Multi-hop Diffusion LMS for Energy-constrained Distributed Estimation

We propose a multi-hop diffusion strategy for a sensor network to perform distributed least mean-squares (LMS) estimation under local and network-wide energy constraints. At each iteration of the strategy, each node can combine intermediate parameter estimates from nodes other than its physical neighbors via a multi-hop relay path. We propose a rule to select combination weights for the multi-hop neighbors, which can balance between the transient and the steady-state network mean-square deviations (MSDs). We study two classes of networks: simple networks with a unique transmission path from one node to another, and arbitrary networks utilizing diffusion consultations over at most two hops. We propose a method to optimize each node's information neighborhood subject to local energy budgets and a network-wide energy budget for each diffusion iteration. This optimization requires the network topology, and the noise and data variance profiles of each node, and is performed offline before the diffusion process. In addition, we develop a fully distributed and adaptive algorithm that approximately optimizes the information neighborhood of each node with only local energy budget constraints in the case where diffusion consultations are performed over at most a predefined number of hops. Numerical results suggest that our proposed multi-hop diffusion strategy achieves the same steady-state MSD as the existing one-hop adapt-then-combine diffusion algorithm but with a lower energy budget.Comment: 14 pages, 12 figures. Submitted for publicatio

Optimization of the long-term planning of supply chains with decaying performance

This master's thesis addresses the optimization of supply and distribution chains considering the effect that equipment aging may cause over the performance of facilities involved in the process. The decaying performance of the facilities is modeled as an exponential equation and can be either physical or economic, thus giving rise to a novel mixed integer non-linear programming (MINLP) formulation. The optimization model has been developed based on a typical chemical supply chain. Thus, the best long-term investment plan has to be determined given production nodes, their production capacity and expected evolution; aggregated consumption nodes (urban or industrial districts) and their lumped demand (and expected evolution); actual and potential distribution nodes; distances between the nodes of the network; and a time horizon. The model includes the balances in each node, a general decaying performance function, and a cost function, as well as constraints to be satisfied. Hence, the investment plan (decision variables) consists not only on the start-up and shutdown of alternative distribution facilities, but also on the sizing of the lines satisfying the flows. The model has been implemented using GAMS optimization software. Results considering a variety of scenarios have been discussed. In addition, different approaches to the starting point for the model have been compared, showing the importance of initializing the optimization algorithm. The capabilities of the proposed approach have been tested through its application to two case studies: a natural gas network with physical decaying performance and an electricity distribution network with economic decaying performance. Each case study is solved with a different procedure to obtain results. Results demonstrate that overlooking the effect of equipment aging can lead to infeasible (for physical decaying performance) or unrealistic (for economic decaying performance) solutions in practice and show how the proposed model allows overcoming such limitations thus becoming a practical tool to support the decision-making process in the distribution secto

Essays on Unit Commitment and Interregional Cooperation in Transmission Planning

One of the most challenging problems in the power industry is deciding which transmission lines to build. The process of answering this question leads to some very interesting and complex optimization problems. Answers to subsidiary questions about the detail of generator operations to simulate, generator siting, environmental regulations, political boundaries, and the ways in which these factors interact with each other, together inform the decision of building transmission lines. For example, carbon taxes may favor transmission expansion to areas with high levels of renewable energy, and consequently, fast ramp-rate generation may be desired to balance the variable nature of renewable energy sources. Transmission investment decisions can have far-reaching consequences for investors and a host of other entities connected to the electric grid. In addition to being expensive and time-consuming to build, these lines influence other transmission and generation investments, operations, and electricity prices. This work presents a series of essays on the transmission planning problem. There are two main themes: the effects of short-term operations, and the effects of political boundaries, on long-term transmission plans. Contributions of these essays include the following: 1. An alternative formulation of the Unit Commitment (UC) problem that solves faster than the standard UC formulation, and UC approximations that improve computational performance while maintaining high fidelity in the quality of the solution (reduction of binary variables and tightening of constraints). 2. Demonstrating how to bridge the gap between short-term (hours) operational models and long-term (years) transmission and generation co-optimization models, using an application of the U.S. Western Interconnection. 3. Demonstrating that short-term operational constraints have the potential to affect long-term transmission and generator investments. As an example, we find that, when operational constraints such as ramp-rates and minimum-run capacities are considered, transmission investment can sometimes act as a substitute to generation investments. 4. A novel formulation of the noncooperative regional transmission planning problem that shows how regional transmission operators acting in their own self-interest can negatively impact transmission investments. 5. Demonstrating that adjoining transmission operators can both benefit from cooperating with each other in the transmission planning process. Interestingly, we find that it is not enough to focus on seam lines connecting two regions. There are lines internal to each region that have interregional benefits and are identified only though a cooperative planning process. 6. Approximations of the non-cooperative transmission planning model that aid scale-up of this framework to large data-sets, further improving computational performance. Limitations of these models, practical issues involved, and future research directions are discussed in the concluding chapter. Together, these essays illuminate the effects of operational constraints and political boundaries on transmission planning, and encourage decision makers to consider them in their planning processes

Computational Optimization Techniques for Graph Partitioning

Partitioning graphs into two or more subgraphs is a fundamental operation in computer science, with applications in large-scale graph analytics, distributed and parallel data processing, and fill-reducing orderings in sparse matrix algorithms. Computing balanced and minimally connected subgraphs is a common pre-processing step in these areas, and must therefore be done quickly and efficiently. Since graph partitioning is NP-hard, heuristics must be used. These heuristics must balance the need to produce high quality partitions with that of providing practical performance. Traditional methods of partitioning graphs rely heavily on combinatorics, but recent developments in continuous optimization formulations have led to the development of hybrid methods that combine the best of both approaches. This work describes numerical optimization formulations for two classes of graph partitioning problems, edge cuts and vertex separators. Optimization-based formulations for each of these problems are described, and hybrid algorithms combining these optimization-based approaches with traditional combinatoric methods are presented. Efficient implementations and computational results for these algorithms are presented in a C++ graph partitioning library competitive with the state of the art. Additionally, an optimization-based approach to hypergraph partitioning is proposed