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This work investigates how different forms of input elicitation obtained from crowdsourcing can be utilized to improve the quality of inferred labels for image classification tasks, where an image must be labeled as either positive or negative depending on the presence/absence of a specified object. Five types of input elicitation methods are tested: binary classification (positive or negative); the (x, y)-coordinate of the position participants believe a target object is located; level of confidence in binary response (on a scale from 0 to 100%); what participants believe the majority of the other participants' binary classification is; and participant's perceived difficulty level of the task (on a discrete scale). We design two crowdsourcing studies to test the performance of a variety of input elicitation methods and utilize data from over 300 participants. Various existing voting and machine learning (ML) methods are applied to make the best use of these inputs. In an effort to assess their performance on classification tasks of varying difficulty, a systematic synthetic image generation process is developed. Each generated image combines items from the MPEG-7 Core Experiment CE-Shape-1 Test Set into a single image using multiple parameters (e.g., density, transparency, etc.) and may or may not contain a target object. The difficulty of these images is validated by the performance of an automated image classification method. Experiment results suggest that more accurate results can be achieved with smaller training datasets when both the crowdsourced binary classification labels and the average of the self-reported confidence values in these labels are used as features for the ML classifiers. Moreover, when a relatively larger properly annotated dataset is available, in some cases augmenting these ML algorithms with the results (i.e., probability of outcome) from an automated classifier can achieve even higher performance than what can be obtained by using any one of the individual classifiers. Lastly, supplementary analysis of the collected data demonstrates that other performance metrics of interest, namely reduced false-negative rates, can be prioritized through special modifications of the proposed aggregation methods.

With the rapidly growing need for long-term decision making in the presence of stochastic future events, it is important to devise novel mathematical optimization tools and develop computationally efficient solution approaches for solving them. Two-stage stochastic programming is one of the powerful modeling tools that allows probabilistic data parameters in mixed integer programming, a well-known tool for optimization modeling with deterministic input data. However, akin to the mixed integer programs, these stochastic models are theoretically intractable and computationally challenging to solve because of the presence of integer variables. This dissertation focuses on theory, algorithms and applications of two-stage stochastic mixed integer (non)linear programs and it has three-pronged plan. In the first direction, we study two-stage stochastic p-order conic mixed integer programs (TSS-CMIPs) with p-order conic terms in the second-stage objectives. We develop so called scenario-based (non)linear cuts which are added to the deterministic equivalent of TSS-CMIPs (a large-scale deterministic conic mixed integer program). We provide conditions under which these cuts are sufficient to relax the integrality restrictions on the second-stage integer variables without impacting the integrality of the optimal solution of the TSS-CMIP. We also introduce a multi-module capacitated stochastic facility location problem and TSS-CMIPs with structured CMIPs in the second stage to demonstrate the significance of the foregoing results for solving these problems. In the second direction, we propose risk-neutral and risk-averse two-stage stochastic mixed integer linear programs for load shed recovery with uncertain renewable generation and demand. The models are implemented using a scenario-based approach where the objective is to maximize load shed recovery in the bulk transmission network by switching transmission lines and performing other corrective actions (e.g. generator re-dispatch) after the topology is modified. Experiments highlight how the proposed approach can serve as an offline contingency analysis tool, and how this method aids self-healing by recovering more load shedding. In the third direction, we develop a dual decomposition approach for solving two-stage stochastic quadratically constrained quadratic mixed integer programs. We also create a new module for an open-source package DSP (Decomposition for Structured Programming) to solve this problem. We evaluate the effectiveness of this module and our approach by solving a stochastic quadratic facility location problem. Doctor of Philosophy With the rapidly growing need for long-term decision making in the presence of stochastic future events, it is important to devise novel mathematical optimization tools and develop computationally efficient solution approaches for solving them. Two-stage stochastic programming is one of the powerful modeling tools that allows two-stages of decision making where the first-stage strategic decisions (such as deciding the locations of facilities or topology of a power transmission network) are taken before the realization of uncertainty, and the second-stage operational decisions (such as transportation decisions between customers and facilities or power flow in the transmission network) are taken in response to the first-stage decision and a realization of the uncertain (demand) data. This modeling tool is gaining wide acceptance because of its applications in healthcare, power systems, wildfire planning, logistics, and chemical industries, among others. Though intriguing, two-stage stochastic programs are computationally challenging. Therefore, it is crucial to develop theoretical results and computationally efficient algorithms, so that these models for real-world applied problems can be solved in a realistic time frame. In this dissertation, we consider two-stage stochastic mixed integer (non)linear programs, provide theoretical and algorithmic results for them, and introduce their applications in logistics and power systems. First, we consider a two-stage stochastic mixed integer program with p-order conic terms in the objective that has applications in facility location problem, power system, portfolio optimization, and many more. We provide a so-called second-stage convexification technique which greatly reduces the computational time to solve a facility location problem, in comparison to solving it directly with a state-of-the-art solver, CPLEX, with its default settings. Second, we introduce risk-averse and risk-neutral two-stage stochastic models to deal with uncertainties in power systems, as well as the risk preference of decision makers. We leverage the inherent flexibility of the bulk transmission network through the systematic switching of transmission lines in/out of service while accounting for uncertainty in generation and demand during an emergency. We provide abundant computational experiments to quantify our proposed models, and justify how the proposed approach can serve as an offline contingency analysis tool. Third, we develop a new solution approach for two-stage stochastic mixed integer programs with quadratic terms in the objective function and constraints and implement it as a new module for an open-source package DSP We perform computational experiments on a stochastic quadratic facility location problem to evaluate the performance of this module.