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.