Multi-objective Optimization Design Of Water Supply Network Based On Non-dominated Sorting-differential Evolution Algorithm

Water supply network is an important part of urban water supply system because of its large volume and large investment proportion.Whether the optimal design of water supply network is reasonable or not directly affects the operation and economic benefits of the whole water supply system.For a long time,the optimal design of water supply network is difficult to deal with,because it's an uncertain polynomial problem.Current studies mostly focus on single-objective optimization of pipeline network economy,and pay less attention to the reliability of pipeline network which directly affects the later operation performance of pipeline network.This leads to many problems in real life,such as pipe burst,leakage,insufficient local water supply and high operating and management costs.In the 12 th Five-Year Plan and the 13 th Five-Year Plan,China clearly pointed out that "we should increase investment in water supply facilities" and "strengthen the construction of water supply network".However,if we continue to optimize the design of new water supply network with imperfect single-objective method,it will cause a lot of waste of resources,which is contrary to the current situation of water shortage and the goal of building a resource-saving society in China.Therefore,it is great significance to find a multi-objective optimization design method for water supply network,which can not only realize the economic optimization of the network,but also realize the reliability optimization of the network.Intelligent evolutionary algorithms are a series of emerging algorithms with powerful computing power and optimization capabilities that simulate some natural processes in the biological world.The Differential Evolution Algorithm(Differential Evolution Algorithm,abbreviated as DEA)and the Improved Non-dominated Sorting Genetic Algorithm(Non-dominated Sorting Genetic Algorithm II,abbreviated as NSGA-II)are two algorithms with superior performance in the intelligent evolutionary algorithm,but they are insufficient in dealing with the multi-objective optimization problem of the water supply network.Therefore,based on the theory and characteristics of water supply network optimization design,the DEA and NSGA-IIalgorithm are mixed and improved,and a new algorithm,Non-dominated Sorting-Differential Evolution Algorithm,is proposed,and EPANET and MATLAB software has established a multi-objective optimization design model for water supply network considering both economy and reliability,which provides an effective method for engineering design of actual pipe network.The main work of this paper is as follows:(1)Research and analysis on the theory of optimal design of water supply network.The hydraulic calculation has always been a difficult design point.The EPANET software that can quickly complete hydraulic calculation is introduced into the optimization design of the pipe network.Starting from the source program of EPANET,the dynamic hydraulic simulation of each alternative pipe diameter combination scheme in the optimization process is realized through programming,and after the simulation is finished,the simulated water pressure value at each node of the pipe network is taken out to judge the violation of the constraint.Then,the obtained violation constraint value is used as the judgment basis for the subsequent algorithm optimization,that is,the smaller the violation constraint value is,the better the corresponding pipe diameter combination scheme is.(2)The DEA and the principle of NSGA-II are studied.The disadvantages of the two algorithms in multi-objective optimization design of pipeline network are proposed.Four aspects are proposed: algorithm framework,multi-objective optimization mechanism,elite strategy and diversity.A new algorithm based on two algorithms,which is more suitable for multi-objective optimization design of water supply network-Non-dominated Sorting-Differential Evolution Algorithm.Non-dominated Sorting-differential Evolutionary Algorithm has no limit on the continuity and discreteness of decision variables.It can be directly optimized with discrete commercial pipelines as decision variables.Non-dominated sorting strategy can be used to optimize multiple conflicting optimization objectives.Optimal screening;adopting global-based elite strategy and weight-receiving strategy to maximize the performance of better solutions while ensuring the diversity of the population and improving the search ability of the algorithm.(3)Establish a multi-objective optimization design model for water supplynetwork based on Non-dominated Sorting-Differential Evolution Algorithm.The mathematical model is established based on the cost of pipe network and pipe network flexibility and various constraints.The hydraulic model is established by EPANET,and the algorithm model is established by Non-dominated Sorting-differential Evolution Algorithm.With the help of MATLAB platform,many elements of pipe network optimization design are programmed.The fusion of the three.Finally,according to the specific information of the input pipe network,it can quickly find a multi-objective optimization model of the pipe network that meets the constraint conditions and meets the minimum Pareto optimal solution with the lowest cost of the pipe network and the highest flexibility of the pipe network.(4)Using the double loop network to verify the multi-objective optimization design model of the water supply network based on the Non-dominated Sorting-Differential Evolution Algorithm,the results show that the model is scientific and effective.Using the above proposed model to deal with the optimization problem of ‘the lowest cost of the pipe network-the highest elasticity of the pipe network' in the Hanoi pipe network,a series of optimal combination of pipe diameters has been successfully obtained,which provides a reference for practical engineering.