Performance Assessment of a Coupled Particle Swarm Optimization and Network Flow Programming Model for Optimum Water Allocation

Water resources allocation problems are mainly categorized in two classes of simulation and optimization. In most cases, optimization problems due to the number of variables, constraints and nonlinear feasible search space are known as a challenging subject in the literature. In this research, by coupling particle swarm optimization (PSO) algorithm and a network flow programming (NFP) based river basin simulation model, a PSO-NFP hybrid structure is constructed for optimum water allocation planning. In the PSO-NFP model, the NFP core roles as the fast inner simulation engine for finding optimum values for a large number of water discharges in the network links (rivers and canals) and nodes (reservoirs and demands) while the heuristic PSO algorithm forms the outer optimization cover to search for the optimum values of reservoirs capacities and their storage priorities. In order to assess the performance of the PSO-NFP model, three hypothetical test problems are defined, and their equivalent nonlinear mathematical programs are developed in LINGO and the results are compared. Finally, the PSO-NFP model is applied in solving a real river basin water allocation problem. Results indicate that the applied method of coupling PSO and NFP has an efficient ability for handling river basin-scale water resources optimization problems.     

Multi-Objective Design Optimization of Branched Pipeline Systems with Analytical Assessment of Fire Flow Failure Probability

This paper develops a multi-objective optimization approach for incorporating the conditional probability of fire flow failure into the design of branched water networks. To this end, a new analytical probabilistic model was developed to quantify the conditional probability of fire flow failure in branched networks and incorporated into the non-dominated sorting genetic algorithm (NSGA-II). The optimization sought to minimize capital cost through pipe diameter and pump selection and to minimize the conditional probability of fire flow failure. The NSGA-II was applied to two branched networks to generate Pareto-optimal solutions. Results indicated a strategic allocation of pipe and pump capacity with limited fiscal resources and with a reduction in uncertainty of fire flow failure. Interestingly, optimization results for a real branched network supported the industry practice of using a minimum 150 mm distribution main sizing to provide fire flow protection.     

Water Supply Network Optimisation Using Equal Flow Algorithms

Algorithms to optimise water supply networks are developed and compared when a given set of transfer arcs is constrained to carry the same (or proportional) amounts of flow. Initially, a dynamic multi-period mathematical model is designed as a network flow model. A network simplex-based algorithm, Equalflow, and a subgradient-based algorithm, SUBeqf, are then presented. Both algorithms are characterised by polynomial complexity and can solve large-scale instances that arise when considering water system requirements. A specialised interface for water supply networks provides a data input processor to generate the overall multi-period network model in the implementation of the procedures. The implementation of the algorithms allows the consideration of different types of equal flow instances that take place in water resource system optimisation. The performances of the two algorithms and analysis of their computational efficiency with respect to state-of-the-art mathematical programming software are reported, considering equal-flow instances from a synthetically generated network and two water supply systems in the Sardinia region of Italy.     

A Model for Solving the Optimal Water Allocation Problem in River Basins with Network Flow Programming When Introducing Non-Linearities

The allocation of water resources between different users is a traditional problem in many river basins. The objective is to obtain the optimal resource distribution and the associated circulating flows through the system. Network flow programming is a common technique for solving this problem. This optimisation procedure has been used many times for developing applications for concrete water systems, as well as for developing complete decision support systems. As long as many aspects of a river basin are not purely linear, the study of non-linearities will also be of great importance in water resources systems optimisation. This paper presents a generalised model for solving the optimal allocation of water resources in schemes where the objectives are minimising the demand deficits, complying with the required flows in the river and storing water in reservoirs. Evaporation from reservoirs and returns from demands are considered, and an iterative methodology is followed to solve these two non-network constraints. The model was applied to the Duero River basin (Spain). Three different network flow algorithms (Out-of-Kilter, RELAX-IV and NETFLO) were used to solve the allocation problem. Certain convergence issues were detected during the iterative process. There is a need to relate the data from the studied systems with the convergence criterion to be able to find the convergence criterion which yields the best results possible without requiring a long calculation time.     

Non-Uniform Flow Effect on Optimal Waste Load Allocation in Rivers

In this study, the effects of non-uniform flow due to: (i) inflow from tributaries and (ii) the presence of a downstream control structure (such as a weir or a barrage), on the optimal waste load allocation decision and the resulting cost-equity trade-off relationships, have been investigated. These effects are illustrated with in the framework of a typical cost-equity multi-objective optimization model for optimal waste load allocation in rivers. This framework consists of an embedded river water quality simulator with gradually varied flow and transport (BOD-DO) modules and a cost-equity multi-objective optimization model. A multi-objective evolutionary algorithm known as Non-dominated Sorting Genetic Algorithm-II is used for solving the optimization problem. The optimal fraction removal levels, the treatment cost and the system inequity measure are under predicted in certain reaches of the river, if the uniform flow assumption is made, while actually non-uniform flow conditions exist. This effect is quite pronounced when the flow non-uniformity results from a downstream control structure such as a weir.     

缺水型灌区水资源优化调度模型研究

长江针对缺水型灌区的供水特点,以云南曲靖灌区为例,应用大系统分解协调原理,将整个系统设计为两层递阶控制结构;以运行费用和系统缺水量最小作为目标函数,建立了灌区库群系统水资源优化调度模型;对模型权重系数进行了率定;根据系统目标重要性的优先次序,确定了灌区优化配水矩阵;并采用模拟技术与优化技术相结合的途径,进行优化模型的求解,给出了优化决策算法的程序框图,所建模型符合曲靖灌区的实际情况,研究成果可为同类灌区水资源调度运行提供依据.     

黄河流域干流河段水资源调配多目标优化模型

目前黄河水资源的分配手段仍存在不少问题,用水量同比例丰增枯减不利于黄河水量的合理利用,传统的调度方式也无法使资源、社会达到协调发展。根据黄河水资源的实际情况,考虑各地区用水的公平合理性,建立黄河干流河段多目标优化配水模型,采用改进遗传算法来求解河段优化配水问题。结果表明:经过改进遗传算法的优化求解,可以将黄河干流水资源量科学合理地分配到各河段,全区缺水率控制在10%以下,并且满足河道断面的生态流量需求,符合社会、生态对于水资源开发利用的要求,最大程度地发挥了水资源的综合效益。     

Optimal allocation of surface water in regional water management

Surface water is a scarce reource that is applied by various users for a variety of activities. The regulation of surface water use is an element of regional water management at various management levels. At each management level, the allocation of surface water supply capacity is a policy instrument. An optimization model has been formulated to support the evaluation of potential allocations at a particular management level. The model describes the allocation problem as a network, in which arcs represent waterways and nodes represent inlets and locations where there is a demand for surface water supply. The use of surface water for a specific activity at a specific node is referred to as an application, for example, for sprinkling, for use as cooling water, for dissolving effluent, and for conservation of environmental areas. The optimization model generates the optimal allocation of surface water and of surface water supply capacity. The operation of the model was demonstrated by a case study, where it was applied to maximize the expected revenues in agriculture (measured as value added).     

A Model for the Optimal Allocation of Water Resources in a Saltwater Intrusion Area: A Case Study in Pearl River Delta in China

This paper presents a model for the optimal allocation of water resources in saltwater intrusion areas. The model is comprised of four modules: a joint operation of river and reservoirs module (JORRM), a saltwater intrusion analysis module (SIAM), an economic analysis and in-stream ecology demand module (EAIEDM) and a water allocation module (WAM). Considering the social, economic and environmental aspects, the model has three objectives: the maximization of economic interest (OF ₁), maximization of social satisfaction (OF ₂) and the minimization of the amounts of polluted water (OF ₃). A genetic algorithm is also employed to optimize the module. The model has then been applied to a case study of optimization of water resources for the Pearl River Delta in China. The results indicate that there is water shortage in Pearl River Delta and engineering projects are needed to satisfy water demand during the dry season when saltwater intrusion happens. The model provides a useful tool for the operation of reservoirs and freshwater allocation in saltwater intrusion area.     

Self-Adaptive Solution-Space Reduction Algorithm for Multi-Objective Evolutionary Design Optimization of Water Distribution Networks

An effective way to improve the computational efficiency of evolutionary algorithms is to make the solution space of the optimization problem under consideration smaller. A new reliability-based algorithm that does this was developed for water distribution networks. The objectives considered in the formulation of the optimization problem were minimization of the initial construction cost and maximization of the flow entropy as a resilience surrogate. After achieving feasible solutions, the active solution space of the optimization problem was re-set for each pipe in each generation until the end of the optimization. The algorithm re-sets the active solution space by reducing the number of pipe diameter options for each pipe, based on the most likely flow distribution. The main components of the methodology include an optimizer, a hydraulic simulator and an algorithm that calculates the flow entropy for any given network configuration. The methodology developed is generic and self-adaptive, and prior setting of the reduced solution space is not required. A benchmark network in the literature was investigated, and the results showed that the algorithm improved the computational efficiency and quality of the solutions achieved by a considerable margin.     

基于生态优先的渝西地区水资源配置研究

重庆市渝西地区自产水资源短缺,河流生态脆弱,水资源和水环境承载能力不足以支撑区域经济社会可持续发展,水资源配置格局亟需优化。因此,基于MIKE BASIN软件平台建立了渝西水资源配置模型,模拟对象包括区内主要水源工程、用水户和河流;然后从生态基流需水、水生生物需水、基本自净功能需水3个方面分析了河流控制断面生态环境需水量。在此基础上提出了在退还现状生产生活挤占的生态用水和区内水资源优先满足生态环境需水的前提下,以提水利用嘉陵江、长江过境水为主要解决生产生活缺水并补充河流生态环境用水的水资源配置方案。     

关于我国水权制度建设若干问题的思考

我国的国情和水情决定了建立水权制度的必要性和紧迫性。水权的内涵非常丰富。包括流域的生态水权和环境水权、社会经济水权、国家预留水权等，水权初始分配应按照公平性、以现状为基础协商调整、效率性、供水优先序、总量控制、保护弱势群体、权利和义务统一性等原则。在这些原则下，考虑国家预留水权、农业水权，以及水权分配与总量控制、定额管理、取水许可等。     

Joint Entropy Based Multi-Objective Evolutionary Optimization of Water Distribution Networks

It is essential to consider resilience when designing any water distribution network and surrogate measures of resilience are used frequently as accurate measures often impose prohibitive computational demands in optimization algorithms. Previous design optimization algorithms based on flow entropy have essentially employed a single loading condition because the flow entropy concept formally has not been extended to multiple loading conditions in water distribution networks. However, in practice, water distribution networks must satisfy multiple loading conditions. The aim of the research was to close the gap between the prevailing entropy-based design optimization approaches based on one loading condition essentially and water distribution practice that must address multiple loading conditions. A methodology was developed and applied to a real-world water distribution network in the literature, based on the concept of the joint entropy of independent probability schemes. The results demonstrated that the critical loading conditions were design specific. In other words, the critical loading and operating conditions cannot readily be determined beforehand. Consequently, maximizing the joint entropy provided the most consistently competitive solutions in terms of the balance between cost and resilience. The results were derived using a penalty-free genetic algorithm with three objectives. Compared to previous research using flow entropy based on a single loading condition and two objectives, there was a substantial increase of 274% in the number of nondominated solutions achieved.     

Multi-Objective Surface Water Resource Management Considering Conflict Resolution and Utility Function Optimization

In the present research, a multi-objective model is developed for surface water resource management in the river basin area which is connected to the lake. This model considers different components of sustainable water resource management including economic, social and environmental aspects, and simultaneously tries to resolve conflicts between different stakeholders by means of non-symmetric Nash bargaining, which is linked to the multi-objective optimization method. This study proposes a new methodology to improve Nash Conflict Resolution through finding the optimum degree of the utility function. The proposed model is examined in the Zarrineh River basin in Iran. The results show that the amount of available resources or volume of reservoirs play a significant role in determining the optimal degree of the utility function and efficiency of the proposed method in such a way that the higher amount of resources or the larger reservoirs will result in the higher optimal degree of the utility function. In the proposed multi-objective model, two different amounts of surface water inflow are considered. The first assumed amount is the long-term average flow rate and the second one is equal to 80% of the first mode, which is reduced based on the estimated impacts of climate changes. This multi-objective allocation model could supply 100 and 97.5% of the environmental demand of Lake Urmia in the first and second situations, respectively.     

Layout and Component Size Optimization of Sewer Network Using Spanning Tree and Modified PSO Algorithm

In the paper, a new method is introduced for optimally solve the problem of the layout and component size determination of sewer network. Simultaneously Layout and component size optimization of sewer network problem consists of many hydraulic constraints which are generally nonlinear and discrete; which creates a challenge even to the modern heuristic search methods. An algorithm generation of a predefined number of spanning trees is introduced to generate a predefined number of sewer layouts of a base sewer network in order of increasing length. These generated layouts are sorted in ascending order of total cumulative flow and sorted layouts are individually optimized for sewer components sizing. It has been found that the optimal sewer layout for total system optimization is one where the total cumulative flow has the minimal value. The modified particle swarm optimization (MPSO) algorithm has been used to optimally determine the component sizes of the selected layouts. The proposed method is applied to the Sudarshanpura sewer network (situated in Jaipur, India) design problem. The results are presented for optimal cost vs cumulative flow of the layouts. Further results of MPSO has been compared with the original PSO algorithm.     

SCE-UA-PP水量分配模型及应用

基于公平和效率原则,构建水量分配指标体系和水量分配投影寻踪(PP)模型。利用SCE-UA算法对PP模型最佳投影方向进行优化,构建SCE-UA-PP水量分配模型,以文山州水资源三级区水量分配为例进行实例研究,并与分类权重法分配结果进行对比。结果表明:SCE-UA算法具有较快的收敛速度、较高的寻优精度和较好的收敛稳定性。SCE-UA-PP模型水量分配结果较目前分类权重法分配结果更科学、客观。模型及方法可为水量分配提供参考和借鉴。     

An Optimization Strategy for Water Distribution Networks

An optimization strategy based on head losses minimization is developed for the least cost design of water distribution networks. A new weighting approach is suggested for calculating the initial flow distribution and optimum pipe diameters of the weighted flow distribution is presented by using least square method. In the mean time homogenous and isotropous head losses are maintained with implications of head loss path choice. The model is employed for designing and/or modifying pipe sizes while the classical Hardy-Cross network solver is used to balance the flows. The whole algorithm is programmed and applied to a two-looped network selected from the literature and the results are presented on a comparative basis. A FORTRAN software with the necessary steps in the flow chart is written for the optimization calculations in this paper.     

Optimal Reservoir Operation with Water Supply Enhancement and Flood Mitigation Objectives Using an Optimization-Simulation Approach

Floods are one of the most destructive natural disasters which compensation of their effects inflicts immense costs especially in areas with human developments such as cities. Moreover, supplying water for demands particularly during the drought period is a challenging issue in water resource planning. The aim of this study is to propose a model for optimal operation of a reservoir with enhancing downstream demands supply and flood damage mitigation objectives. The model is developed by coupling MODSIM, river network simulation DSS with the imperialist competitive optimization algorithm (ICA). Gotvand Dam in southwestern Iran is the case of study and amounts of water storage in the reservoir in daily time-steps are the decision variable. Results indicate efficiency of the proposed optimization-simulation approach, suggesting that flood damages can be controlled with proper planning while ensuring that downstream water demands are satisfied. As an instance of results, the optimum reservoir rule curve obtained by the proposed model is able to manage a flood entering to the reservoir 11 times greater than the safe flow in the downstream reach and release it lower than the safe flow rate.     

基于区间犹豫模糊语言集的水资源多目标决策

以鄂北水资源配置工程为对象,研究大型调水工程背景下的多水源多目标优化配置。将鄂北地区水库分为充蓄水库、补偿水库与在线水库等3类,根据各类水库特点对鄂北水资源配置工程进行系统概化,建立以年缺水量最小和调水成本最低为目标函数的多水源多目标优化配置模型。采用权重系数法进行求解得到非劣解集。最后采用基于区间犹豫模糊语言与TOPSIS的多目标决策方法对各方案的缺水量与调水量作出评价并遴选出最优方案。研究结果表明:对鄂北水资源配置工程而言,缺水量与调水量的权重比为7∶3的方案综合评价最优,重视缺水的同时兼顾调水成本;基于区间犹豫模糊语言集与TOPSIS的水资源多目标决策方法经本文实例验证具有较高的稳定性与可行性。     

IB-ICCMSP: An Integrated Irrigation Water Optimal Allocation and Planning Model Based on Inventory Theory under Uncertainty

In this study, an inventory-theory-based inexact chance-constrained multi-stage stochastic programming (IB-ICCMSP) model under multi-uncertainties is developed. IB-ICCMSP integrates inventory theory into an inexact chance-constrained multi-stage stochastic optimization framework. This method can not only effectively address system multiple uncertainties (e.g. discrete intervals and probability density functions) and dynamic features, but also provide water transferring and allocating schemes among multiple stages. The developed model is applied to irrigation water allocation optimization system in Zhangye City, Gansu province, China. Based on the runoff simulation prediction of Yingluo Gorge and water supply–demand balance analysis of the 12 irrigation areas in Zhangye City, different optimal irrigation water measures are generated under different flow levels and different probabilities in the planning year. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identifying desired water-allocation plans for irrigation under multi-uncertainties.