Vehicle Routing Problems that Minimize the Completion Time: Heuristics, Worst-Case Analyses, and Computational Results

In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants of the VRP that minimize the completion time, i.e., we minimize the distance of the longest route. We call it the min-max objective function. In applications such as disaster relief efforts and military operations, the objective is often to finish the delivery or the task as soon as possible, not to plan routes with the minimum total distance. Even in commercial package delivery nowadays, companies are investing in new technologies to speed up delivery instead of focusing merely on the min-sum objective. In this dissertation, we compare the min-max and the standard (min-sum) objective functions in a worst-case analysis to show that the optimal solution with respect to one objective function can be very poor with respect to the other. The results motivate the design of algorithms specifically for the min-max objective. We study variants of min-max VRPs including one problem from the literature (the min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery Multi-Depot VRP with Minimum Service Requirement and the min-max Close-Enough VRP). We develop heuristics to solve these three problems. We compare the results produced by our heuristics to the best-known solutions in the literature and find that our algorithms are effective. In the case where benchmark instances are not available, we generate instances whose near-optimal solutions can be estimated based on geometry. We formulate the Vehicle Routing Problem with Drones and carry out a theoretical analysis to show the maximum benefit from using drones in addition to trucks to reduce delivery time. The speed-up ratio depends on the number of drones loaded onto one truck and the speed of the drone relative to the speed of the truck.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Energy Management of a Battery-Ultracapacitor Hybrid Energy Storage System in Electric Vehicles

Electric vehicle (EV) batteries tend to have accelerated degradation due to high peak power and harsh charging/discharging cycles during acceleration and deceleration periods, particularly in urban driving conditions. An oversized energy storage system (ESS) can meet the high power demands; however, it suffers from increased size, volume and cost. In order to reduce the overall ESS size and extend battery cycle life, a battery-ultracapacitor (UC) hybrid energy storage system (HESS) has been considered as an alternative solution. In this work, we investigate the optimized configuration, design, and energy management of a battery-UC HESS. One of the major challenges in a HESS is to design an energy management controller for real-time implementation that can yield good power split performance. We present the methodologies and solutions to this problem in a battery-UC HESS with a DC-DC converter interfacing with the UC and the battery. In particular, a multi-objective optimization problem is formulated to optimize the power split in order to prolong the battery lifetime and to reduce the HESS power losses. This optimization problem is numerically solved for standard drive cycle datasets using Dynamic Programming (DP). Trained using the DP optimal results, an effective real-time implementation of the optimal power split is realized based on Neural Network (NN). This proposed online energy management controller is applied to a midsize EV model with a 360V/34kWh battery pack and a 270V/203Wh UC pack. The proposed online energy management controller effectively splits the load demand with high power efficiency and also effectively reduces the battery peak current. More importantly, a 38V-385Wh battery and a 16V-2.06Wh UC HESS hardware prototype and a real-time experiment platform has been developed. The real-time experiment results have successfully validated the real-time implementation feasibility and effectiveness of the real-time controller design for the battery-UC HESS. A battery State-of-Health (SoH) estimation model is developed as a performance metric to evaluate the battery cycle life extension effect. It is estimated that the proposed online energy management controller can extend the battery cycle life by over 60%.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Integrating Architecture for a Live-Work Lifestyle

Urban centers all around the world are striving to re-orient themselves to promoting ideals of human engagement, flexibility, openness and synergy, that thoughtful architecture can provide. From a time when solitude in one’s own backyard was desirable, today’s outlook seeks more, to cater to the needs of diverse individuals and that of collaborators. This thesis is an investigation of the role of architecture in realizing how these ideals might be achieved, using Mixed Use Developments as the platform of space to test these designs ideas on. The author also investigates, identifies, and re-imagines how the idea of live-work excites and attracts users and occupants towards investing themselves in Mixed Used Developments (MUD’s), in urban cities. On the premise that MUDs historically began with an intention of urban revitalization, lying in the core of this spatial model, is the opportunity to investigate what makes mixing of uses an asset, especially in the eyes to today’s generation. Within the framework of reference to the current generation, i.e. the millennial population and alike, who have a lifestyle core that is urban-centric, the excitement for this topic is in the vision of MUD’s that will spatially cater to a variety in lifestyles, demographics, and functions, enabling its users to experience a vibrant 24/7 destination. Where cities are always in flux, the thesis will look to investigate the idea of opportunistic space, in a new MUD, that can also be perceived as an adaptive reuse of itself. The sustainability factor lies in the foresight of the transformative and responsive character of the different uses in the MUD at large, which provides the possibility to cater to a changing demand of building use over time. Delving into the architectural response, the thesis in the process explores, conflicts, tensions, and excitements, and the nature of relationships between different spatial layers of permanence vs. transformative, public vs. private, commercial vs. residential, in such an MUD. At a larger scale, investigations elude into the formal meaning and implications of the proposed type of MUD’s and the larger landscapes in which they are situated, with attempts to blur the fine line between architecture and urbanism. A unique character of MUD’s is the power it has to draw in people at the ground level and lead them into exciting spatial experiences. While the thesis stemmed from a purely objective and theoretical standpoint, the author believes that it is only when context is played into the design thinking process, that true architecture may start to flourish. The unique The significance of this thesis lies on the premise that the author believes that this re-imagined MUD has immense opportunity to amplify human engagement with designed space, and in the belief that it will better enable fostering sustainable communities and in the process, enhance people’s lives.

Generating Discriminative Objective Proposals via Submodular Ranking

Object recognition has long been a core problem in computer vision. To improve object spatial support and speed up object localization for object recognition, generating high-quality category-independent object proposals as the input for object recognition system has drawn attention recently. Given an image, we generate a limited number of high-quality and category-independent object proposals in advance and used as inputs for many computer vision tasks. We present an efficient dictionary-based model for image classification task. We further extend the work to a discriminative dictionary learning method for tensor sparse coding. In the first part, a multi-scale greedy-based object proposal generation approach is presented. Based on the multi-scale nature of objects in images, our approach is built on top of a hierarchical segmentation. We first identify the representative and diverse exemplar clusters within each scale. Object proposals are obtained by selecting a subset from the multi-scale segment pool via maximizing a submodular objective function, which consists of a weighted coverage term, a single-scale diversity term and a multi-scale reward term. The weighted coverage term forces the selected set of object proposals to be representative and compact; the single-scale diversity term encourages choosing segments from different exemplar clusters so that they will cover as many object patterns as possible; the multi-scale reward term encourages the selected proposals to be discriminative and selected from multiple layers generated by the hierarchical image segmentation. The experimental results on the Berkeley Segmentation Dataset and PASCAL VOC2012 segmentation dataset demonstrate the accuracy and efficiency of our object proposal model. Additionally, we validate our object proposals in simultaneous segmentation and detection and outperform the state-of-art performance. To classify the object in the image, we design a discriminative, structural low-rank framework for image classification. We use a supervised learning method to construct a discriminative and reconstructive dictionary. By introducing an ideal regularization term, we perform low-rank matrix recovery for contaminated training data from all categories simultaneously without losing structural information. A discriminative low-rank representation for images with respect to the constructed dictionary is obtained. With semantic structure information and strong identification capability, this representation is good for classification tasks even using a simple linear multi-classifier.