Keywords: 
• multi-source water supply /
• optimization model /
• network topology /
• urban water supply system /
• NSGA-II /
• Mid-route of South-to-North Water Diversion Project

Abstract: Joint operation of multiple water sources plays a significant role in alleviating the conflict between urban water supply and demand. Firstly, to achieve the effective distribution of various urban water sources, an optimization model based on the network topology of "Source—Plant—User" urban water supply system is proposed. The objectives of this model include social benefit and total water supply cost, subject to the capacity of water sources, water pipes and water plants, and the water demand of users. Secondly, NSGA-II algorithm is applied to solve the model, based on which the optimal condition for the equilibrium solution is obtained. Thirdly, as a case study, the water-supply system in Tianjin city is a complex multi-source water-supply system after the Mid-route of South-to-North Water Diversion Project (SNWDP) begins to divert water to Tianjin. The optimization results show that this model could successfully provide corresponding reasonable allocation solutions compromising social benefit and water supply cost under different wetness and dryness probabilities at water sources. And the causes of water shortage and the existing design deficiency in the urban water supply network could be reflected through result analysis. For example, the water supply capacity (1 473 million m³) of the worst condition could satisfy the water demand of Tianjin (1 377 million m³); whereas, the water shortage of recommended solution, which balances the social benefits and water shortage, is 244 million m³ with water supply cost of 3 260 million yuan due to the capacity restriction of the pipelines under the specific water supply rule. Above all, this model is feasible to a certain extent and provides technical support for ensuring urban water-supply security of Tianjin city.