The cost of construction and operation of the water transmission conduits and water distribution networks is constantly increasing along with the development of city, industry and rural economics in our country. There is great economic and social benefit adopting the optimal design to reduce investment and energy consumption of the water transmission conduits and water distribution networks. Based on optimization theories of genetic algorithms and the linear programming, a series of optimal design mathematics models and methods of water transmission conduits and water distribution networks have been presented, in the light of their characteristics. The results are as follows:1 The linear programming models and calculations of the pressure gravity conduit, the gravity pressure conduit and channel, the pressure conduit with pump station and the pressure conduit in considering pump station flow variations are presented respectively.2 The linear programming models and calculations of the single source gravity branch network, the single source branch network with pump station, the branch network with water tower ahead of network, the branch network with water tower back of network and the branch network with water tower in the middle of network are presented respectively.3 The concept of basics pipe segment flow is presented. This is a new approach to determine optimal flow distribution of pipe segment and water source.4 A new method called genetic algorithms- linear programming (GALP) is presented, by which the optimal design a looped water distribution network can be obtained.5 The optimal design mathematics models and calculations of the single source looped network which source pressure is undecided and the single source looped network which source pressure is decided are presented respectively.6 The optimal design mathematics models and calculations of the multi-source and multi-load looped network which source pressure and flow is undecided and the multi-source and multi-load looped network which source pressure and flow is decided are presented respectively, according to analysis load of multi-source looped network.7 The corresponding programs are developed, based on the optimal design mathematics models and calculations of the water transmission conduits and water distribution networks, by adopting MATLAB .A lot of calculating examples show: the optimal design mathematics models are reasonable, the calculation methods is feasible, the economic benefit of optimal design is obvious. |