Investigation Of The Machanism Of Evolutionary Algorithms For The Optimization Of Water Distribution Systems

Urban water distribution systems?WDS?is an important part of the city's infrastructure.It not only protects the daily life of urban residents,but also supports the urban public services and industrial production.The water distribution network is a key part of the water distribution system.When the water distribution system is constructed,the cost of the water distribution pipe network accounts for more than 50%of the total investment.With the development of the city,the demand for urban water distribution is also increasing.In order to meet the complex water distribution requirements,the shape of the water distribution has also changed from a simple tree structure to a large and complex ring network.During the early design,the design method was inefficient and unreasonable,resulting in the design of the pipeline network is mostly unreasonable.As a result,most of the current water distribution pipeline network is in overload operation,and a lot of water resources and funds are wasted every year.Therefore,it is of great significance to optimize the design of the water distribution.At present,evolutionary algorithms have been favored by researchers and related practitioners because of their strong performance and potential in solving nonlinear and multi-modal problems,and are used to solve various complex large-scale water distribution optimizing design.Research on the optimization mechanism and search performance of intelligent algorithm has become the focus of current.Current research on the search mechanism of the EA algorithm is relatively shallow and mostly stays on the surface performance.The real-time measurement index can be used to solve this problem,which can explore the deep mechanism of the algorithm,well show the search characteristics and performance of the algorithm,and provide reference for the selection of the researchers.But most of them are limited to a single algorithm and its variants or the multi-objective.There is little study carried on the comparison of the search characteristics of different types of EA algorithms by using real-time metrics of search behavior in the optimization design of a single target water distribution system.In this study,the genetic algorithm?GA?,the differential evolution?DE?,and the ant colony optimization?ACO?which are the three most widely used and representative EA algorithms are selected as research objects.Five search metrics suitable for these three algorithms are selected and added to the algorithm program,and the program outputs the metric data in real time when it runs.In order to make the research universally applicable,five benchmark WDS optimization design problems with different scales and degrees of complexity were selected.In addition,the three EA algorithms were applied to these five practical cases with appropriate parameters.For relatively small cases?HP34 and EHP34?,the algorithm program was executed 50 times using different random number seeds,while for the three relatively large-scale and relatively complex cases of ZJ₁₆₄,BN₄₅₄,and RN₄₇₆,the algorithm's arithmetic program executed 10 runs using different random number seeds to ensure the validity of the experimental results and to avoid accidental influence on the experimental results.The analysis of the test results proves that the real-time search metrics can effectively reveal the search characteristics of EA.The results show that there are three phases in the process of optimization of EA.In the beginning phase,there is a rapid improvement of the solution quality and a rapid convergence of the solution population.In the middle phase,the speed of the improvement of the solution quality is slower.In the end phase,the efficiency of the improvement of the solution quality is low.Moreover,experimental results show that DE has the overall best ability to find feasible solutions and high-quality solutions for WD design problems.In this study,ACO performed the worst in determining the best solution.If the computational budget is quite limited,GA can find a better solution than DE.These conclusions provide important guidance for the researchers on how to choose the right EA algorithm and provide important supports for the researches on the development of EA in the further.