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Sensor placement for municipal water networks

Phillips, Cynthia A.; Boman, Erik G.; Carr, Robert D.; Hart, William E.; Berry, Jonathan W.; Watson, Jean-Paul W.; Hart, David B.; Mckenna, Sean A.; Riesen, Lee A.

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.

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TYPE Conference YEAR 2010
OSTI

Scheduling error correction operations for a quantum computer

Phillips, Cynthia A.; Carr, Robert D.; Ganti, Anand G.; Landahl, Andrew J.

In a (future) quantum computer a single logical quantum bit (qubit) will be made of multiple physical qubits. These extra physical qubits implement mandatory extensive error checking. The efficiency of error correction will fundamentally influence the performance of a future quantum computer, both in latency/speed and in error threshold (the worst error tolerated for an individual gate). Executing this quantum error correction requires scheduling the individual operations subject to architectural constraints. Since our last talk on this subject, a team of researchers at Sandia National Labortories has designed a logical qubit architecture that considers all relevant architectural issues including layout, the effects of supporting classical electronics, and the types of gates that the underlying physical qubit implementation supports most naturally. This is a two-dimensional system where 2-qubit operations occur locally, so there is no need to calculate more complex qubit/information transportation. Using integer programming, we found a schedule of qubit operations that obeys the hardware constraints, implements the local-check code in the native gate set, and minimizes qubit idle periods. Even with an optimal schedule, however, parallel Monte Carlo simulation shows that there is no finite error probability for the native gates such that the error-correction system would be benecial. However, by adding dynamic decoupling, a series of timed pulses that can reverse some errors, we found that there may be a threshold. Thus finding optimal schedules for increasingly-refined scheduling problems has proven critical for the overall design of the logical qubit system. We describe the evolving scheduling problems and the ideas behind the integer programming-based solution methods. This talk assumes no prior knowledge of quantum computing.

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TYPE Conference YEAR 2010
OSTI

Better relaxations of classical discrete optimization problems

Carr, Robert D.

A mathematical program is an optimization problem expressed as an objective function of multiple variables subject to set of constraints. When the optimization problem has specific structure, the problem class usually has a special name. A linear program is the optimization of a linear objective function subject to linear constraints. An integer program is a linear program where some of the variables must take only integer values. A semidefinite program is a linear program where the variables are arranged in a matrix and for all feasible solutions, this matrix must be positive semidefinite. There are general-purpose solvers for each of these classes of mathematical program. There are usually many ways to express a problem as a correct, say, linear program. However, equivalent formulations can have significantly different practical tractability. In this poster, we present new formulations for two classic discrete optimization problems, maximum cut (max cut) and the graphical traveling salesman problem (GTSP), that are significantly stronger, and hence more computationally tractable, than any previous formulations of their class. Both partially answer longstanding open theoretical questions in polyhedral combinatorics.

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TYPE Conference YEAR 2008
OSTI

LDRD final report : robust analysis of large-scale combinatorial applications

Hart, William E.; Carr, Robert D.; Phillips, Cynthia A.; Watson, Jean-Paul W.

Discrete models of large, complex systems like national infrastructures and complex logistics frameworks naturally incorporate many modeling uncertainties. Consequently, there is a clear need for optimization techniques that can robustly account for risks associated with modeling uncertainties. This report summarizes the progress of the Late-Start LDRD 'Robust Analysis of Largescale Combinatorial Applications'. This project developed new heuristics for solving robust optimization models, and developed new robust optimization models for describing uncertainty scenarios.

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TYPE SAND Report YEAR 2007
OSTIDOI
Results 1–25 of 39
Results 1–25 of 39