Carl D. Laird

Time Dependent Contamination Source Determination: A Network Subdomain Approach for Very Large Water Networks.

This paper presents an approach for identifying contamination sources in very large municipal water networks. The vulnerability of municipal drinking water networks to intentional and accidental contaminations requires investigation of alternative protection measures. If a contamination occurs, it is important to identify both the time and location of the contamination source. A dynamic optimization approach for estimating contamination sources was previously presented. The approach developed an origin tracking algorithm that reformulated the partial dieren tial pipe expressions, removing the need to discretize in space. Although this allowed for ecien t solutions using a direct simultaneous technique for a network of approximately 500 nodes, the approach does not scale indenitely to very large networks. This current paper handles very large water networks by performing the optimization on a smaller, subdomain of the entire network. This approach considers the hydraulics and sensor measurements for the entire network, but formulates the dynamic optimization problem for a subset of the network nodes. A subdomain approach is introduced, forming a geographic window around the rst sensor to detect contaminant. Numerical results indicate that this subdomain approach is eectiv e at identifying contamination sources. Furthermore, since the required subdomain size is not dependent on the size of the entire network, this approach scales to very large municipal water networks.

Benchmarking ADMM in nonconvex NLPs

Abstract We study connections between the alternating direction method of multipliers (ADMM), the classical method of multipliers (MM), and progressive hedging (PH). The connections are used to derive benchmark metrics and strategies to monitor and accelerate convergence and to help explain why ADMM and PH are capable of solving complex nonconvex NLPs. Specifically, we observe that ADMM is an inexact version of MM and approaches its performance when multiple coordination steps are performed. In addition, we use the observation that PH is a specialization of ADMM and borrow Lyapunov function and primal-dual feasibility metrics used in ADMM to explain why PH is capable of solving nonconvex NLPs. This analysis also highlights that specialized PH schemes can be derived to tackle a wider range of stochastic programs and even other problem classes. Our exposition is tutorial in nature and seeks to to motivate algorithmic improvements and new decomposition strategies

Mathematical Modeling and Optimization

This chapter provides a primer on optimization and mathematical modeling. It does not provide a complete description of these topics. Instead, this chapter provides enough background information to support reading the rest of the book. For more discussion of optimization modeling techniques see, for example, Williams [86]. Implementations of simple examples of models are shown to provide the reader with a quick start to using Pyomo.

Mathematical Programs with Equilibrium Constraints

This chapter documents how to formulate mathematical programs with equilibrium constraints (MPECs), which naturally arise in a wide range of engineering and economic systems. We describe Pyomo components for complementarity conditions, and transformation capabilities that automate the reformulation of MPEC models, and meta-solvers that leverage these transformations to support global and local optimization of MPEC models.

Differential Algebraic Equations

This chapter documents how to formulate and solve optimization problems with differential and algebraic equations (DAEs). The pyomo.dae package allows users to easily incorporate detailed dynamic models within an optimization framework and is flexible enough to represent a wide variety of differential equations. We also demonstrate several automated solution techniques included in pyomo.dae that apply a simultaneous discretization approach to solve dynamic optimization problems.

Structured Modeling with Blocks

This chapter documents how to express hierarchically-structured models using Pyomo’s Block component. Many models contain significant hierarchical structure; that is, they are composed of repeated groups of conceptually related modeling components. Pyomo allows the modeler to define fundamental building blocks, and then construct the overall problem by connecting these building blocks together in an object-oriented manner. In this chapter, we describe the fundamental Block component along with common examples of its use, including repeated components and managing model scope.

Generalized Disjunctive Programming

This chapter documents how to express and solve Generalized Disjunctive Programs (GDPs). GDP models provide a structured approach for describing logical relationships in optimization models.We show how Pyomo blocks provide a natural base for representing disjuncts and forming disjunctions, and we how to solve GDP models through the use of automated problem transformations.

Pyomo Models and Components: An Introduction

This chapter describes the core classes that are used to define optimization models in Pyomo. Most of the discussion focuses on modeling components that are used to declare parts of a model. We include a discussion of the options that can be used when declaring the components and information about key component attributes and methods.

The Pyomo Command

This chapter describes Pyomo’s command-line interface, which includes a variety of subcommands that support common workflows and provide information about Pyomo and its installation.

Data Command Files

Data command files allow users to define set and parameter data with a high-level language. This chapter discusses the format of these data commands, as well as the various data declarations that Pyomo supports. Pyomo’s data commands include both direct specifications of data, as well as specifications that indicate how data is to be extracted from a variety of different sources, including table files, CSV files, spreadsheets, and databases.