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Title: Robust optimization of contaminant sensor placement for community water systems.

Abstract

We present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected.We formulate sensor placement problems as mixed-integer programs, for which the objective coefficients are not known with certainty. We consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data, and we define three robust optimization models that differ in how the coefficients in the objective vary. Under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients. Under other assumptions, we can apply sorting to solve each worst-case realization efficiently, or we can apply duality to integrate the worst-case outcome and have one integer program. The most difficult case is where the objective parameters are bilinear, and we prove its complexity is NP-hard even under simplifying assumptions. We consider a relaxation that provides an approximation, giving an overall guarantee of nearoptimality when used with branch-and-bound search. We present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications.

Authors:
 [1]; ;  [2]; ;  [2]; ;  [3];
  1. Arizona State University, Tempe, AZ
  2. University of Colorado at Denver, Denver, CO
  3. University of California at Berkeley, Berkeley, CA
Publication Date:
Research Org.:
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
990958
Report Number(s):
SAND2004-4530J
Journal ID: ISSN 0025-5610; TRN: US201020%%635
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
Proposed for publication in Mathematical Programming Series B.
Additional Journal Information:
Journal Volume: 107; Journal Issue: 1; Journal ID: ISSN 0025-5610
Country of Publication:
United States
Language:
English
Subject:
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; WATER SUPPLY; SENSORS; POSITIONING; POLLUTANTS; DETECTION; PUBLIC UTILITIES

Citation Formats

Konjevod, Goran, Carr, Robert D, Greenberg, Harvey J, Hart, William Eugene, Morrison, Tod, Phillips, Cynthia Ann, Lin, Henry, and Lauer, Erik. Robust optimization of contaminant sensor placement for community water systems.. United States: N. p., 2004. Web.
Konjevod, Goran, Carr, Robert D, Greenberg, Harvey J, Hart, William Eugene, Morrison, Tod, Phillips, Cynthia Ann, Lin, Henry, & Lauer, Erik. Robust optimization of contaminant sensor placement for community water systems.. United States.
Konjevod, Goran, Carr, Robert D, Greenberg, Harvey J, Hart, William Eugene, Morrison, Tod, Phillips, Cynthia Ann, Lin, Henry, and Lauer, Erik. 2004. "Robust optimization of contaminant sensor placement for community water systems.". United States.
@article{osti_990958,
title = {Robust optimization of contaminant sensor placement for community water systems.},
author = {Konjevod, Goran and Carr, Robert D and Greenberg, Harvey J and Hart, William Eugene and Morrison, Tod and Phillips, Cynthia Ann and Lin, Henry and Lauer, Erik},
abstractNote = {We present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected.We formulate sensor placement problems as mixed-integer programs, for which the objective coefficients are not known with certainty. We consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data, and we define three robust optimization models that differ in how the coefficients in the objective vary. Under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients. Under other assumptions, we can apply sorting to solve each worst-case realization efficiently, or we can apply duality to integrate the worst-case outcome and have one integer program. The most difficult case is where the objective parameters are bilinear, and we prove its complexity is NP-hard even under simplifying assumptions. We consider a relaxation that provides an approximation, giving an overall guarantee of nearoptimality when used with branch-and-bound search. We present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications.},
doi = {},
url = {https://www.osti.gov/biblio/990958}, journal = {Proposed for publication in Mathematical Programming Series B.},
issn = {0025-5610},
number = 1,
volume = 107,
place = {United States},
year = {Wed Sep 01 00:00:00 EDT 2004},
month = {Wed Sep 01 00:00:00 EDT 2004}
}