Research And Application On The Optimal Design Of Loop Water Distribution Networks Based On Improved Discrete Cuckoo Algorithm

Water distribution system is a bridge linking waterworks with users,and its construction is often costly,the investment of water distribution networks(WDN)accounts for 50%?80%of the total investment.The loop WDN is widely used in urban because of its high reliability and uniform pressure.Therefore,optimizing the loop WDN has direct practical significance to reduce its investment cost.With the rapid development of computer technology and its application software,optimization loop WDN based on intelligent optimization algorithm has become one of the main research direction in WDN design field.Due to its unique logical mind,strong global search ability,fast convergence speed,high solution accuracy,few control parameters and easy implementation,the cuckoo search algorithm(CS)has attracted extensive attention from researchers.However,the optimization design of loop WDN is a type of discrete,strongly constrained and highly nonlinear optimization problem,which is difficult to directly optimization by CS algorithm.Therefore,in this study,the CS algorithm has discretization,coupling EPANET and parameter optimization,so that it applied to the optimization design of loop WDN quickly and effectively.The main research contents of this paper are as follows:(1)Based on the mathematical model of optimization design of loop WDN,the random number generation method and the nest generated by levy flight has improved to realize the CS algorithm discretization.The mathematical model is constructed by taking the minimum investment of WDN as the objective function,taking the pipe diameters as the decision variables,taking the node continuity equation,the energy equation,the node minimum head constraint,the pipe diameter constraint as the constraints.In this mathematical model,the decision variables(pipe diameters)are discrete,and CS algorithm has usually used to solve the continuous optimization problem,so it is necessary to discretize CS algorithm.In this study,the "sample" function in R language is used to generate initial random number,and the new nest generated by Levy flight is modeled and rounded to realize the CS algorithm discretization,so that it can be used to solve discrete optimization design problems.(2)Coupling discrete cuckoo search algorithm(DCS)with hydraulic simulation software EPANET,it is applied to the two-benchmark examples(two-loop WDN and Go Yang WDN)and a specific engineering example(a WDN in Liyang city),and the performance of this optimization method was tested.In order to solve the strong hydraulic constraint in the mathematical model,this study improved the return information based on the EPANET hydraulic calculation engine "epanet2toolkit" R package.The solutions that do not satisfy the constraints have discarded,and a corresponding number of new solutions have generated to replace the discarded solutions,until the reserved candidate solutions in each generation all satisfy the constraints,and finally the coupling between DCS algorithm and EPANET is realized.Subsequently,this algorithm successfully used to optimize the two-benchmark examples(two-loop WDN and Go Yang WDN)and a specific engineering example(a WDN in Liyang city).The investment cost of WDN in Liyang city is 87895723.51 yuan according to the design specification for outdoor water supply,and the optimized investment is 68307492.61 yuan,which saved by about 22.3%.The optimization results show that this optimization method can not only obtain a better design scheme,but also satisfy all constraints,which proves the feasibility of this method.(3)The DCS algorithm is dynamically improved and applied to the two-benchmark examples(two-loop WDN and Go Yang WDN)and a specific engineering example(a WDN in Liyang city),which improved algorithm calculation time and convergence speed.The dynamic abandoned fraction(Pa)is used to replace the fixed fraction(Pa=0.6),which increased the number of population evolution in the later search stage,thus improved the calculation speed of the algorithm.In addition,the step size of Levy flight is dynamically improved,make its value gradually decreases with the iterations increase,so as ensure this algorithm's global optimization ability in the early search stage and the convergence speed in the later search stage.By comparing the optimization results,it is found that in the optimization design of two-loop WDN,the algorithm calculation time has shortened by about 42%,and the convergence speed has increased by about 35%;in the optimization design of Go Yang WDN,the algorithm calculation time has shortened by about 13%,and the convergence speed has increased by about 40%.In the optimization design of a WDN in Liyang city,the algorithm calculation time has shortened by about 32%,and the convergence speed has increased by about 35%In conclusion,in this study,the CS algorithm has discretized,the DCS algorithm has coupled with the EPANET,and the abandonment probability and Levy flight step size are dynamically improved.This study provides technical support for the research on the optimization design of loop WDN and further enriches and develops the optimal theory of loop WDN.