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Adaptive Dynamic Optimization |
Accidental drinking water contamination has long been and remains a
major threat to water security throughout the world. Consequently,
contamination source identification is an important and difficult
problem in the managing safety in water distribution systems. This
problem involves the characterization of the contaminant source based on
observations that are streaming from a set of sensors in the
distribution network. Since contamination spread in a water
distribution network is relatively quick and unpredictable, rapid
identification of the source location and related characteristics is
important to take contaminant control and containment actions. As the
contaminant event unfolds, the streaming data could be processed over
time to adaptively estimate the source characteristics. This provides
an estimate of the source characteristics at any time after a
contamination event is detected, and this estimate is continually
updated as new observations become available. We pose and solve this
problem using a dynamic optimization procedure that could potentially
provide a real-time response. As time progresses, additional data is
observed at a set of sensors, changing the vector of observations that
should be predicted. Thus, the prediction error function is updated
dynamically, changing the objective function in the optimization model.
We investigate a new multi population-based search using an
evolutionary algorithm (EA) that at any time represents the solution
state that best matches the available observations. The set of
populations migrates to represent updated solution states as new
observations are added over time. At the initial detection period,
non-uniqueness is inherent in the source-identification due to
inadequate information, and, consequently, several solutions may predict
similarly well. To address non-uniqueness at the initial stages of the
search and prevent premature convergence of the EA to an incorrect
solution, the multiple populations in the proposed methodology are
designed to maintain a set of alternative solutions representing
different non-unique solutions. As more observations are added, the EA
solutions not only migrate to better solution states, but also reduce
the number of solutions as the degree of non-uniqueness diminishes.
This new dynamic optimization algorithm adaptively converges to the best
solution(s) to match the observations available at any time. The new
method is being tested for numerous contamination source identification
problems in realistic water distribution networks.
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