Publications

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The optimization of sensor placements is a key aspect of the design of contaminant warning systems for automatically detecting contaminants in water distribution systems. Although researchers have generally assumed that all sensors are placed at the same time, in practice sensor networks will likely grow and evolve over time. For example, limitations for a water utility's budget may dictate an staged, incremental deployment of sensors over many years. We describe optimization formulations of multi-stage sensor placement problems. The objective of these formulations includes an explicit trade-off between the value of the initially deployed and final sensor networks. This trade-off motivates the deployment of sensors in initial stages of the deployment schedule, even though these choices typically lead to a solution that is suboptimal when compared to placing all sensors at once. These multi-stage sensor placement problems can be represented as mixed-integer programs, and we illustrate the impact of this trade-off using standard commercial solvers. We also describe a multi-stage formulation that models budget uncertainty, expressed as a tree of potential budget scenarios through time. Budget uncertainty is used to assess and hedge against risks due to a potentially incomplete deployment of a planned sensor network. This formulation is a multi-stage stochastic mixed-integer program, which are notoriously difficult to solve. We apply standard commercial solvers to small-scale test problems, enabling us to effectively analyze multi-stage sensor placement problems subject to budget uncertainties, and assess the impact of accounting for such uncertainty relative to a deterministic multi-stage model. © 2012 ASCE.

We present a mixed-integer linear programming formulation to determine optimal locations for manual grab sampling after the detection of contaminants in a water distribution system. The formulation selects optimal manual grab sample locations that maximize the total pair-wise distinguishability of candidate contamination events. Given an initial contaminant detection location, a source inversion is performed that will eliminate unlikely events resulting in a much smaller set of candidate contamination events. We then propose a cyclical process where optimal grab samples locations are determined and manual grab samples taken. Relying only on YES/NO indicators of the presence of contaminant, source inversion is performed to reduce the set of candidate contamination events. The process is repeated until the number of candidate events is sufficiently small. Case studies testing this process are presented using water network models ranging from 4 to approximately 13000 nodes. The results demonstrate that the contamination event can be identified within a remarkably small number of sampling cycles using very few sampling teams. Furthermore, solution times were reasonable making this formulation suitable for real-time settings. © 2012 ASCE.

Decision makers increasingly rely on large-scale computational models to simulate and analyze complex man-made systems. For example, computational models of national infrastructures are being used to inform government policy, assess economic and national security risks, evaluate infrastructure interdependencies, and plan for the growth and evolution of infrastructure capabilities. A major challenge for decision makers is the analysis of national-scale models that are composed of interacting systems: effective integration of system models is difficult, there are many parameters to analyze in these systems, and fundamental modeling uncertainties complicate analysis. This project is developing optimization methods to effectively represent and analyze large-scale heterogeneous system of systems (HSoS) models, which have emerged as a promising approach for describing such complex man-made systems. These optimization methods enable decision makers to predict future system behavior, manage system risk, assess tradeoffs between system criteria, and identify critical modeling uncertainties.

We present a methodology for optimally locating disinfectant booster stations for response to contamination events in water distribution systems. A stochastic programming problem considering uncertainty in both the location and time of the contamination event is formulated resulting in an extensive form that is equivalent to the weighted maximum coverage problem. Although the original full-space problem is intractably large, we show a series of reductions that reduce the size of the problem by five orders of magnitude and allow solutions of the optimal placement problem for realistically sized water network models. © 2012 Elsevier B.V.

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We describe Pyomo, an open source software package for modeling and solving mathematical programs in Python. Pyomo can be used to define abstract and concrete problems, create problem instances, and solve these instances with standard open-source and commercial solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages such as AMPL, AIMMS, and GAMS. In contrast, Pyomo's modeling objects are embedded within a full-featured highlevel programming language with a rich set of supporting libraries. Pyomo leverages the capabilities of the Coopr software library, which together with Pyomo is part of IBM's COIN-OR open-source initiative for operations research software. Coopr integrates Python packages for defining optimizers, modeling optimization applications, and managing computational experiments. Numerous examples illustrating advanced scripting applications are provided. © Springer and Mathematical Optimization Society 2011.

We consider the design of a sensor network to serve as an early warning system against a potential suite of contamination incidents. Given any measure for evaluating the quality of a sensor placement, there are two ways to model the objective. One is to minimize the impact or damage to the network, the other is to maximize the reduction in impact compared to the network without sensors. These objectives are the same when the problem is solved optimally. But when given equally-good approximation algorithms for each of this pair of complementary objectives, either one might be a better choice. The choice generally depends upon the quality of the approximation algorithms, the impact when there are no sensors, and the number of sensors available. We examine when each objective is better than the other by examining multiple real world networks. When assuming perfect sensors, minimizing impact is frequently superior for virulent contaminants. But when there are long response delays, or it is very difficult to reduce impact, maximizing impact reduction may be better. © 2011 ASCE.

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We consider the problem of placing a limited number of sensors in a municipal water distribution network to minimize the impact over a given suite of contamination incidents. In its simplest form, the sensor placement problem is a p-median problem that has structure extremely amenable to exact and heuristic solution methods. We describe the solution of real-world instances using integer programming or local search or a Lagrangian method. The Lagrangian method is necessary for solution of large problems on small PCs. We summarize a number of other heuristic methods for effectively addressing issues such as sensor failures, tuning sensors based on local water quality variability, and problem size/approximation quality tradeoffs. These algorithms are incorporated into the TEVA-SPOT toolkit, a software suite that the US Environmental Protection Agency has used and is using to design contamination warning systems for US municipal water systems.

The Python Optimization Modeling Objects (Pyomo) package [1] is an open source tool for modeling optimization applications within Python. Pyomo provides an objected-oriented approach to optimization modeling, and it can be used to define symbolic problems, create concrete problem instances, and solve these instances with standard solvers. While Pyomo provides a capability that is commonly associated with algebraic modeling languages such as AMPL, AIMMS, and GAMS, Pyomo's modeling objects are embedded within a full-featured high-level programming language with a rich set of supporting libraries. Pyomo leverages the capabilities of the Coopr software library [2], which integrates Python packages (including Pyomo) for defining optimizers, modeling optimization applications, and managing computational experiments. A central design principle within Pyomo is extensibility. Pyomo is built upon a flexible component architecture [3] that allows users and developers to readily extend the core Pyomo functionality. Through these interface points, extensions and applications can have direct access to an optimization model's expression objects. This facilitates the rapid development and implementation of new modeling constructs and as well as high-level solution strategies (e.g. using decomposition- and reformulation-based techniques). In this presentation, we will give an overview of the Pyomo modeling environment and model syntax, and present several extensions to the core Pyomo environment, including support for Generalized Disjunctive Programming (Coopr GDP), Stochastic Programming (PySP), a generic Progressive Hedging solver [4], and a tailored implementation of Bender's Decomposition.

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These slides describe different strategies for installing Python software. Although I am a big fan of Python software development, robust strategies for software installation remains a challenge. This talk describes several different installation scenarios. The Good: the user has administrative privileges - Installing on Windows with an installer executable, Installing with Linux application utility, Installing a Python package from the PyPI repository, and Installing a Python package from source. The Bad: the user does not have administrative privileges - Using a virtual environment to isolate package installations, and Using an installer executable on Windows with a virtual environment. The Ugly: the user needs to install an extension package from source - Installing a Python extension package from source, and PyCoinInstall - Managing builds for Python extension packages. The last item referring to PyCoinInstall describes a utility being developed for the COIN-OR software, which is used within the operations research community. COIN-OR includes a variety of Python and C++ software packages, and this script uses a simple plug-in system to support the management of package builds and installation.

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We consider the problem of placing sensors in a municipal water network when we can choose both the location of sensors and the sensitivity and specificity of the contamination warning system. Sensor stations in a municipal water distribution network continuously send sensor output information to a centralized computing facility, and event detection systems at the control center determine when to signal an anomaly worthy of response. Although most sensor placement research has assumed perfect anomaly detection, signal analysis software has parameters that control the tradeoff between false alarms and false negatives. We describe a nonlinear sensor placement formulation, which we heuristically optimize with a linear approximation that can be solved as a mixed-integer linear program. We report the results of initial experiments on a real network and discuss tradeoffs between early detection of contamination incidents, and control of false alarms.

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The sensor placement problem in contamination warning system design for municipal water distribution networks involves maximizing the protection level afforded by limited numbers of sensors, typically quantified as the expected impact of a contamination event; the issue of how to mitigate against high-consequence events is either handled implicitly or ignored entirely. Consequently, expected-case sensor placements run the risk of failing to protect against high-consequence 9/11-style attacks. In contrast, robust sensor placements address this concern by focusing strictly on high-consequence events and placing sensors to minimize the impact of these events. We introduce several robust variations of the sensor placement problem, distinguished by how they quantify the potential damage due to high-consequence events. We explore the nature of robust versus expected-case sensor placements on three real-world large-scale distribution networks. We find that robust sensor placements can yield large reductions in the number and magnitude of high-consequence events, with only modest increases in expected impact. The ability to trade-off between robust and expected-case impacts is a key unexplored dimension in contamination warning system design. © 2009 ASCE.

Biofouling, the unwanted growth of biofilms on a surface, of water-treatment membranes negatively impacts in desalination and water treatment. With biofouling there is a decrease in permeate production, degradation of permeate water quality, and an increase in energy expenditure due to increased cross-flow pressure needed. To date, a universal successful and cost-effect method for controlling biofouling has not been implemented. The overall goal of the work described in this report was to use high-performance computing to direct polymer, material, and biological research to create the next generation of water-treatment membranes. Both physical (micromixers - UV-curable epoxy traces printed on the surface of a water-treatment membrane that promote chaotic mixing) and chemical (quaternary ammonium groups) modifications of the membranes for the purpose of increasing resistance to biofouling were evaluated. Creation of low-cost, efficient water-treatment membranes helps assure the availability of fresh water for human use, a growing need in both the U. S. and the world.

Currently, electrical power generation uses about 140 billion gallons of water per day accounting for over 39% of all freshwater withdrawals thus competing with irrigated agriculture as the leading user of water. Coupled to this water use is the required pumping, conveyance, treatment, storage and distribution of the water which requires on average 3% of all electric power generated. While water and energy use are tightly coupled, planning and management of these fundamental resources are rarely treated in an integrated fashion. Toward this need, a decision support framework has been developed that targets the shared needs of energy and water producers, resource managers, regulators, and decision makers at the federal, state and local levels. The framework integrates analysis and optimization capabilities to identify trade-offs, and 'best' alternatives among a broad list of energy/water options and objectives. The decision support framework is formulated in a modular architecture, facilitating tailored analyses over different geographical regions and scales (e.g., national, state, county, watershed, NERC region). An interactive interface allows direct control of the model and access to real-time results displayed as charts, graphs and maps. Ultimately, this open and interactive modeling framework provides a tool for evaluating competing policy and technical options relevant to the energy-water nexus.

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We present the TEVA-SPOT Toolkit, a sensor placement optimization tool developed within the USEPA TEVA program. The TEVA-SPOT Toolkit provides a sensor placement framework that facilitates research in sensor placement optimization and enables the practical application of sensor placement solvers to real-world CWS design applications. This paper provides an overview of its key features, and then illustrates how this tool can be flexibly applied to solve a variety of different types of sensor placement problems. © 2008 ASCE.

The practical utility of optimization technologies is often impacted by factors that reflect how these tools are used in practice, including whether various real-world constraints can be adequately modeled, the sophistication of the analysts applying the optimizer, and related environmental factors (e.g. whether a company is willing to trust predictions from computational models). Other features are less appreciated, but of equal importance in terms of dictating the successful use of optimization. These include the scale of problem instances, which in practice drives the development of approximate solution techniques, and constraints imposed by the target computing platforms. End-users often lack state-of-the-art computers, and thus runtime and memory limitations are often a significant, limiting factor in algorithm design. When coupled with large problem scale, the result is a significant technological challenge. We describe our experience developing and deploying both exact and heuristic algorithms for placing sensors in water distribution networks to mitigate against damage due intentional or accidental introduction of contaminants. The target computing platforms for this application have motivated limited-memory techniques that can optimize large-scale sensor placement problems. © 2008 Springer Berlin Heidelberg.

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Recently, extensive focus has been placed on determining the optimal locations of sensors within a distribution system to minimize the impact on public health from intentional intrusion events. Modified versions of these tools may have additional benefits for determining monitoring locations for other more common objectives associated with distribution systems. A modified Sensor Placement Optimization Tool (SPOT) is presented that can be used for satisfying more generic location problems such as determining monitoring locations for tracer tests or disinfectant byproduct sampling. The utility for the modified SPOT algorithm is discussed with respect to implementing a distribution system field-scale tracer study. © 2007 ASCE.