Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters

Thesis (Ph.D.)--University of Washington, 2016-08

Differential Evolution: A Tool for Global Optimization

This report describes a tool for global optimization that implements the Differential Evolution optimization algorithm as a new Excel add-in. The tool takes a step beyond Excel’s Solver add-in, because Solver often returns a local minimum, that is, a minimum that is less than or equal to nearby points, while Differential Evolution solves for the global minimum, which includes all feasible points. Despite complex underlying mathematics, the tool is relatively easy to use, and can be applied to practical optimization problems, such as establishing pricing and awards in a hotel loyalty program. The report demonstrates an example of how to develop an optimum approach to that problem.

Problems of optimal transportation on the circle and their mechanical applications

We consider a mechanical problem concerning a 2D axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry. The body moves through a medium of non-interacting particles at rest, and collisions of particles with the body's boundary are perfectly elastic (billiard-like). The body has a blunt nose: a line segment orthogonal to the symmetry axis. It is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance. This problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transfer problem on the circle with the transportation cost being the squared Euclidean distance. We find the exact solution for this problem when the amplitude of rotation is smaller than a fixed critical value, and give a numerical solution otherwise. As a by-product, we get explicit description of the solution for a class of optimal transfer problems on the circle.

Optimization of the Ion Source-Mass Spectrometry Parameters in Non-Steroidal Anti-Inflammatory and Analgesic Pharmaceuticals Analysis by a Design of Experiments Approach

The flow rates of drying and nebulizing gas, heat block and desolvation line temperatures and interface voltage are potential electrospray ionization parameters as they may enhance sensitivity of the mass spectrometer. The conditions that give higher sensitivity of 13 pharmaceuticals were explored. First, Plackett-Burman design was implemented to screen significant factors, and it was concluded that interface voltage and nebulizing gas flow were the only factors that influence the intensity signal for all pharmaceuticals. This fractionated factorial design was projected to set a full 2(2) factorial design with center points. The lack-of-fit test proved to be significant. Then, a central composite face-centered design was conducted. Finally, a stepwise multiple linear regression and subsequently an optimization problem solving were carried out. Two main drug clusters were found concerning the signal intensities of all runs of the augmented factorial design. p-Aminophenol, salicylic acid, and nimesulide constitute one cluster as a result of showing much higher sensitivity than the remaining drugs. The other cluster is more homogeneous with some sub-clusters comprising one pharmaceutical and its respective metabolite. It was observed that instrumental signal increased when both significant factors increased with maximum signal occurring when both codified factors are set at level +1. It was also found that, for most of the pharmaceuticals, interface voltage influences the intensity of the instrument more than the nebulizing gas flowrate. The only exceptions refer to nimesulide where the relative importance of the factors is reversed and still salicylic acid where both factors equally influence the instrumental signal. Graphical Abstract ᅟ.

Combination of Evolutionary Algorithms with Experimental Design, Traditional Optimization and Machine Learning

Evolutionary algorithms alone cannot solve optimization problems very efficiently since there are many random (not very rational) decisions in these algorithms. Combination of evolutionary algorithms and other techniques have been proven to be an efficient optimization methodology. In this talk, I will explain the basic ideas of our three algorithms along this line (1): Orthogonal genetic algorithm which treats crossover/mutation as an experimental design problem, (2) Multiobjective evolutionary algorithm based on decomposition (MOEA/D) which uses decomposition techniques from traditional mathematical programming in multiobjective optimization evolutionary algorithm, and (3) Regular model based multiobjective estimation of distribution algorithms (RM-MEDA) which uses the regular property and machine learning methods for improving multiobjective evolutionary algorithms.

JOINT ENERGY BEAMFORMING AND TIME ASSIGNMENT FOR COOPERATIVE WIRELESS POWERED NETWORKS

Wireless power transfer (WPT) and radio frequency (RF)-based energy har- vesting arouses a new wireless network paradigm termed as wireless powered com- munication network (WPCN), where some energy-constrained nodes are enabled to harvest energy from the RF signals transferred by other energy-sufficient nodes to support the communication operations in the network, which brings a promising approach for future energy-constrained wireless network design. In this paper, we focus on the optimal WPCN design. We consider a net- work composed of two communication groups, where the first group has sufficient power supply but no available bandwidth, and the second group has licensed band- width but very limited power to perform required information transmission. For such a system, we introduce the power and bandwidth cooperation between the two groups so that both group can accomplish their expected information delivering tasks. Multiple antennas are employed at the hybrid access point (H-AP) to en- hance both energy and information transfer efficiency and the cooperative relaying is employed to help the power-limited group to enhance its information transmission throughput. Compared with existing works, cooperative relaying, time assignment, power allocation, and energy beamforming are jointly designed in a single system. Firstly, we propose a cooperative transmission protocol for the considered system, where group 1 transmits some power to group 2 to help group 2 with information transmission and then group 2 gives some bandwidth to group 1 in return. Sec- ondly, to explore the information transmission performance limit of the system, we formulate two optimization problems to maximize the system weighted sum rate by jointly optimizing the time assignment, power allocation, and energy beamforming under two different power constraints, i.e., the fixed power constraint and the aver- age power constraint, respectively. In order to make the cooperation between the two groups meaningful and guarantee the quality of service (QoS) requirements of both groups, the minimal required data rates of the two groups are considered as constraints for the optimal system design. As both problems are non-convex and have no known solutions, we solve it by using proper variable substitutions and the semi-definite relaxation (SDR). We theoretically prove that our proposed solution method can guarantee to find the global optimal solution. Thirdly, consider that the WPCN has promising application potentials in future energy-constrained net- works, e.g., wireless sensor network (WSN), wireless body area network (WBAN) and Internet of Things (IoT), where the power consumption is very critical. We investigate the minimal power consumption optimal design for the considered co- operation WPCN. For this, we formulate an optimization problem to minimize the total consumed power by jointly optimizing the time assignment, power allocation, and energy beamforming under required data rate constraints. As the problem is also non-convex and has no known solutions, we solve it by using some variable substitutions and the SDR method. We also theoretically prove that our proposed solution method for the minimal power consumption design guarantees the global optimal solution. Extensive experimental results are provided to discuss the system performance behaviors, which provide some useful insights for future WPCN design. It shows that the average power constrained system achieves higher weighted sum rate than the fixed power constrained system. Besides, it also shows that in such a WPCN, relay should be placed closer to the multi-antenna H-AP to achieve higher weighted sum rate and consume lower total power.

Real-time load-side control of electric power systems

Two trends are emerging from modern electric power systems: the growth of renewable (e.g., solar and wind) generation, and the integration of information technologies and advanced power electronics. The former introduces large, rapid, and random fluctuations in power supply, demand, frequency, and voltage, which become a major challenge for real-time operation of power systems. The latter creates a tremendous number of controllable intelligent endpoints such as smart buildings and appliances, electric vehicles, energy storage devices, and power electronic devices that can sense, compute, communicate, and actuate. Most of these endpoints are distributed on the load side of power systems, in contrast to traditional control resources such as centralized bulk generators. This thesis focuses on controlling power systems in real time, using these load side resources. Specifically, it studies two problems.

(1) Distributed load-side frequency control: We establish a mathematical framework to design distributed frequency control algorithms for flexible electric loads. In this framework, we formulate a category of optimization problems, called optimal load control (OLC), to incorporate the goals of frequency control, such as balancing power supply and demand, restoring frequency to its nominal value, restoring inter-area power flows, etc., in a way that minimizes total disutility for the loads to participate in frequency control by deviating from their nominal power usage. By exploiting distributed algorithms to solve OLC and analyzing convergence of these algorithms, we design distributed load-side controllers and prove stability of closed-loop power systems governed by these controllers. This general framework is adapted and applied to different types of power systems described by different models, or to achieve different levels of control goals under different operation scenarios. We first consider a dynamically coherent power system which can be equivalently modeled with a single synchronous machine. We then extend our framework to a multi-machine power network, where we consider primary and secondary frequency controls, linear and nonlinear power flow models, and the interactions between generator dynamics and load control.

(2) Two-timescale voltage control: The voltage of a power distribution system must be maintained closely around its nominal value in real time, even in the presence of highly volatile power supply or demand. For this purpose, we jointly control two types of reactive power sources: a capacitor operating at a slow timescale, and a power electronic device, such as a smart inverter or a D-STATCOM, operating at a fast timescale. Their control actions are solved from optimal power flow problems at two timescales. Specifically, the slow-timescale problem is a chance-constrained optimization, which minimizes power loss and regulates the voltage at the current time instant while limiting the probability of future voltage violations due to stochastic changes in power supply or demand. This control framework forms the basis of an optimal sizing problem, which determines the installation capacities of the control devices by minimizing the sum of power loss and capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments show that the proposed sizing and control schemes significantly improve the reliability of voltage control with a moderate increase in cost.

Dynamic Multi-Objective Optimization With jMetal and Spark: a Case Study

Technologies for Big Data and Data Science are receiving increasing research interest nowadays. This paper introduces the prototyping architecture of a tool aimed to solve Big Data Optimization problems. Our tool combines the jMetal framework for multi-objective optimization with Apache Spark, a technology that is gaining momentum. In particular, we make use of the streaming facilities of Spark to feed an optimization problem with data from different sources. We demonstrate the use of our tool by solving a dynamic bi-objective instance of the Traveling Salesman Problem (TSP) based on near real-time traffic data from New York City, which is updated several times per minute. Our experiment shows that both jMetal and Spark can be integrated providing a software platform to deal with dynamic multi-optimization problems.

Distributed optimization in transportation and logistics networks

Many important problems in communication networks, transportation networks, and logistics networks are solved by the minimization of cost functions. In general, these can be complex optimization problems involving many variables. However, physicists noted that in a network, a node variable (such as the amount of resources of the nodes) is connected to a set of link variables (such as the flow connecting the node), and similarly each link variable is connected to a number of (usually two) node variables. This enables one to break the problem into local components, often arriving at distributive algorithms to solve the problems. Compared with centralized algorithms, distributed algorithms have the advantages of lower computational complexity, and lower communication overhead. Since they have a faster response to local changes of the environment, they are especially useful for networks with evolving conditions. This review will cover message-passing algorithms in applications such as resource allocation, transportation networks, facility location, traffic routing, and stability of power grids.

Distributed Large-scale Mixed-Integer Optimization with Application to Energy and Multi-robot Networks

Several decision and control tasks in cyber-physical networks can be formulated as large- scale optimization problems with coupling constraints. In these "constraint-coupled" problems, each agent is associated to a local decision variable, subject to individual constraints. This thesis explores the use of primal decomposition techniques to develop tailored distributed algorithms for this challenging set-up over graphs. We first develop a distributed scheme for convex problems over random time-varying graphs with non-uniform edge probabilities. The approach is then extended to unknown cost functions estimated online. Subsequently, we consider Mixed-Integer Linear Programs (MILPs), which are of great interest in smart grid control and cooperative robotics. We propose a distributed methodological framework to compute a feasible solution to the original MILP, with guaranteed suboptimality bounds, and extend it to general nonconvex problems. Monte Carlo simulations highlight that the approach represents a substantial breakthrough with respect to the state of the art, thus representing a valuable solution for new toolboxes addressing large-scale MILPs. We then propose a distributed Benders decomposition algorithm for asynchronous unreliable networks. The framework has been then used as starting point to develop distributed methodologies for a microgrid optimal control scenario. We develop an ad-hoc distributed strategy for a stochastic set-up with renewable energy sources, and show a case study with samples generated using Generative Adversarial Networks (GANs). We then introduce a software toolbox named ChoiRbot, based on the novel Robot Operating System 2, and show how it facilitates simulations and experiments in distributed multi-robot scenarios. Finally, we consider a Pickup-and-Delivery Vehicle Routing Problem for which we design a distributed method inspired to the approach of general MILPs, and show the efficacy through simulations and experiments in ChoiRbot with ground and aerial robots.

Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose to learn a variable selection policy for branch-and-bound in mixed-integer linear programming, by imitation learning on a diversified variant of the strong branching expert rule. We encode states as bipartite graphs and parameterize the policy as a graph convolutional neural network. Experiments on a series of synthetic problems demonstrate that our approach produces policies that can improve upon expert-designed branching rules on large problems, and generalize to instances significantly larger than seen during training.

Adjustable robust optimization with nonlinear recourses

Over the last century, mathematical optimization has become a prominent tool for decision making. Its systematic application in practical fields such as economics, logistics or defense led to the development of algorithmic methods with ever increasing efficiency. Indeed, for a variety of real-world problems, finding an optimal decision among a set of (implicitly or explicitly) predefined alternatives has become conceivable in reasonable time. In the last decades, however, the research community raised more and more attention to the role of uncertainty in the optimization process. In particular, one may question the notion of optimality, and even feasibility, when studying decision problems with unknown or imprecise input parameters. This concern is even more critical in a world becoming more and more complex —by which we intend, interconnected —where each individual variation inside a system inevitably causes other variations in the system itself. In this dissertation, we study a class of optimization problems which suffer from imprecise input data and feature a two-stage decision process, i.e., where decisions are made in a sequential order —called stages —and where unknown parameters are revealed throughout the stages. The applications of such problems are plethora in practical fields such as, e.g., facility location problems with uncertain demands, transportation problems with uncertain costs or scheduling under uncertain processing times. The uncertainty is dealt with a robust optimization (RO) viewpoint (also known as "worst-case perspective") and we present original contributions to the RO literature on both the theoretical and practical side.

GOOAL: A routine based on Genetic Algorithms to track harmonics in electric power systems

Voltage and current waveforms of a distribution or transmission power system are not pure sinusoids. There are distortions in these waveforms that can be represented as a combination of the fundamental frequency, harmonics and high frequency transients. This paper presents a novel approach to identifying harmonics in power system distorted waveforms. The proposed method is based on Genetic Algorithms, which is an optimization technique inspired by genetics and natural evolution. GOOAL, a specially designed intelligent algorithm for optimization problems, was successfully implemented and tested. Two kinds of representations concerning chromosomes are utilized: binary and real. The results show that the proposed method is more precise than the traditional Fourier Transform, especially considering the real representation of the chromosomes.

Multiobjective Particle Swarm Approach for the Design of a Brushless DC Wheel Motor

The roots of swarm intelligence are deeply embedded in the biological study of self-organized behaviors in social insects. Particle swarm optimization (PSO) is one of the modern metaheuristics of swarm intelligence, which can be effectively used to solve nonlinear and non-continuous optimization problems. The basic principle of PSO algorithm is formed on the assumption that potential solutions (particles) will be flown through hyperspace with acceleration towards more optimum solutions. Each particle adjusts its flying according to the flying experiences of both itself and its companions using equations of position and velocity. During the process, the coordinates in hyperspace associated with its previous best fitness solution and the overall best value attained so far by other particles within the group are kept track and recorded in the memory. In recent years, PSO approaches have been successfully implemented to different problem domains with multiple objectives. In this paper, a multiobjective PSO approach, based on concepts of Pareto optimality, dominance, archiving external with elite particles and truncated Cauchy distribution, is proposed and applied in the design with the constraints presence of a brushless DC (Direct Current) wheel motor. Promising results in terms of convergence and spacing performance metrics indicate that the proposed multiobjective PSO scheme is capable of producing good solutions.

Adequacy of Cold Rolling Models to Upgrade Set-up Generation Systems

This paper presents two strategies for the upgrade of set-up generation systems for tandem cold mills. Even though these mills have been modernized mainly due to quality requests, their upgrades may be made intending to replace pre-calculated reference tables. In this case, Bryant and Osborn mill model without adaptive technique is proposed. As a more demanding modernization, Bland and Ford model including adaptation is recommended, although it requires a more complex computational hardware. Advantages and disadvantages of these two systems are compared and discussed and experimental results obtained from an industrial cold mill are shown.