Risk-Based Models for Optimal Sensor Location Problems in Water Networks

Water distribution networks (WDNs), as vital systems of any city, are vulnerable to the intrusion of contamination, and the security of WDNs is of great importance. A promising approach for the protection of WDNs against such threats is to deploy contaminant detection sensors in the network. One of the modeling strategies to identify an appropriate configuration of sensors is the expectation-based model. In this model, the location of sensors is determined so that the expected impact of contamination events is minimized. In this work, we consider two existing expectation-based models that have been presented in the literature. Although both models identified the same optimal sensor placements, choosing the better model in practical implementation may not be clear to practitioners, who must consider complexity and resolution times. This work first answers this question and proves that both models have the same quality-and hence, in terms of solution time, it makes no difference which model is used. As the second contribution of this work, the expectation-based model is extended to incorporate worst-case, value-at-risk (VaR), and conditional VaR (CVaR) measures. Computational results compare the damage of risk-based models with real-world WDNs, and indicate that the CVaR-based model may be an excellent approach to address risk measures in this problem. The CVaR-based model optimizes the CVaR measure and, at the same time, does not cause a significant increase in the optimal value of other risk measures.