A two-stage stochastic multi-objective resilience optimization model for network expansion of interdependent power–water networks under disruption

Network expansion of interdependent critical infrastructures under disruption uncertainty is modeled as a mixed-integer two-stage stochastic multi-objective optimization program. In this model, expected total cost and expected post-disaster resilience are considered competing objectives. Network resilience is quantified through network complexity and unmet demand. Functional relationships between critical infrastructures are modeled using a network-based approach with the physical interdependency enforced through demand constraints. Uncertainty is introduced as a set of random parameters corresponding to disruption scenarios. The proposed model is demonstrated in a case study of coupled power–water networks with the power flow in the grid modeled using linear DC power flow approximation equations. The deterministic-equivalent multi-objective model is solved using the augmented $ϵ$-constraint method. Solutions from stochastic and deterministic models are compared and the value of stochastic optimization is discussed.