Application Of Stochastic Programming To Optimal Design Of Aqueduct And Branch Pipe Network

Random variables are seldom considered in the optimum design of water distribution network at present,and all water distribution networks are designed by the determinate optimal methed. The stochastic chance of nodal flow and pipe resistance coefficient doesn't consider in determinate models,the determinate models simplify the factors influencing optimum design in order to establish optimal models,but the stochastic chance of flow and pipe resistance coefficient is ignored to the optimation results.In order to refect impersonally the actual dynamic state of the aqueduct and branch pipe network, and make the optimal design adaptable to practice, this paper takes the minimum annual cost of the system as objective function and the chance-constraint model is established to optimal design of aqueduct and branch pipe network, according to analysis the determinate models.The results are follows:1. In view of the factor influencing gravity conduit optimum design, this paper takes minimum cost of the parallel gravity conduits as objective function,and establishs a linear programming models, and applies simplex method to solve the model.2. Based on the stochastic chance of flow and pipe resistance coefficient, random variable is introduced according to analysis the factor influenci-ng the optimization of pressurizing aqueduct for pumping station,chance constraining programming models of pressurizing aqueduct for pumpings tation is established.3. Random variable is introduced based on the deterministic model of the optimization of branch pipe network ,and chance constraining programming models of pressurizing branch pipe network for pumping station is established to tackle such optimization problem containing random variables. According to the optimal design models of aqueduct and branch pipe network,a genetic algorithm bases on stochastic simulation technique is applied to calculate the models, the calculating examples show the optimal design models are reasonable, the optimation results are adaptable to practice.