Two objectives are considered, minimisation of the total capital cost associated with pipe components and maximisation of the network resilience. The mathematical expression of each objective is given in Eq. 1 and Eq. 2, respectively.
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(1) |
Where C=total cost (monetary units problem dependant); np=number of pipes; Uc=unit pipe cost depending on the diameter selected in a specific problem; Di=diameter of pipe i; Li=length of pipe i.
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(2) |
Where In=network resilience; nn=number of demand nodes; Cj, Qj, Hj and Hjreq=uniformity, demand, actual head and minimum head of node j; nr=number of reservoirs; Qk and Hk=discharge and actual head of reservoir k; npu=number of pumps; Pi=power of pump i if any; γ=specific weight of water; npj=number of pipes connected to node j; Di=diameter of pipe i connected to demand node j.
