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Browsing by Author "Xie, Weijun"

Now showing 1 - 15 of 15
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    Advanced Data Analytics for Quality Assurance of Smart Additive Manufacturing
    Shen, Bo (Virginia Tech, 2022-07-07)
    Additive manufacturing (AM) is a powerful emerging technology for fabricating components with complex geometries using a variety of materials. However, despite the promising potential, due to the complexity of the process dynamics, how to ensure product quality and consistency of AM parts efficiently during the process remains challenging. Therefore, this dissertation aims to develop advanced machine learning methods for online process monitoring and quality assurance of smart additive manufacturing. Driven by edge computing, the Industrial Internet of Things (IIoT), sensors and other smart technologies, data collection, communication, analytics, and control are infiltrating every aspect of manufacturing. The data provides excellent opportunities to improve and revolutionize manufacturing for both quality and productivity. Despite the massive volume of data generated during a very short time, approximately 90 percent of data gets wasted or unused. The goal of sensing and data analytics for advanced manufacturing is to capture the full insight that data and analytics can discover to help address the most pressing problems. To achieve the above goal, several data-driven approaches have been developed in this dissertation to achieve effective data preprocessing, feature extraction, and inverse design. We also develop related theories for these data-driven approaches to guarantee their performance. The performances have been validated using sensor data from AM processes. Specifically, four new methodologies are proposed and implemented as listed below: 1. To make the unqualified thermal data meet the spatial and temporal resolution requirement of microstructure prediction, a super resolution for multi-sources image stream data using smooth and sparse tensor completion is proposed and applied to data acquisition of additive manufacturing. The qualified thermal data is able to extract useful information like boundary velocity, thermal gradient, etc. 2. To effectively extract features for high dimensional data with limited samples, a clustered discriminant regression is created for classification problems in healthcare and additive manufacturing. The proposed feature extraction method together with classic classifiers can achieve better classification performance than the convolutional neural network for image classification. 3. To extract the melt pool information from the processed X-ray video in metal AM process, a smooth sparse Robust Tensor Decomposition model is devised to decompose the data into the static background, smooth foreground, and noise, respectively. The proposed method exhibits superior performance in extracting the melt pool information on X-ray data. 4. To learn the material property for different printing settings, a multi-task Gaussian process upper confidence bound is developed for the sequential experiment design, where a no-regret algorithm is implemented. The proposed algorithm aims to learn the optimal material property for different printing settings. By fully utilizing the sensor data with innovative data analytics, the above-proposed methodologies are used to perform interdisciplinary research, promote technical innovations, and achieve balanced theoretical/practical advancements. In addition, these methodologies are inherently integrated into a generic framework. Thus, they can be easily extended to other manufacturing processes, systems, or even other application areas such as healthcare systems.
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    The CCP Selector: Scalable Algorithms for Sparse Ridge Regression from Chance-Constrained Programming
    Xie, Weijun; Deng, Xinwei (2018-06-11)
    Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades. This work focuses on sparse ridge regression, which considers the exact $L_0$ norm to pursue the sparsity. We pave out a theoretical foundation to understand why many existing approaches may not work well for this problem, in particular on large-scale datasets. Inspired by reformulating the problem as a chance-constrained program, we derive a novel mixed integer second order conic (MISOC) reformulation and prove that its continuous relaxation is equivalent to that of the convex integer formulation proposed in a recent work. Based upon these two formulations, we develop two new scalable algorithms, the greedy and randomized algorithms, for sparse ridge regression with desirable theoretical properties. The proposed algorithms are proved to yield near-optimal solutions under mild conditions. In the case of much larger dimensions, we propose to integrate the greedy algorithm with the randomized algorithm, which can greedily search the features from the nonzero subset identified by the continuous relaxation of the MISOC formulation. The merits of the proposed methods are elaborated through a set of numerical examples in comparison with several existing ones.
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    Clustered Discriminant Regression for High-Dimensional Data Feature Extraction and Its Applications in Healthcare and Additive Manufacturing
    Shen, Bo; Xie, Weijun; James Kong, Zhenyu (IEEE, 2021-10-01)
    The recent increase in applications of high-dimensional data poses a severe challenge to data analytics, such as supervised classification, particularly for online applications. To tackle this challenge, efficient and effective methods for feature extraction are critical to the performance of classification analysis. The objective of this work is to develop a new supervised feature extraction method for high-dimensional data. It is achieved by developing a clustered discriminant regression (CDR) to extract informative and discriminant features for high-dimensional data. In CDR, the variables are clustered into different groups or subspaces, within which feature extraction is performed separately. The CDR algorithm, which is a greedy approach, is implemented to obtain the solution toward optimal feature extraction. One numerical study is performed to demonstrate the performance of the proposed method for variable selection. Three case studies using healthcare and additive manufacturing data sets are accomplished to demonstrate the classification performance of the proposed methods for real-world applications. The results clearly show that the proposed method is superior over the existing method for high-dimensional data feature extraction. Note to Practitioners - This article forwards a new supervised feature extraction method termed clustered discriminant regression. This method is highly effective for classification analysis of high-dimensional data, such as images or videos, where the number of variables is much larger than the number of samples. In our case studies on healthcare and additive manufacturing, the performance of classification analysis based on our method is superior over the existing feature extraction methods, which is confirmed by using various popular classification algorithms. For image classification, our method with elaborately selected classification algorithms can outperform a convolutional neural network. In addition, the computation efficiency of the proposed method is also promising, which enables its online applications, such as advanced manufacturing process monitoring and control.
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    Coping Uncertainty in Wireless Network Optimization
    Li, Shaoran (Virginia Tech, 2022-10-24)
    Network optimization plays an important role in 5G/next-G networks, which requires knowledge of network parameters (e.g., channel state information). The majority of existing works assume that all network parameters are either given a prior or can be accurately estimated. However, in many practical scenarios, some parameters are uncertain at the time of allocating resources and can only be modeled by random variables. Further, we only have limited knowledge of those uncertain parameters. For instance, channel gains are not exactly known due to channel estimation errors, network delay, limited feedback, and a lack of cooperation (between networks). Therefore, a practical solution to network optimization must address such uncertainty inside wireless networks. There are three approaches to address such a network uncertainty: stochastic programming, worst-case optimization, and chance-constrained programming (CCP). Among the three, CCP has some unique benefits compared to the other two approaches. Stochastic programming explicitly requires full distribution knowledge, which is usually unavailable in practice. In comparison, CCP can work with various settings of available knowledge such as first and second order statistics, symmetric properties, or limited data samples. Therefore, CCP is more flexible to handle different network settings, which is important to address problems in 5G/next-G networks. Further, worst-case optimization assumes upper or lower bounds (i.e., worst cases) for the uncertain parameters and it is known to be conservative due to its focus on extreme cases. In contrast, CCP allows occasional and controllable violations for some constraints and thus offers much better performance in resource utilization compared to worst-case optimization. The only drawback of CCP is that it may lead to intractability due to its probabilistic formulation and limited knowledge of the underlying random variables. To date, CCP has not been well utilized in the wireless communication and networking community. The goal of this dissertation is to extend the state-of-the-art of CCP techniques and address a number of challenging network optimization problems. This dissertation is correspondingly organized into two parts. In the first part, we assume the uncertain parameters are only known by their mean and covariance (without distribution knowledge). We assume these statistics are rather stationary (i.e., time-invariant for a sufficiently long time) and thus can be accurately estimated. In this setting, we introduce a novel reformulation technique based on the mean and covariance to derive a solution. In the second part, we assume these statistics are time-varying and thus cannot be accurately estimated.In this setting, we employ limited data samples that are collected in a small time window and use them to derive a solution. For the first part, we investigate four research problems based on the mean and covariance of the uncertain parameters: - In the first problem, we study how to maximize spectrum efficiency in underlay coexistence.The interference from all secondary users to each primary user must be kept below a given threshold. However, there is much uncertainty about the channel gains between the primary users and the second users due to a lack of cooperation between them. We formulate probabilistic interference constraints using CCP for the primary users. For tractability, we introduce a novel and powerful reformulation technique called Exact Conic Reformulation (ECR). With limited knowledge of mean and covariance, ECR offers an equivalent reformulation for the intractable chance constraints with tractable deterministic constraints without relaxation errors. After reformulation, we employ linearization techniques to the mixed-integer non-linear problem to reduce the computation complexity. We show that our proposed approach can achieve near-optimal performance and stands as a performance benchmark for the underlay coexistence problem. - To find a solution for the same underlay coexistence problem that can be used in the real world, we need to find a solution in "real-time". The real-time requirement here refers to finding a solution in 125 us (the minimum time slot for small cells in 5G). Our proposed solution has three steps. First, it employs ECR to reformulate the original CCP into a deterministic optimization problem. Then it decomposes the problem and narrows down the search space into a smaller but promising one. By random sampling inside the promising search space and through local search, our proposed solution can meet the 125 us requirement in 5G while achieving 90% optimality on average. - We further apply CCP, predicated on the reformulation technique ECR, to two other problems. * We study the problem of power control in concurrent transmissions. Our objective is to maximize energy efficiency for all transmitter-receiver pairs with capacity requirements. This problem is challenging due to mutual interference among different transmitter-receiver pairs and the uncertain channel gain between any transmitter and receiver. We formulate a CCP and reformulate it into a deterministic problem using ECR. Then we employ Geometric Programming (GP) with a tight approximation to derive a near-optimal solution. * We study task offloading in Mobile Edge Computing (MEC) where the number of processing cycles of a task is unknown until completion. The goal is to minimize the energy consumption of the users while meeting probabilistic deadlines for the tasks. We formulate the probabilistic deadlines into chance constraints and then use ECR to reformulate them into deterministic constraints. We propose a solution that consists of periodic scheduling and schedule updates to choose the offloaded tasks and task-to-processor assignments at the base station. In the second part, we investigate two research problems based on limited data samples of the uncertain parameters: - We study MU-MIMO beamforming based on Channel State Information (CSI). The goal is to derive a beamforming solution---minimizing power consumption at the BS while meeting the probabilistic data rate requirements of the users---by using very limited CSI data samples. For our CCP formulation, we explore the idea of Wasserstein ambiguity set to quantify the distance between the true (but unknown) distribution and the empirical distribution based on the limited data samples. Our proposed solution---Data-Driven Beamforming (D^2BF)---reformulates the CCP into a non-convex deterministic optimization problem based on the properties of Wasserstein ambiguity set. Then D^2BF employs a novel convex approximation to the non-convex deterministic problem, which can be directly solved by commercial solvers. - For a solution to the MU-MIMO beamforming to be useful in the real world, it must meet the "real-time" requirement. Here, the real-time requirement refers to 1 ms, which is one transmission time interval (TTI) under 5G numerology 0. We present ReDBeam---a Real-time Data-driven Beamforming solution for the MU-MIMO beamforming problem (minimizing power consumption while offering probabilistic data rate guarantees to the users) with limited CSI data samples. RedBeam is a parallel algorithm and is purposefully designed to take advantage of the vast parallel processing capability offered by GPU. ReDBeam generates a large number of initial solutions from a promising search space and then refines each solution by a local search. We show that ReDBeam meets the 1 ms real-time requirement on a commercial GPU and is orders of magnitude faster than other state-of-the-art algorithms for the same problem.
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    Efficient Prevalence Estimation for Emerging and Seasonal Diseases Under Limited Resources
    Nguyen, Ngoc Thu (Virginia Tech, 2019-05-30)
    Estimating the prevalence rate of a disease is crucial for controlling its spread, and for planning of healthcare services. Due to limited testing budgets and resources, prevalence estimation typically entails pooled, or group, testing where specimens (e.g., blood, urine, tissue swabs) from a number of subjects are combined into a testing pool, which is then tested via a single test. Testing outcomes from multiple pools are analyzed so as to assess the prevalence of the disease. The accuracy of prevalence estimation relies on the testing pool design, i.e., the number of pools to test and the pool sizes (the number of specimens to combine in a pool). Determining an optimal pool design for prevalence estimation can be challenging, as it requires prior information on the current status of the disease, which can be highly unreliable, or simply unavailable, especially for emerging and/or seasonal diseases. We develop and study frameworks for prevalence estimation, under highly unreliable prior information on the disease and limited testing budgets. Embedded into each estimation framework is an optimization model that determines the optimal testing pool design, considering the trade-off between testing cost and estimation accuracy. We establish important structural properties of optimal testing pool designs in various settings, and develop efficient and exact algorithms. Our numerous case studies, ranging from prevalence estimation of the human immunodeficiency virus (HIV) in various parts of Africa, to prevalence estimation of diseases in plants and insects, including the Tomato Spotted Wilt virus in thrips and West Nile virus in mosquitoes, indicate that the proposed estimation methods substantially outperform current approaches developed in the literature, and produce robust testing pool designs that can hedge against the uncertainty in model inputs.Our research findings indicate that the proposed prevalence estimation frameworks are capable of producing accurate prevalence estimates, and are highly desirable, especially for emerging and/or seasonal diseases under limited testing budgets.
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    Electric Field Grading and Electrical Insulation Design for High Voltage,  High Power Density Wide Bandgap Power Modules
    Mesgarpour Tousi, Maryam (Virginia Tech, 2020-10-19)
    The trend towards more and all-electric apparatuses and more electrification will lead to higher electrical demand. Increases in electrical power demand can be provided by either higher currents or higher voltages. Due to "weight" and "voltage" drop, a raise in the current is not preferred; so, "higher voltages" are being considered. Another trend is to reduce the size and weight of apparatuses. Combined, these two trends result in the high voltage, high power density concept. It is expected that by 2030, 80% of all electric power will flow through "power electronics systems". In regards to the high voltage, high power density concept described above, "wide bandgap (WBG) power modules" made from materials such as "SiC and GaN (and, soon, Ga2O3 and diamond)", which can endure "higher voltages" and "currents" rather than "Si-based modules", are considered to be the most promising solution to reducing the size and weight of "power conversion systems". In addition to the trend towards higher "blocking voltage", volume reduction has been targeted for WBG devices. The blocking voltage is the breakdown voltage capability of the device, and volume reduction translates into power density increase. This leads to extremely high electric field stress, E, of extremely nonuniform type within the module, leading to a higher possibility of "partial discharge (PD)" and, in turn, insulation degradation and, eventually, breakdown of the module. Unless the discussed high E issue is satisfactorily addressed and solved, realizing next-generation high power density WBG power modules that can properly operate will not be possible. Contributions and innovations of this Ph.D. work are as follows. i) Novel electric field grading techniques including (a) various geometrical techniques, (b) applying "nonlinear field-dependent conductivity (FDC) materials" to high E regions, and (c) combination of (a) and (b), are developed; ii) A criterion for the electric stress intensity based upon accurate dimensions of a power device package and its "PD measurement" is presented; iii) Guidelines for the electrical insulation design of next-generation high voltage (up to 30 kV), high power density "WBG power modules" as both the "one-minute insulation" and PD tests according to the standard IEC 61287-1 are introduced; iv) Influence of temperature up to 250°C and frequency up to 1 MHz on E distribution and electric field grading methods mentioned in i) is studied; and v) A coupled thermal and electrical (electrothermal) model is developed to obtain thermal distribution within the module precisely. All models and simulations are developed and carried out in COMSOL Multiphysics.
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    Embeddings for Disjunctive Programs with Applications to Political Districting and Rectangle Packing
    Fravel III, William James (Virginia Tech, 2024-11-08)
    This dissertations represents a composite of three papers which have been submitted for publication: The first chapter deals with a non-convex knapsack which is inspired by a simplified political districting problem. We present and derive a constant time solution to the problem via a reduced-dimensional reformulation, the Karash-Kuhn-Tucker optimality conditions, and gradient descent. The second chapter covers a more complete form of the political districting problem. We attempt to overcome the non-convex objective function and combinatorially massive solution space through a variety of linearization techniques and cutting planes. Our focus on dual bounds is novel in the space. The final chapter develops a framework for identifying ideal mixed binary linear programs and applies it to several rectangle packing formulations. These include both existing and novel formulations for the underlying disjunctive program. Additionally, we investigate the poor performance of branch-and-cut on the example problems.
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    Fair and Risk-Averse Resource Allocation in Transportation Systems under Uncertainties
    Sun, Luying (Virginia Tech, 2023-07-11)
    Addressing fairness among users and risk mitigation in the context of resource allocation in transportation systems under uncertainties poses a crucial challenge yet to be satisfactorily resolved. This dissertation attempts to address this challenge, focusing on achieving a balance between system-wide efficiency and individual fairness in stochastic transportation resource allocation problems. To study complicated fair and risk-averse resource allocation problems - from public transit to urban air mobility and multi-stage infrastructure maintenance - we develop three models: DrFRAM, FairUAM, and FCMDP. Each of these models, despite being proven NP-hard even in a simplistic case, inspires us to develop efficient solution algorithms. We derive mixed-integer linear programming (MILP) formulations for these models, leveraging the unique properties of each model and linearizing non-linear terms. Additionally, we strengthen these models with valid inequalities. To efficiently solve these models, we design exact algorithms and approximation algorithms capable of obtaining near-optimal solutions. We numerically validate the effectiveness of our proposed models and demonstrate their capability to be applied to real-world case studies to adeptly address the uncertainties and risks arising from transportation systems. This dissertation provides a foundational platform for future inquiries of risk-averse resource allocation strategies under uncertainties for more efficient, equitable, and resilient decision-making. Our adaptable framework can address a variety of transportation-related challenges and can be extended beyond the transportation domain to tackle resource allocation problems in a broader setting.
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    Load Learning and Topology Optimization for Power Networks
    Bhela, Siddharth (Virginia Tech, 2019-06-21)
    With the advent of distributed energy resources (DERs), electric vehicles, and demand-response programs, grid operators are in dire need of new monitoring and design tools that help improve efficiency, reliability, and stability of modern power networks. To this end, the work in this thesis explores a generalized modeling and analysis framework for two pertinent tasks: i) learning loads via grid probing, and; ii) optimizing power grid topologies for stability. Distribution grids currently lack comprehensive real-time metering. Nevertheless, grid operators require precise knowledge of loads and renewable generation to accomplish any feeder optimization task. At the same time, new grid technologies, such as solar panels and energy storage units are interfaced via inverters with advanced sensing and actuation capabilities. In this context, we first put forth the idea of engaging power electronics to probe an electric grid and record its voltage response at actuated and metered buses to infer non-metered loads. Probing can be accomplished by commanding inverters to momentarily perturb their power injections. Multiple probing actions can be induced within a few tens of seconds. Load inference via grid probing is formulated as an implicit nonlinear system identification task, which is shown to be topologically observable under certain conditions. The analysis holds for single- and multi-phase grids, radial or meshed, and applies to phasor or magnitude-only voltage data. Using probing to learn non-constant-power loads is also analyzed as a special case. Once a probing setup is deemed topologically observable, a methodology for designing probing injections abiding by inverter and network constraints to improve load estimates is provided. The probing task under noisy phasor and non-phasor data is tackled using a semidefinite-program relaxation. As a second contribution, we also study the effect of topology on the linear time-invariant dynamics of power networks. For a variety of stability metrics, a unified framework based on the H2-norm of the system is presented. The proposed framework assesses the robustness of power grids to small disturbances and is used to study the optimal placement of new lines on existing networks as well as the design of radial topologies for new networks.
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    Machine Learning-Based Receiver in Multiple Input Multiple Output Communications Systems
    Zhou, Zhou (Virginia Tech, 2021-08-10)
    Bridging machine learning technologies to multiple-input-multiple-output (MIMO) communications systems is a primary driving force for next-generation wireless systems. This dissertation introduces a variety of neural network structures for symbol detection/equalization tasks in MIMO systems configured with two different waveforms, orthogonal frequency-division multiplexing (OFDM) and orthogonal time frequency and space (OTFS). The former one is the major air interface in current cellular systems. The latter one is developed to handle high mobility. For the sake of real-time processing, the introduced neural network structures are incorporated with inductive biases of wireless communications signals and operate in an online training manner. The utilized inductive priors include the shifting invariant property of quadrature amplitude modulation, the time-frequency relation inherent in OFDM signals, the multi-mode feature of massive antennas, and the delay-Doppler representation of doubly selective channel. In addition, the neural network structures are rooted in reservoir computing - an efficient neural network computational framework with decent generalization performance for limited training datasets. Therefore, the resulting neural network structures can learn beyond observation and offer decent transmission reliability in the low signal-to-noise ratio (SNR) regime. This dissertation includes comprehensive simulation results to justify the effectiveness of the introduced NN architectures compared with conventional model-based approaches and alternative neural network structures.
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    Real-Time Resource Optimization for Wireless Networks
    Huang, Yan (Virginia Tech, 2021-01-11)
    Resource allocation in modern wireless networks is constrained by increasingly stringent real-time requirements. Such real-time requirements typically come from, among others, the short coherence time on a wireless channel, the small time resolution for resource allocation in OFDM-based radio frame structure, or the low-latency requirements from delay-sensitive applications. An optimal resource allocation solution is useful only if it can be determined and applied to the network entities within its expected time. For today's wireless networks such as 5G NR, such expected time (or real-time requirement) can be as low as 1 ms or even 100 μs. Most of the existing resource optimization solutions to wireless networks do not explicitly take real-time requirement as a constraint when developing solutions. In fact, the mainstream of research works relies on the asymptotic complexity analysis for designing solution algorithms. Asymptotic complexity analysis is only concerned with the growth of its computational complexity as the input size increases (as in the big-O notation). It cannot capture the real-time requirement that is measured in wall-clock time. As a result, existing approaches such as exact or approximate optimization techniques from operations research are usually not useful in wireless networks in the field. Similarly, many problem-specific heuristic solutions with polynomial-time asymptotic complexities may suffer from a similar fate, if their complexities are not tested in actual wall-clock time. To address the limitations of existing approaches, this dissertation presents novel real- time solution designs to two types of optimization problems in wireless networks: i) problems that have closed-form mathematical models, and ii) problems that cannot be modeled in closed-form. For the first type of problems, we propose a novel approach that consists of (i) problem decomposition, which breaks an original optimization problem into a large number of small and independent sub-problems, (ii) search intensification, which identifies the most promising problem sub-space and selects a small set of sub-problems to match the available GPU processing cores, and (iii) GPU-based large-scale parallel processing, which solves the selected sub-problems in parallel and finds a near-optimal solution to the original problem. The efficacy of this approach has been illustrated by our solutions to the following two problems. • Real-Time Scheduling to Achieve Fair LTE/Wi-Fi Coexistence: We investigate a resource optimization problem for the fair coexistence between LTE and Wi-Fi in the unlicensed spectrum. The real-time requirement for finding the optimal channel division and LTE resource allocation solution is on 1 ms time scale. This problem involves the optimal division of transmission time for LTE and Wi-Fi across multi- ple unlicensed bands, and the resource allocation among LTE users within the LTE's "ON" periods. We formulate this optimization problem as a mixed-integer linear pro- gram and prove its NP-hardness. Then by exploiting the unique problem structure, we propose a real-time solution design that is based on problem decomposition and GPU-based parallel processing techniques. Results from an implementation on the NVIDIA GPU/CUDA platform demonstrate that the proposed solution can achieve near-optimal objective and meet the 1 ms timing requirement in 4G LTE. • An Ultrafast GPU-based Proportional Fair Scheduler for 5G NR: We study the popular proportional-fair (PF) scheduling problem in a 5G NR environment. The real-time requirement for determining the optimal (with respect to the PF objective) resource allocation and MCS selection solution is 125 μs (under 5G numerology 3). In this problem, we need to allocate frequency-time resource blocks on an operating channel and assign modulation and coding scheme (MCS) for each active user in the cell. We present GPF+ — a GPU based real-time PF scheduler. With GPF+, the original PF optimization problem is decomposed into a large number of small and in- dependent sub-problems. We then employ a cross-entropy based search intensification technique to identify the most promising problem sub-space and select a small set of sub-problems to fit into a GPU. After solving the selected sub-problems in parallel using GPU cores, we find the best sub-problem solution and use it as the final scheduling solution. Evaluation results show that GPF+ is able to provide near-optimal PF performance in a 5G cell while meeting the 125 μs real-time requirement. For the second type of problems, where there is no closed-form mathematical formulation, we propose to employ model-free deep learning (DL) or deep reinforcement learning (DRL) techniques along with judicious consideration of timing requirement throughout the design. Under DL/DRL, we employ deep function approximators (neural networks) to learn the unknown objective function of an optimization problem, approximate an optimal algorithm to find resource allocation solutions, or discover important mapping functions related to the resource optimization. To meet the real-time requirement, we propose to augment DL or DRL methods with optimization techniques at the input or output of the deep function approximators to reduce their complexities and computational time. Under this approach, we study the following two problems: • A DRL-based Approach to Dynamic eMBB/URLLC Multiplexing in 5G NR: We study the problem of dynamic multiplexing of eMBB and URLLC on the same channel through preemptive resource puncturing. The real-time requirement for determining the optimal URLLC puncturing solution is 1 ms (under 5G numerology 0). A major challenge in solving this problem is that it cannot be modeled using closed-form mathematical expressions. To address this issue, we develop a model-free DRL approach which employs a deep neural network to learn an optimal algorithm to allocate the URLLC puncturing over the operating channel, with the objective of minimizing the adverse impact from URLLC traffic on eMBB. Our contributions include a novel learning method that exploits the intrinsic properties of the URLLC puncturing optimization problem to achieve a fast and stable learning convergence, and a mechanism to ensure feasibility of the deep neural network's output puncturing solution. Experimental results demonstrate that our DRL-based solution significantly outperforms state-of-the-art algorithms proposed in the literature and meets the 1 ms real-time requirement for dynamic multiplexing. • A DL-based Link Adaptation for eMBB/URLLC Multiplexing in 5G NR: We investigate MCS selection for eMBB traffic under the impact of URLLC preemptive puncturing. The real-time requirement for determining the optimal MCSs for all eMBB transmissions scheduled in a transmission interval is 125 μs (under 5G numerology 3). The objective is to have eMBB meet a given block-error rate (BLER) target under the adverse impact of URLLC puncturing. Since this problem cannot be mathematically modeled in closed-form, we proposed a DL-based solution design that uses a deep neural network to learn and predict the BLERs of a transmission under each MCS level. Then based on the BLER predictions, an optimal MCS can be found for each transmission that can achieve the BLER target. To meet the 5G real-time requirement, we implement this design through a hybrid CPU and GPU architecture to minimize the execution time. Extensive experimental results show that our design can select optimal MCS under the impact of preemptive puncturing and meet the 125 μs timing requirement.
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    Regret in the Newsvendor Model with Demand and Yield Randomness
    Chen, Zhi; Xie, Weijun (Wiley, 2021-07-28)
    We study the fundamental stochastic newsvendor model that considers both demand and yield randomness. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data-driven distributionally robust optimization approach to hedge against all distributions that are sufficiently close to a uniform and discrete distribution of empirical data, where closeness is measured by the type-∞ Wasserstein distance. We adopt the minimax regret decision criterion to assess the optimal order quantity that minimizes the worst-case regret. Several properties about the minimax regret model, including optimality condition, regret bound, and the worst-case distribution, are presented. The optimal order quantity can be determined via an efficient golden section search. We extend the analysis to the Hurwicz criterion model, which generalizes the popular albeit pessimistic maximin model (maximizing the worst-case expected profit) and its (less noticeable) more optimistic counterpart—the maximax model (maximizing the best-case expected profit). Finally, we present numerical comparisons of our data-driven minimax regret model with data-driven models based on the Hurwicz criterion and with a minimax regret model based on partial statistical information on moments.
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    Robust and Equitable Public Health Screening Strategies, with Application to Genetic and Infectious Diseases
    El Hajj, Hussein Mohammad (Virginia Tech, 2021-06-07)
    Public health screening plays an important role in the overall healthcare system. As an example, consider newborn screening, a state-level initiative that screens newborns for life-threatening genetic disorders for which early treatment can substantially improve health outcomes. Another topical example is in the realm of infectious disease screening, e.g., screening for COVID-19. The common features of both public health screening problems include large testing populations and resource limitations that inhibit screening efforts. Cost is a major barrier to the inclusion of genetic disorders in newborn screening, and thus screening must be both highly accurate and efficient; and for COVID-19, limited testing kits, and other shortages, have been major barriers to screening efforts. Further, for both newborn screening and infectious disease screening, equity (reducing health disparities among different sub-populations) is an important consideration. We study the testing process design for newborn screening for genetic diseases, considering cystic fibrosis as a model disorder. Our optimization-based models take into account disease-related parameters, subject risk factors, test characteristics, parameter uncertainty, and limited testing resources so as to design equitable, accurate, and robust screening processes that classify newborns as positive or negative for cystic fibrosis. Our models explicitly consider the trade-off between false-negatives, which lead to missed diagnoses, and the required testing resources; and the trade-off between the accuracy and equity of screening. We also study the testing process design for infectious disease screening, considering COVID-19 as a model disease. Our optimization-based models account for key subject risk factors that are important to consider, including the likelihood of being disease-positive, and the potential harm that could be averted through testing and the subsequent interventions. Our objectives include the minimization of harm (through detection and mitigation) or maximization of testing coverage. These are complex problems. We develop novel mathematical models and characterize key structural properties of optimal solutions. This, in turn, allows the development of effective and efficient algorithms that exploit these structural properties. These algorithms are either polynomial- or pseudo-polynomial-time algorithms, and are able to solve realistic-sized problems efficiently. Our case studies on cystic fibrosis screening and COVID-19 screening, based on realistic data, underscore the value of the proposed optimization-based approaches for public health screening, compared to current practices. Our findings have important implications for public policy.
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    Robust multi-product newsvendor model with uncertain demand and substitution
    Zhang, Jie; Xie, Weijun; Sarin, Subhash C. (Elsevier, 2021-08-16)
    This work studies a Robust Multi-product Newsvendor Model with Substitution (R-MNMS), where the demand and the substitution rates are stochastic and are subject to cardinality-constrained uncertainty sets. The goal of this work is to determine the optimal order quantities of multiple products to maximize the worst-case total profit. To achieve this, we first show that for given order quantities, computing the worst-case total profit, in general, is NP-hard. Therefore, we derive the closed-form optimal solutions for the following three special cases: (1) if there are only two products, (2) if there is no substitution among different products, and (3) if the budget of demand uncertainty is equal to the number of products. For a general R-MNMS, we formulate it as a mixed-integer linear program with an exponential number of constraints and develop a branch and cut algorithm to solve it. For large-scale problem instances, we further propose a conservative approximation of R-MNMS and prove that under some certain conditions, this conservative approximation yields an exact optimal solution to R-MNMS. The numerical study demonstrates the effectiveness of the proposed approaches and the robustness of our model.
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    Stochastic Programming Approaches to Multi-product Inventory Management Problems with Substitution
    Zhang, Jie (Virginia Tech, 2019-10-29)
    The presence of substitution among multiple similar products plays an important role in inventory management. It has been observed in the literature that incorporating the impact of substitution among products can substantially improve the profit and reduce the understock or overstock risk. This thesis focuses on exploring and exploiting the impact of substitution on inventory management problems by theoretically analyzing mathematical models and developing efficient solution approaches. To that end, we address four problems. In the first problem, we study different pricing strategies and the role of substitution for new and remanufactured products. Our work presents a two-stage model for an original equipment manufacturer (OEM) in this regard. A closed-form one-to-one mapping of product designs onto the optimal product strategies is developed, which provides useful information for the retailer. Our second problem is a multi-product newsvendor problem with customer-driven demand substitution. We completely characterize the optimal order policy when the demand is known and reformulate this nonconvex problem as a binary quadratic program. When the demand is stochastic, we formulate the problem as a two-stage stochastic program with mixed integer recourse, derive several necessary optimality conditions, prove the submodularity of the profit function, develop polynomial-time approximation algorithms, and show their performance guarantees. Our numerical investigation demonstrates the effectiveness of the proposed algorithms and, furthermore, reveals several useful findings and managerial insights. In the third problem, we study a robust multi-product newsvendor model with substitution (R-MNMS), where both demand and substitution rates are uncertain and are subject to cardinality-constrained uncertainty set. We show that for given order quantities, computing the worst-case total profit, in general, is NP-hard, and therefore, address three special cases for which we provide closed-form solutions. In practice, placing an order might incur a fixed cost. Motivated by this fact, our fourth problem extends the R-MNMS by incorporating fixed cost (denoted as R-MNMSF) and develop efficient approaches for its solution. In particular, we propose an exact branch-and-cut algorithm to solve small- or medium-sized problem instances of the R-MNMSF, and for large-scale problem instances, we develop an approximation algorithm. We further study the effects of the fixed cost and show how to tune the parameters of the uncertainty set.