dimensional physics-based parameterization in combination with machine learning methods to construct a map from model inputs to POD coefficients. A comparison of four machine learning methods is provided through an application of predicting flow around an airfoil. This framework also provides a way to enforce a number of linear constraints by modifying the data with a particular solution. The results help to highlight the importance of including physics knowledge when learning from small amounts of data. We also apply a data-driven approach to learning the operators of low-dimensional models. This method provides an avenue for constructing low-dimensional models of systems where the operators of discretized governing equations are unknown or too complex, while also having the ability to enforce physical constraints. The methodology is applied to a two-dimensional combustion problem, where discretized model operators are unavailable. The results show that the method is able to accurately make predictions and enforce important physical constraints. / by Renee C. Swischuk. / S.M. / S.M. Massachusetts Institute of Technology, Computation for Design and Optimization Program

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2011. / Page 118 blank. Cataloged from PDF version of thesis. / Includes bibliographical references (p. 112-117). / The Bayesian approach to inference problems provides a systematic way of updating prior knowledge with data. A likelihood function involving a forward model of the problem is used to incorporate data into a posterior distribution. The standard method of sampling this distribution is Markov chain Monte Carlo which can become inefficient in high dimensions, wasting many evaluations of the likelihood function. In many applications the likelihood function involves the solution of a partial differential equation so the large number of evaluations required by Markov chain Monte Carlo can quickly become computationally intractable. This work aims to reduce the computational cost of sampling the posterior by introducing a multiscale framework for inference problems involving elliptic forward problems. Through the construction of a low dimensional prior on a coarse scale and the use of iterative conditioning technique the scales are decouples and efficient inference can proceed. This work considers nonlinear mappings from a fine scale to a coarse scale based on the Multiscale Finite Element Method. Permeability characterization is the primary focus but a discussion of other applications is also provided. After some theoretical justification, several test problems are shown that demonstrate the efficiency of the multiscale framework. / by Matthew David Parno. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 61-65). / Dynamical systems are subjected to various random external forcings that complicate theie control. In order to achieve optimal performance, these systems need to continually adapt to external disturbances in real time. This capability is provided by feedback based control strategies that derive an optimal control from the current state of the system. Model Predictive Control(MPC) is one such feedback-based technique. This thesis explores the application of a stochastic version of MPC to a reservoir system. The reservoir system is designed to maximize the revenue generated from the hydroelectricity while simultaneously obeying several exogenous constraints. An ensemble based version of the stochastic MPC technique is studied and applied to the reservoir to determine the optimal water release strategies. Further analysis is performed to understand the sensitivity of different parameters in the MPC technique. / by Reetik Kumar Sahu. / S.M.