The goal is to find the optimal partition of G considering the following objectives and constraints:
| Objectives: | ||
| Minimise cut size: | (1) | |
| Minimise cut weight: | (2) | |
| Minimise sector size imbalance: | (3) | |
| Minimise average customer exposure: | (4) | |
| Minimise maximum customer exposure: | (5) | |
| Minimise average pipe length exposure: | (6) | |
| Minimise maximum pipe exposure: | (7) | |
| Minimise pressure requirements violations (da Conceição Cunha & de Oliveira Sousa 2010): | (8) | |
| Minimise dissipated power (Di Nardo et al. 2013b): | (9) | |
| Minimise elevation difference within sectors: | (10) | |
| Maximise resilience index (Todini 2000): | (11) | |
| Minimise average of water age in the network in last 24 hours: | (12) | |
| Minimise background leakage: | (13) | |
| Subject to (constraints): | ||
| Connectedness of the partitioned network (PN): | (14) | |
| Direct access to a source for each sector: | (15) | |
| Isolation of sectors: | (16) | |
| Sector size constraint: | (17) | |
| Conservation of mass (Walski et al. 2003): | (18) | |
| Conservation of energy (Walski et al. 2003): | (19) | |
| Pressure constraints: | (20) | |
| Water velocity constraint: | (21) | |
| Tanks level constraints: | (22) | |
| (23) | ||
| Decision variables domain: | (24) | |
| Objectives: | ||
| Minimise cut size: | (1) | |
| Minimise cut weight: | (2) | |
| Minimise sector size imbalance: | (3) | |
| Minimise average customer exposure: | (4) | |
| Minimise maximum customer exposure: | (5) | |
| Minimise average pipe length exposure: | (6) | |
| Minimise maximum pipe exposure: | (7) | |
| Minimise pressure requirements violations (da Conceição Cunha & de Oliveira Sousa 2010): | (8) | |
| Minimise dissipated power (Di Nardo et al. 2013b): | (9) | |
| Minimise elevation difference within sectors: | (10) | |
| Maximise resilience index (Todini 2000): | (11) | |
| Minimise average of water age in the network in last 24 hours: | (12) | |
| Minimise background leakage: | (13) | |
| Subject to (constraints): | ||
| Connectedness of the partitioned network (PN): | (14) | |
| Direct access to a source for each sector: | (15) | |
| Isolation of sectors: | (16) | |
| Sector size constraint: | (17) | |
| Conservation of mass (Walski et al. 2003): | (18) | |
| Conservation of energy (Walski et al. 2003): | (19) | |
| Pressure constraints: | (20) | |
| Water velocity constraint: | (21) | |
| Tanks level constraints: | (22) | |
| (23) | ||
| Decision variables domain: | (24) | |