Failures within water distribution systems are usually not isolated and tend to propagate to corresponding transportation infrastructure, yet most criticality and resilience analyses of water distribution networks are conducted for the individual water infrastructure without accounting for interdependence. To address this research gap, this study investigates how the critical components identified within water distribution systems may be different when accounting for failure propagation to the transportation road network. In this study, failure propagation is assumed to be based on geospatial interdependence and unidirectional, starting from water distribution network components to transportation network components. A logical interaction network is constructed considering the interdependence between both infrastructures, and multiobjective optimization is used to solve for the critical water distribution components considering: quantity of failures, performance loss, and financial costs. This work presents a modular workflow for water distribution criticality analysis and proposes the Kolmogorov‐Smirnov distance statistic between solution sets as a measure of the significance of interdependency for decision making. Results from the case study suggest that as the magnitude of water infrastructure failure increases beyond a threshold, the interdependency between water distribution and transportation becomes more significant. The difference between identified critical components using only information from water distribution and using both water distribution and transportation is significantly different (with greater than 95% confidence) for the city of Tampa, when more than 40 components fail (are isolated). These results will assist utilities in asset management and strategy assessment, by helping prioritize component repair and better allocate resources for critical interdependent infrastructures.
We study the fluency map optimization problem in Intensity Modulated Radiation Therapy from a cooperative game theory point of view. We consider the cancerous and healthy organs in a patient’s body as players of a game, where cancerous organs seek to eliminate the cancerous cells and healthy organs seek to receive no harm. The goal is to balance the trade-offs between the utility of players by forming a grand coalition between them. We do so by proposing a methodology that solves a few convex optimization problems in order to transform the fluency map optimization problem into a bargaining game. To solve the bargaining game, we employ the concept of Nash Social Welfare (NSW) optimization due to the desirable efficiency and fairness properties of its outcomes. The proposed NSW optimization is convex and can be solved by powerful commercial solvers such as CPLEX. An additional advantage of the proposed approach is that it has a new control lever for the fluency map optimization, the so-called negotiation powers, which enables practitioners to put more emphasis on an organ by changing its negotiation power. To show the efficacy of our proposed methodology, we apply it to the TG-119 case and a liver case. We compare our proposed approach with a state-of-the-art approach through creating Dose Volume Histograms.
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