On Degeneracy Issues in Multi-parametric Programming and Critical Region Exploration based Distributed Optimization in Smart Grid Operations

Improving renewable energy resource utilization efficiency is crucial to reducing carbon emissions, and multi-parametric programming has provided a systematic perspective in conducting analysis and optimization toward this goal in smart grid operations. This paper focuses on two aspects of interest related to multi-parametric linear/quadratic programming (mpLP/QP). First, we study degeneracy issues of mpLP/QP. A novel approach to deal with degeneracies is proposed to find all critical regions containing the given parameter. Our method leverages properties of the multi-parametric linear complementary problem, vertex searching technique, and complementary basis enumeration. Second, an improved critical region exploration (CRE) method to solve distributed LP/QP is proposed under a general mpLP/QP-based formulation. The improved CRE incorporates the proposed approach to handle degeneracies. A cutting plane update and an adaptive stepsize scheme are also integrated to accelerate convergence under different problem settings. The computational efficiency is verified on multi-area tie-line scheduling problems with various testing benchmarks and initial states

Advancing Multiparametric Programming for Model Predictive Control

Model predictive control provides the optimal operation for chemical processes by explicitly accounting for the system, constraints, and costs. In an online setting, developing the implicit optimal control action under time consideration is non-trivial. Over a decade ago, it was demonstrated through multiparametric programming that the implicit control law defining the model predictive controller can be determined explicitly, once and offline. The benefit of such an approach is the (i) improved online computational time, (ii) the development of the offline map of solution \textit{a priori}, and (iii) the derivation of the optimal control laws under any state variation. In recent years there has been a significant push for the development of novel algorithms and theoretical advancements for multiparametric model predictive control. These algorithms and theoretical underpinnings have expanded the problem classes that are solvable and improved the computational efficiency. However, there is still a need to provide analysis for formulations based on different surrogate models, and to tackle large scale multiparametric model predictive control problems. In this dissertation, the research focus is (i) the inclusion of a new surrogate modeling technique from the machine learning community, (ii) developing a criterion to compare multiparametric model predictive control formulations based on different surrogate models, (iii) the development of an algorithm to solve large scale multiparametric optimization problems, and (iv) improving the online computational performance of online solvers via multiparametric programming. To this end, tools from data science, computational geometry, and the operations research community contributed greatly to the results presented in this work. This research is verified via the optimal operation of chemical engineering processes and the efficacy of the developed algorithms is demonstrated on computational studies

When Deep Learning Meets Polyhedral Theory: A Survey

In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure of neural networks converged back to simpler representations based on piecewise constant and piecewise linear functions such as the Rectified Linear Unit (ReLU), which became the most commonly used type of activation function in neural networks. That made certain types of network structure \unicode{x2014}such as the typical fully-connected feedforward neural network\unicode{x2014} amenable to analysis through polyhedral theory and to the application of methodologies such as Linear Programming (LP) and Mixed-Integer Linear Programming (MILP) for a variety of purposes. In this paper, we survey the main topics emerging from this fast-paced area of work, which bring a fresh perspective to understanding neural networks in more detail as well as to applying linear optimization techniques to train, verify, and reduce the size of such networks

Novel Semi-Supervised Learning Models to Balance Data Inclusivity and Usability in Healthcare Applications

abstract: Semi-supervised learning (SSL) is sub-field of statistical machine learning that is useful for problems that involve having only a few labeled instances with predictor (X) and target (Y) information, and abundance of unlabeled instances that only have predictor (X) information. SSL harnesses the target information available in the limited labeled data, as well as the information in the abundant unlabeled data to build strong predictive models. However, not all the included information is useful. For example, some features may correspond to noise and including them will hurt the predictive model performance. Additionally, some instances may not be as relevant to model building and their inclusion will increase training time and potentially hurt the model performance. The objective of this research is to develop novel SSL models to balance data inclusivity and usability. My dissertation research focuses on applications of SSL in healthcare, driven by problems in brain cancer radiomics, migraine imaging, and Parkinson’s Disease telemonitoring. The first topic introduces an integration of machine learning (ML) and a mechanistic model (PI) to develop an SSL model applied to predicting cell density of glioblastoma brain cancer using multi-parametric medical images. The proposed ML-PI hybrid model integrates imaging information from unbiopsied regions of the brain as well as underlying biological knowledge from the mechanistic model to predict spatial tumor density in the brain. The second topic develops a multi-modality imaging-based diagnostic decision support system (MMI-DDS). MMI-DDS consists of modality-wise principal components analysis to incorporate imaging features at different aggregation levels (e.g., voxel-wise, connectivity-based, etc.), a constrained particle swarm optimization (cPSO) feature selection algorithm, and a clinical utility engine that utilizes inverse operators on chosen principal components for white-box classification models. The final topic develops a new SSL regression model with integrated feature and instance selection called s2SSL (with “s2” referring to selection in two different ways: feature and instance). s2SSL integrates cPSO feature selection and graph-based instance selection to simultaneously choose the optimal features and instances and build accurate models for continuous prediction. s2SSL was applied to smartphone-based telemonitoring of Parkinson’s Disease patients.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

Research in Structures, Structural Dynamics and Materials, 1990

The Structural Dynamics and Materials (SDM) Conference was held on April 2 to 4, 1990 in Long Beach, California. This publication is a compilation of presentations of the work-in-progress sessions and does not contain papers from the regular sessions since those papers are published by AIAA in the conference proceedings

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform

Quantitative Techniques in Participatory Forest Management

Forest management has evolved from a mercantilist view to a multi-functional one that integrates economic, social, and ecological aspects. However, the issue of sustainability is not yet resolved. Quantitative Techniques in Participatory Forest Management brings together global research in three areas of application: inventory of the forest variables that determine the main environmental indices, description and design of new environmental indices, and the application of sustainability indices for regional implementations. All these quantitative techniques create the basis for the development of scientific methodologies of participatory sustainable forest management