Comparison of the robustness-based optimal designs of water distribution systems in three different formulations

Robustness is generally defined as a system's ability to stay within satisfactory bounds against variations in system factors. Recently, robustness has been indicated to be a useful objective function for the optimal design of water distribution systems (WDSs). While various formulations are possible to represent WDS robustness, few efforts have been made to compare the performances of these formulations. This study examined three potential formulations for quantifying system robustness to provide guidelines on the usage of a robustness index. Giustolisi et al.'s robustness index (see Giustolisi et al. (2009) ‘Deterministic versus stochastic design of water distribution networks’, J. Water Resour. Plann. Manage.135 (2), 117–127) was adopted to calculate nodal robustness, while the system robustness was defined using three different formulations: (1) minimum among nodal robustness values; (2) total sum of nodal robustness; and (3) sum of nodal robustness at multiple critical nodes. The three proposed formulations were compared through application to identify the most appropriate one for enhancing system robustness in general; three representative benchmark networks were optimally designed to minimize the economic cost while maximizing the system robustness.