Application of Dynamic Programming Method in Optimization of Water Distribution Pipe Network

With a water-supply network by dynamic programming. The minimal as an example, the network was optimized annual discounted costs were taken as an objective function and node pressure etc. as constraint conditions. The alternative pipe diameters were optimized as per enumeration method and the group allowing objective function with the least values would be the optimized one. It is proved the optimized pipe network reduced by 11.49% in terms of cost and the optimized ben- efits proved much significant.

Conjunctive Use of Engineering and Optimization in Water Distribution System Design

Water Distribution Systems (WDSs) design and operation are usually done on a case-by-case basis. Numerous models have been proposed in the literature to solve specific problems in this field. The implementation of these models to any real-world WDS optimization problem is left to the discretion of designers who lack the necessary tools that will guide them in the decision-making process for a given WDS design project. Practitioners are not always very familiar with optimization applied to water network design. This results in a quasi-exclusive use of engineering judgment when dealing with this issue. In order to support a decision process in this field, the present article suggests a step-by-step approach to solve the multi-objective design problem by using both engineering and optimization. A genetic algorithm is proposed as the optimization tool and the targeted objectives are: 1) to minimize the total cost (capital and operation), 2) to minimize the residence time of the water within the system and 3) to maximize a network reliability metric. The results of the case study show that preliminary analysis can significantly reduce decision variables and computational burden. Therefore, the approach will help network design practitioners to reduce optimization problems to a more manageable size.

Multi-objective Optimisation Design of Water Distribution Systems:Comparison of Two Evolutionary Algorithms

In order to compare two advanced multi-objective evolutionary algorithms,a multi-objective water distribution problem is formulated in this paper.The multi-objective optimization has received more attention in the water distribution system design.On the one hand the cost of water distribution system including capital,operational,and maintenance cost is mostly concerned issue by the utilities all the time;on the other hand improving the performance of water distribution systems is of equivalent importance,which is often conflicting with the previous goal.Many performance metrics of water networks are developed in recent years,including total or maximum pressure deficit,resilience,inequity,probabilistic robustness,and risk measure.In this paper,a new resilience metric based on the energy analysis of water distribution systems is proposed.Two optimization objectives are comprised of capital cost and the new resilience index.A heuristic algorithm,speedconstrained multi-objective particle swarm optimization( SMPSO) extended on the basis of the multi-objective particle swarm algorithm,is introduced to compare with another state-of-the-art heuristic algorithm,NSGA-II.The solutions are evaluated by two metrics,namely spread and hypervolume.To illustrate the capability of SMPSO to efficiently identify good designs,two benchmark problems( two-loop network and Hanoi network) are employed.From several aspects the results demonstrate that SMPSO is a competitive and potential tool to tackle with the optimization problem of complex systems.

Distributed versus Lumped Optimization of Cropping Pattern and Water Resources Utilization

Several whole-farm agro-economic optimization models have been developed to deal with lumped planning issues in the agriculture sector. However, these models cannot be used to devise appropriate management strategies at land parcel level, because of the differences between farm characteristics, and the increased complexity of the hydrological processes. Based on Spatial Farm Database (SFD) which is consisted of a number of farm-level spatial data, including location, paddock properties, owner specifications and budgets, it is possible to provide the farm manager with some suggestions regarding the optimal choice of crops and the area to be allocated for each one. To this end, genetic algorithm is used in order to cope with model nonlinearity and a large number of decision variables. In order to test the proposed model, the Mobarakabad district is modeled with 126 agriculture fields, and the optimization model is run for this area. Results showed that the optimization procedure can find more realistic farm-level optimal solutions due to its advantage in adequate modeling of field characteristics, common groundwater resources, and the associated constraints. The results of lumped optimizations could also be used as benchmarks for the purposes of comparison and interpretation.

Hydraulic Reliability Assessment and Optimal Rehabilitation/Upgrading Schedule for Water Distribution Systems

This paper develops an innovative approach to optimize a long-term rehabilitation and upgrading schedule (RUS) for a water distribution system with considering both hydraulic failure and mechanical performance failure circumstances. The proposed approach assesses hydraulic reliability dynamically and then optimizes the long-term RUS in sequence for a water distribution system. The uncertain hydraulic parameters are treated as random numbers in a stochastic hydraulic reliability assessment. The methodologies used for optimization in a stochastic environment are: Monte Carlo Simulation, EPANET Simulation, Genetic Algorithms, Shamir and Howard’s Exponential Model, Threshold Break Rate Model and Two-Stage Optimization Model. The proposed approach is conducted on a simulation model of water distribution network in a computer by two universal codes, namely the hydraulic reliability code and the optimal RUS code. The applicability of this approach is verified in an example of a benchmark water distribution network.

STUDY ON OPTIMAL CONTROL OF MUNICIPAL WATER DISTRIBUTION NETWORK

A systematic investigation is made on the problems which are related to the optimal control of the municipal water distribution network.A mathematical model of forecasting the water short term demand is proposed using the time series trigonometric function analysis method;the service discharge based macroscopic model of network performance is established using the network structuring method;a relatively satisfactory mathematical model for the optimal control of water distribution network is put forward in view of security and economy,and solved by the constrained mixed discrete variable complex arithmetic.The model is applied in many examples and the results are satisfactory.

Optimal operation of water distribution networks under local pipe failures

The optimal operation of water distribution networks under local pipe failures, such as water main breaks, was proposed. Based on a hydraulic analysis and a simulation of water distribution networks, a macroscopic model for a network under a local pipe failure was established by the statistical regression. After the operation objectives under a local pipe failure were determined, the optimal operation model was developed and solved by the genetic algorithm. The program was developed and examined by a city distribution network. The optimal operation alternative shows that the electricity cost is saved approximately 11%, the income of the water corporation is increased approximately 5%, and the pressure in the water distribution network is distributed evenly to ensure the network safe operation. Therefore, the proposed method for optimal operation under local pipe failure is feasible and cost-effective.

Game Theory Applications in a Water Distribution Problem

A water distribution problem in the Mexican Valley is modeled first as a three-person noncooperative game. Each player has a five-dimensional strategy vector, the strategy sets are defined by 15 linear constraints, and the three payoff functions are also linear. A nonlinear optimization problem is first formulated to obtain the Nash equilibrium based on the Kuhn-Tucker conditions, and then, duality theorem is used to develop a computational procedure. The problem can also be considered as a conflict between the three players. The non-symmetric Nash bargaining solution is suggested to find the solution. Multiobjective programming is an alternative solution concept, when the water supply of the three players are the objectives, and the water authority is considered to be the decision maker. The optimal water distribution strategies are determined by using these solution concepts and methods.

Optimization of the Open Degree of Key Valves Based on Relative Entropy and Pipeline Leakage

Based on information entropy theory, the definition of relative entropy, and the relative entropy minimum principle, this study establishes a multi-objective optimization model for a key valve opening of an urban water distribution network (WDN). Each node pressure is taken as the main research object to reduce pipeline leakage. Moreover, genetic algorithm is applied in the proposed model to solve the key valve opening of the actual WDN in a city in southern China. Using the proposed model, the relevant decision variables of a WDN can be optimized to provide a new manner of network dispatching. © 2017, Tianjin University and Springer-Verlag GmbH Germany.

RESEARCH ON MATHEMATICAL SIMULATION OF RESIDUAL CHLORINE DECAY AND OPTIMIZATION OF CHLORINATION ALLOCATION OF URBAN WATER DISTRIBUTION SYSTEM

The concentration of Residual Chlorine (RC) frequently violates the standard in situations of urban water distribution system with large water supply area and long time of distribution. If chlorine dosage increases within water treatment plant, although RC in distribution system could meet water quality standard, Disinfection By-Products (DBPs) such as hydrocarbon halide rises. In the paper, a mathematical model of chlorine allocation optimization was presented based on reaction kinetics mechanism and optimization theory to solve the problem. The model includes the objective function of minimizing annual operation cost and constraints of RC standard and rational chlorination station distribution, and solving by 0-1 Integer Programming (IP). The model had been applied to a real water distribution system. The simulation results of the model showed that adding chlorine in water distribution system remarkably improved water quality and reduced the operation cost by 49.3% per year less than chlorine dosed only in water treatment plant to meet RC standard. The results prove adding chlorine in water distribution system based on the model can bring both technological and economic advancement.

基于代理指标的供水管网抗震改造优化

基于水力模型计算的管网供水量满足率(SSIQ)指标,是评估供水管网震后性能的常用指标。在供水管网抗震改造优化模型中,若采用SSIQ表示优化目标函数,优化求解需进行大量水力模型计算,计算耗时很长。为减小管网抗震改造优化模型的计算量,对节点流量韧性指标(FR)进行了改进,增加了管道破坏漏水能量损失的影响项,提出了一种管网能量指标(Energy Resilience, ER)表示震后管网性能;以ER指标作为SSIQ的代理指标,用于量化抗震改造优化模型的目标函数。仅通过管道地震失效概率、管网震前正常运行工况的水力参数计算ER指标,不必进行震后管网水力模型计算,以期提升优化模型计算效率。以供水管网震后性能最大化和改造费用最小化为目标,以管道抗震改造措施为优化变量,建立了管网抗震改造多目标优化模型,并比较了ER指标、FR指标以及两个拓扑代理指标的替代效果。案例管网应用结果表明,ER指标与SSIQ指标相关系数呈现强相关性,基于ER指标的优化方案与基于SSIQ指标的优化方案的差异小于3%,ER指标优化模型计算时间不足SSIQ指标优化模型计算时间的1%。

换热站并联水泵分布式优化控制

针对现有换热站并联水泵优化算法在集中式架构下控制适应性不足的问题,本文提出了一种改进的分布式并联水泵优化算法.首先,建立了并联水泵的分布式控制系统,并对该优化问题的数学模型进行描述,在目标函数中引入自适应非线性因子;然后,设计了改进的分布式果蝇优化算法,在该算法中每台水泵的控制器仅通过与邻居控制器交互信息即可完成并联水泵的优化;并且,在嗅觉搜索阶段,使用正弦余弦策略替代赋予个体距离与方向的随机策略;最后,以两个实际换热站中不同并联水泵系统为例对算法进行仿真验证,并基于仿真结果进行性能分析.结果表明,相较于传统算法,改进的分布式果蝇优化算法能得到更优的控制策略,有着收敛速度快、稳定性好和鲁棒性强的特点;并且该算法适用于不同系统的并联水泵优化问题,具有可扩展性.在实际工程验证中相较于集中式算法,该算法在总功率和计算时间上分别平均降低了5.47%和29.90%,因此,能够满足实际换热站中对并联水泵热负荷优化分配的需求.

Optimal locations of monitoring stations in water distribution systems under multiple demand patterns： a flaw of demand coverage method and modification

A flaw of demand coverage method in solving optimal monitoring stations problem under multiple demand patterns was identified in this paper. In the demand coverage method, the demand coverage of each set of monitoring stations is calculated by accumulating their demand coverage under each demand pattern, and the impact of temporal distribution between different time periods or demand patterns is ignored. This could lead to miscalculation of the optimal locations of the monitoring stations. To overcome this flaw, this paper presents a Demand Coverage Index （DCI） based method. The optimization considers extended period unsteady hydrau- lics due to the change of nodal demands with time. The method is cast in a genetic algorithm framework for integration with Environmental Protection Agency Net （EPANET） and is demonstrated through example applica- tions. Results show that the set of optimal locations of monitoring stations obtained using the DCI method can represent the water quality of water distribution systems under multiple demand patterns better than the one obtained using previous methods.

A comparative study of differential evolution and genetic algorithms for optimizing the design of water distribution systems

The differential evolution （DE） algorithm has been received increasing attention in terms of optimizing the design for the water distribution systems （WDSs）. This paper aims to carry out a comprehensive performarice comparison between the new emerged DE algorithm and the most popular algorithm-the genetic algorithm （GA）. A total of six benchmark WDS case studies were used with the number of decision variables ranging from 8 to 454. A preliminary sensitivity analysis was performed to select the most effective parameter values for both algorithms to enable the fair comparison. It is observed from the results that the DE algorithm consistently outperforms the GA in terms of both efficiency and the solution quality for each case study. Additionally, the DE algorithm was also compared with the previously published optimization algorithms based on the results for those six case studies, indicating that the DE exhibits comparable performance with other algorithms. It can be concluded that the DE is a newly promising optimization algorithm in the design of WDSs.

泵站-水库原水调水系统经济运行方式优化

为提高泵站-水库原水调水系统中泵站的运行效益,最大限度降低输水系统的运行成本.通过分析该类输水系统特性以及供水方式,基于遗传算法构建泵站机组流量分配模型,优化分配泵站运行流量.在此基础上,考虑泵站时间维度上的运行方式,结合亳州加压泵站的工程状况和区域分时电价,以单位提水费用最小为优化目标,构建经济运行模型.将该方法应用于亳州供水工程,结果表明模型效果显著,并对历史运行区间内周期输水量进行离散计算,拟合得出周期内单位提水费用最低工况,进而对拟合结果进行分析.结果表明:所构建经济运行模型具有较好的适用性,可降低工程运行费用,为工程优化调度提供指导;受到泵站运行效率和分时电价的影响,泵站单位提水费用随调水量增加先降低后升高.

基于供水量的两级渠系优化配水模型

【目的】基于灌区实际供水量构建两级渠系优化配水模型,提供各用水单元的配水量、配水流量、配水时间。【方法】本文分2种情形构建模型,情形1:非充分灌溉,作物某生育时期内供水无法满足需水,模型首先通过水资源配置确定每个用水户的分配水量,再通过渠系优化配水模型确定每条渠道的配水流量和配水时间;情形2:充分灌溉,供水能够满足需水,根据配置系数确定各渠道配水的优先次序,再确定配水流量和配水时间。【结果】将模型运用到山东省簸箕李灌区,验证模型的适用性,结果表明本模型能够根据灌区的供水量提供水资源配置方案和渠系配水方案。供水充足时,模型根据配置系数确定配水次序;供水不足时,模型根据分配系数确定水资源分配量。情形1和情形2支渠的配水流量分别在流量上限的0.8倍与0.75倍以上,做到了大流量配水;2种情形的配水周期分别为10.90、17.84 d,缩短了灌溉周期。【结论】本文建立的模型能够依据供水量首先提供水资源分配方案或配置次序,再以此为基础,提供配水方案,即配水流量、配水开始时间、配水结束时间,从而指导灌区的配水工作。

THE OPTIMAL DESIGN BASED ON RELIABILITY OF WATER DISTRIBUTION SYSTEM BY LINEAR MODEL

In this paper, a new technique are developed for optimal design of water distribution system besed on reliability. It applies a linear programming algorithm to the optimal design based on reliability. Within a small optimal search step range,the objective function and constraints can be expressed in the first order Taylor-expanding form,and three sub-models (a steady-state simulation model, a reliability model and a linear optimization model) are linked each in optimal searches. Thus, a traditional non linear problem can be solved by a linear model, the computing burden is significantly decreased. Therefore, the linear optimal model developed by the paper has more practical significance.

Convexification and Hierarchical Optimization Algorithm for Distribution of Water Supply Systems

This paper deals with the optimal distribution problem of large urban water supply systems in our country.The mathematical model of the problem is developed.It possesses the separable,but nonconvex structure.In order for primal-dual methods to be applicable to this type of largescale and nonconvex optimization problem,a method by means of which a nonconvex problem is convexified is studied based on the principle of the multiplier methods in the paper.The decomposition-coordination optimization algorithm is proposed based on the convexification method and the multiplier methods.The algorithm has been simulated in some real urban water supply systems,and the satisfactory results are obtained.

明渠模型预测控制快速优化计算方法

针对基于圣维南方程使用启发式算法进行渠道预测控制时,现有优化计算方法生成调控方案时间过长、无法满足实时控制需求的问题,提出了一种基于多目标优化算法的快速优化方法.以一处试验渠道的数值模型作为控制对象,应用此方法构建了预测控制模型以生成调控方案,并构建了一维水动力模型对调控方案进行验证.研究发现在闸门控制系统中,超出水位控制范围的最大值最小、超出水位控制范围的平均值最小、闸门动作次数最少、闸门开度总变化量最小4个目标间能够相互诱导,加速优化计算过程4倍以上.在该试验渠道的流量计划调整工况中,验证了此种方法的有效性,将单次计算时间缩短至1 s内.验证效果表明,该方法在提高了水位控制效果的同时,能够减少由单独设置超出水位控制范围的最大值最小目标导致的非必要闸门调控,总计减少69%的闸门调控次数.

农业灌溉水资源优化配置研究进展

水资源短缺是制约农业可持续发展的关键因素,因此农业灌溉水资源的优化配置对于保障粮食安全和水安全具有重要意义。该研究基于农业灌溉水资源优化配置的主要类型,对单一作物灌溉优化决策、多作物水土资源优化配置和灌溉渠系水资源优化调度3个方面的研究进展进行了系统综述。同时指出了当前农业灌溉水资源优化配置中存在的主要问题和未来研究方向,研究认为当前的农业灌溉水资源优化配置应在如下4个方面进行完善:1)建立更具生理意义的作物水分-产量-品质模型;2)在气候变化和人类活动的情景下实现农业灌溉水资源的优化配置;3)构建全面考虑水源、渠系、灌区面积、作物配置以及生育阶段的系统性农业灌溉水资源优化配置模型;4)建立以棵间蒸发最小为目标的动态灌溉优化决策模型。研究可为中国的粮食安全和水安全提供理论指导。