Problem Formulation

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.


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.


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.