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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