*2.6. Resilience Indicator*

In this study, Todini [40]'s resilience is quantified from a range of designs of the Anytown network and compared with seismic reliability. Todini [40] introduced a resilience index to quantify the resilience of looped network. Resilience is defined as surplus power available within the network as a percentage of net input power as:

$$\text{Resil} = \frac{\sum\_{\text{j}}^{\text{m}} \text{Q}\_{\text{req}\text{j}} \left( \text{H}\_{\text{j}} - \text{H}\_{\text{req}\text{j}} \right)}{\sum\_{\text{k}=1}^{\text{n}\text{r}} \text{Q}\_{\text{k}} \text{H}\_{\text{k}} + \sum\_{\text{l}=1}^{\text{n}\text{p}} \frac{\text{Power}\_{\text{i}}}{\gamma} - \sum\_{\text{j}}^{\text{m}} \text{Q}\_{\text{req}\text{j}} \text{H}\_{\text{neq}}} \tag{11}$$

where Hj = total head of the jth node; Qk = flow provided by reservoir k (m3/s); Hk = head at reservoir k; Poweri = power of the ith pump (Nm/s); γ = specific weight of water (N/m3); nr and np = number of reservoir and pumps, respectively. Note that this indicator was used only for a postoptimization analysis.

Todini's resilience is one of the most popular and widely used surrogate measures of WDS reliability. Farmani *et al.* [53] investigated the trade-off between economic cost and the resilience for a rehabilitation problem of the Anytown network. Prasad and Park [54] proposed a multiobjective optimization approach to minimize cost and maximize modified version of Todini's resilience indicator. Recently, Gheisi and Naser [55] compared entropy-based reliability, Todini's resilience, and three modified versions of Todini's resilience in the twenty-two potential pipe layouts of a hypothetical network.
