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.     

Optimal allocation of water resources in large river basins: II. Application to Yellow River Basin

In this paper, the theoretical approach presented in Part I is demonstrated by means of case study on the optimal allocation water resources for Yellow River Basin of China. The object of the case study was to find the optimization of water allocation among subregions and trunk streams of the basin in order to achieve the maximum national economic benefits and the optimal reservoir storage required to maintain the long-term balance of water resources.The optimal allocation of water resources pattern caters for irrigation, hydropower generation, navigation, water supply and other sectors, depending to a large extent on the objective economic benefits obtained from the whole valley and on the objective of reservoir storage. Other factors incapable of being expressed in terms of the two objectives considered in the section concerning constrained conditions. This research is applicable widely and suitable for the solution of complicated, multi-objective large-system problems involving non-linearity, numerous variables and various constrained conditions. Finally, the results of optimal allocation of water resources for Yellow River Basin (OAWRYRB) have been selected on an optimum basis in accordance with the multi-objective method.The application of our optimization techniques to the Yellow River basic showed that the total water of the Yellow River over a year can be allocated by optimization. The maximum national economic benefits and the optimal reservoir storage required to maintain the long-term balance of water resources can also be obtained by the optimal techniques.     

Robust Methods for Identifying Optimal Reservoir Operation Strategies Using Deterministic and Stochastic Formulations

Water allocation in a competing environment is a major social and economic challenge especially in water stressed semi-arid regions. In developing countries the end users are represented by the water sectors in most parts and conflict over water is resolved at the agency level. In this paper, two reservoir operation optimization models for water allocation to different users are presented. The objective functions of both models are based on the Nash Bargaining Theory which can incorporate the utility functions of the water users and the stakeholders as well as their relative authorities on the water allocation process. The first model is called GA–KNN (Genetic Algorithm–K Nearest Neighborhood) optimization model. In this model, in order to expedite the convergence process of GA, a KNN scheme for estimating initial solutions is used. Also KNN is utilized to develop the operating rules in each month based on the derived optimization results. The second model is called the Bayesian Stochastic GA (BSGA) optimization model. This model considers the joint probability distribution of inflow and its forecast to the reservoir. In this way, the intrinsic and forecast uncertainties of inflow to the reservoir are incorporated. In order to test the proposed models, they are applied to the Satarkhan reservoir system in the north-western part of Iran. The models have unique features in incorporating uncertainties, facilitating the convergence process of GA, and handling finer state variable discretization and utilizing reliability based utility functions for water user sectors. They are compared with the alternative models. Comparisons show the significant value of the proposed models in reservoir operation and supplying the demands of different water users.     

Application of a Genetic Algorithm for the Optimization of a Complex Reservoir System in Tunisia

A genetic algorithm (GA) model is developed and used for optimizing the allocation of water resources within a complex multiple reservoir system located in Tunisia. The GA model considers two objectives: the water allocation to demand centers and the salinity level of the water supply to end users. These two objectives are combined into a single objective function using a weighting factor approach. Five different cases (representing five different weighting factor combinations) were analyzed by the GA model to produce the “optimum” allocation of water resources for each case. The generated solutions exhibited low variability. The results are then compared using a range of system performance indicators to measure reliability, resilience, and vulnerability. The evaluation of the system performance is an essential step to help system managers identify the preferred allocation strategy and it provides a comprehensive insight into system behavior.     

Optimal reservoir operation using Nash bargaining solution and evolutionary algorithms

Optimizing reservoir operation is critical to ongoing sustainable water resources management. However, different stakeholders in reservoir management often have different interests and resource competition may provoke conflicts. Resource competition warrants the use of bargaining solution approaches to develop an optimal operational scheme. In this study, the Nash bargaining solution method was used to formulate an objective function for water allocation in a reservoir. Additionally, the genetic and ant colony optimization algorithms were used to achieve optimal solutions of the objective function. The Mahabad Dam in West Azerbaijan, Iran, was used as a case study site due to its complex water allocation requirements for multiple stakeholders, including agricultural, domestic, industrial, and environmental sectors. The relative weights of different sectors in the objective function were determined using a discrete kernel based on the priorities stipulated by the government (the Lake Urmia National Restoration Program). According to the policies for the agricultural sector, water allocation optimization for different sectors was carried out using three scenarios: (1) the current situation, (2) optimization of the cultivation pattern, and (3) changes to the irrigation system. The results showed that the objective function and the Nash bargaining solution method led to a water utility for all stakeholders of 98%. Furthermore, the two optimization algorithms were used to achieve the global optimal solution of the objective function, and reduced the failure of the domestic sector by 10% while meeting the required objective in water-limited periods. As the conflicts among stakeholders may become more common with a changing climate and an increase in water demand, these results have implications for reservoir operation and associated policies.     

Development of an Optimal Reservoir Operation Scheme Using Extended Evolutionary Computing Algorithms Based on Conflict Resolution Approach: A Case Study

Optimal reservoir operation and water allocation are critical issues in sustainable water resource management due to increasing water demand. Multiplicity of stockholders with different objectives and utilities makes reservoir operation a complicated problem with a variety of constraints and objectives to be considered. In this case, the conflict resolution models can be efficiently used to determine the optimal water allocation scheme considering the utility and relative authority of different stakeholders. In this study, the Nash product is used for formulation of the objective function of a reservoir water allocation model. The Analytic Hierarchy Process (AHP) is used to determine the importance of each stockholder in bargaining for water. The Particle Swarm Optimization algorithm (PSO) and the Imperialism Competitive Algorithm (ICA) are applied to solve the proposed optimization model. System performance indices including reliability, resiliency and vulnerability are used to evaluate the performance of optimization algorithms. The simplest and most often-used reservoir policy (Standard Operating Policy, SOP) is also used in order to evaluate the performance of the proposed models. The proposed model is applied to the Karkheh River-Reservoir system located in south western part of Iran as a case study. Results show the significance of the application of conflict resolution models, such as the Nash theory and proposed optimization algorithms, for water allocation in the regional scale especially in complicated water supply systems.     

Multiobjective management of a contaminated aquifer for agricultural use

Planned utilization of groundwater from a contaminated aquifer requires development of management strategies that determine the spatial distribution of withdrawal for allocation, as well as for control of water quality. Minimization of groundwater allocation for different purposes, and the control of contamination in the aquifer by a specified pumping strategy constitute a management problem with two conflicting objectives. In order to demonstrate possible tradeoffs between water quality control objective and minimum groundwater withdrawal objective, a multiobjective optimization model is formulated. The solution of the model specifies a strategy to control pollution distribution in the aquifer as per agricultural needs, and also evolve an optimal allocation policy to statisfy agricultural demands. Pareto-optimal solutions representing the tradeoff between the two noncommensurate objectives are established. The formulated model uses the embedding technique for simulating the flow and the transport processes in the aquifer. The constraint method is used to transform the multiobjective optimization model into a single objective optimization model. The resulting model is solved using the exterior penalty function method in conjunction with the Hooke-Jeeves method. The proposed model is easily adoptable for various agroclimatic regions and cropping patterns. For illustrative purposes, the model is applied to a specified study area. Although solutions of the model are presented and discussed as per agricultural requirements in terms of both quality and quantity, solutions for other kinds of water demands can be obtained using the same model with minor modifications. Results show that an optimal pumping strategy can be effectively utilized for controlling contamination in the aquifer.     

Optimal Development of Agricultural Sectors in the Basin Based on Economic Efficiency and Social Equality

The limitation of freshwater resources and the growing demand for water, make the issue of water resource development planning and water allocation among stakeholders even more important. Ideally, water allocation should be economically efficient and socially equitable. In this study, a water allocation model is presented in an integrated framework that considers the interaction of water supply and demand according to economic and social factors. To achieve this, a reliability-based multi-objective optimization - simulation approach has been employed. The objective functions of the problem are: 1) maximizing GDP from agricultural sectors and 2) maximizing social equality in different provinces of the basin (measured using the Williamson coefficient). The fair development and allocation among the shared provinces in the basin can reduce conflicts in the region. Karkheh basin has been considered as a case study and decision variables of the problem are area under cultivation of agricultural development sectors in different provinces. The results show that, without harming the income of the agricultural sector, the spatial distribution of development projects can be done in such a way that equality (according to income level and the number of people working in each province) is achieved. One of the solutions of Pareto front compared to previous studies shows that, in addition to an increase of about 12% of the objective function 1 (GDP), the value of the objective function 2 (Williamson coefficient) decreased from 1.19 to 0.98. This indicates a decrease in income inequality among the provinces of the basin.

     

区际调水时空优化配置理论模型探讨

我国水资源供需平衡在空间上的巨大差异造成了区际调水的需求。在决策中常遇到的问题是：是否确实需要调水、调多少水和如何分水。在扣除保障用水(生活、生态、维持生产)之后，这3个问题都决定于调水的经济效益(利润和回报期).为此，本文提出了水资源在时间、部门和空间上的三维优化分配理论模型体系，包括含4类经济目标的目标集、7类变量组合的模型集和6种边际效益类型的边际效益集，由此可以组合成168种优化问题。实际问题可从中挑选对应者进行求解。作为例子，本文给出了若干分析解。     

不确定性多目标模糊规划在水资源优化配置中的应用

在充分考虑水资源系统中供需水不确定性的基础上,基于多目标规划、模糊规划和区间规划原理,以经济效益、社会效益和环境效益最大为目标,以需水量、可供水量和不同子区用水部门间的用水公平性为主要约束,构建一种适用于多水源、多子区、多用户的考虑供需水不确定性的多目标模糊规划模型,以期通过平衡水资源配置系统中用户配置水量、缺水风险与系统收益三者的关系,实现系统综合效益最大。模型以衡水市历年供水、用水及社会经济等数据确定规划年的水资源参数及经济参数,采用区间参数反映系统中的不确定性,通过引入模糊隶属度函数,利用两步交互式算法,将多目标规划转化为单目标规划进行求解,以2025年为衡水市规划水平年,得到规划水平年下的11个子区、4种水源、4个用水行业的最优配水方案。结果表明：本研究制定的水资源优化配置方案可实现“外调水优先利用、地下水控制利用”,同时考虑用水的公平性约束后,在缺水条件下可有效控制水资源向每立方米水效益高的区域和部门流动,有利于多区域、多部门共担缺水风险;该水资源优化配置方案可有效缓解衡水市水资源供需矛盾,实现多水源和多目标之间的协同互补。研究成果可为河北省其他县域的水资源优化配置提供技术参...     

Multiple-objective stochastic waste-load allocation

The practice of waste-load allocation in water quality management involves several noncommensurate and conflicting objectives. In particular, the objectives considered in this multiobjective stochastic waste-load allocation study are (1) maximization of total waste discharge, (2) maximization of instream dissolved oxygen concentration, (3) minimization of difference in equity measures, and (4) maximization of reliability of water quality compliance. To demonstrate the analysis, the model was applied to an example involving six waste dischargers.On sabbatical leave from the Wyoming Water Research Center, University of Wyoming, Laramie, WY 82071, U.S.A.     

Application of multi‐objective analysis to water storage

A multi‐objective analysis was applied to allocation of water storage for food control and irrigation water supply in the Bili‐Bili reservoir in South Sulawesi, Indonesia. In order to recognize the stochastic nature of floods and irrigation demands, the two objectives were measured in terms of expected annual flood damage and expected annual irrigation‐water deficit respectively. The multi‐objective analysis was performed by developing the line of non‐inferior solutions for these two objectives to show how each objective is changed with variation in the allocation of storage.     

Development of a Long-term, Ecologically Oriented Dam Release Plan for the Lake Baiyangdian Sub-basin, Northern China

Using China’s Lake Baiyangdian sub-basin for a case study, we developed an ecologically oriented dam release plan that can be used to define an optimal dam operation scheme that provides both the environmental flows required by bodies of water and wetlands downstream from the Xidayang Reservoir dam and enough water for agricultural, and industrial water users. In addition, we evaluated the benefits that might be provided by modifying releases of water from the reservoir. To attain ecological sustainability in the sub-basin, we used the supply for each water user as a decision variable based on three objectives: (1) to achieve sustainable socioeconomic development; (2) to keep the water volume as close as possible to the ideal environmental flows in the urban rivers of Baoding City; and (3) to keep the water amount as close as possible to Lake Baiyangdian’s ideal environmental water requirements. We used the ideal-point method to provide dimensionless values for the first objective, and then used a weighting method to integrate the three objectives into a single holistic goal. We then used the GAMS/CONOPT software to solve the nonlinear model and predict the optimal results. We discuss the optimal water allocation and ecologically oriented dam release plans for the three scenarios. To determine the limitations of the method, we performed a sensitivity analysis, and discuss the optimal results for different weightings of objectives provided by decision-makers. The results of the optimization analysis provide a set of effective compromises among the target objectives that can guide future management of water releases from the reservoir.     

Integrated Management of a Canal Command in a River Delta using Multi-Objective Techniques

Multi-criteria or multi-objective decision-making is becoming increasingly popular as a decision support tool for natural resource management.Stakeholders as well as the planners can be involved in the decision making process, using this approach. This article deals with the use of multi-criteria (multi-objective) technique in solving some complex problems related to water resource management. Five objectives were considered in the study. The benefit of combining these objective functions with the decisionsupport tool is that the management of land and water resourcescan be made more effectively. Based on this concept, a methodology was developed through this study, for the water managers and decision-makers, to obtain a compromising solutionin terms of area allocated under different crops and the magnitude of farming system variables in a canal command area. This study was under taken in the Mahanadi Delta of India. Multi-objective techniques such as Sequential Linear Fuzzy Programming and Goal Programming were used for their simplicity in computation and flexibility in application. Using Fuzzy programming technique, the objective function values under benefit maximization, production maximization, investmentminimization, labour maximization and labour minimizationwere found to be 44.26 M INR, 8795 tonnes, 42.00 M INR and548 150 man-days, respectively. These results were found tobe quite compromising in nature. Goal programming technique wasalso used to arrive at a consensus in allocation of the resources. It was used to decide the best out of the eight alternative priorities. Results indicated that only five alternative goals (Goal1, Goal2, Goal3, Goal6 and Goal8) had distinct allocations while the other three alternatives (Goal4,Goal5 and Goal7) had allocations similar to either of the abovefive alternatives irrespective of their priority levels. Croppingintensity was found to be the maximum (238%) for two of thegoals (Goal6 and Goal7). Though the results of the study were forthe specific site, the multi-criteria techniques used and therecommendations evolved are of objective nature and are applicable at any location for decision-making.     

Operating Rules of an Irrigation Purposes Reservoir Using Multi-Objective Optimization

A multi-objective optimization technique for the operation of an irrigation reservoir is presented in this paper. The study deals with two different objective functions (OF): the minimization of reservoir release deficit from the irrigation demand (OF1) and the maximization of net benefit by the demand sector (OF2). In the first step, monthly optimization of each individual objective was performed with a deterministic non-linear programming (NLP) algorithm, that gave the lower and upper bounds for the multi-objective analysis. In the second step, multi-objective optimization was performed through the Constraint method that operates by optimising the objective function OF1, while the other (OF2) was constrained to satisfy release strategies generated by the optimization. Non-dominated set of release strategies is generated by parametrically varying the bounds of the constraints obtained from the individual optimal solutions. In the third step, the interactive analytical Step method was applied to find the best compromise solution, between the two OFs, by minimizing the distance of each non-dominated solution to an ideal solution that represents the utopian optimum for both OF1 and OF2. Furthermore, the interactive approach allows to improve the performance of the reservoir in terms of compromise irrigation releases, by changing the OF values until the satisfaction of predetermined criteria fixed by the planners and decision makers. The proposed water allocation model was applied to the Pozzillo reservoir operation, that supplies the Catania Plain irrigation area (Eastern Sicily).     

Optimal Size of Auxiliary Storage Reservoir for Rain Water Harvesting and Better Crop Planning in a Minor Irrigation Project

The scope and feasibility of auxiliary storage reservoir in the outlet command of a flow based minor irrigation project was studied to overcome the inadequate irrigation water availability during the dry season. A multi objective optimization model was developed to determine the optimal size of auxiliary storage reservoir and optimal cropping pattern. Assuming that about 50% main reservoir capacity water will be available for irrigating dry season crops and fixing the first priority level of the objective function as maximization of net seasonal benefit and maximization of cropped area, the optimal surface area for auxiliary storage reservoir as the percentage of the command area was obtained as 17.40% and 10.92%, respectively. The performance of the minor irrigation project significantly increased due to provision of auxiliary storage reservoir. The economic analysis also revealed that the intervention is economically viable.     

丰台区水资源耦合配置模型研究

以丰台区水资源配置系统为研究对象,在分析供需水的基础上,构建双层优化模型,其中从环境角度体现对污染物排放量的严格控制,从经济角度体现区域水资源系统经济效益最大化。最终,体现区域水资源数量和质量的统一和不同需水部门之间的合理配置,并达到环境目标和经济目标的集成化。基于模糊满意度算法求解模型,模型结果表明:丰台区各规划水平年的供水量基本上可以满足各用户的需水要求,其中南水北调工程将在区域水资源配置系统中发挥重要作用。进一步地将双层规划模型和两个传统的单目标优化模型的结果进行对比分析,以期为不同决策者提供的规划方案。     

Modelling Intelligent Water Resources Allocation for Multi-users

This study proposes intelligent water resources allocation strategies for multiple users through hybrid artificial intelligence techniques implemented for reservoir operation optimization and water shortage rate estimation. A two-fold scheme is developed for (1) knowledge acquisition through searching input–output patterns of optimal reservoir operation by optimization methods and (2) the inference system through mapping the current input pattern to estimate the water shortage rate by artificial neural networks (ANNs). The Shihmen Reservoir in northern Taiwan is the study case. We first design nine possible water demand conditions by investigating the changes in historical water supply. With the nine designed conditions and 44-year historical 10-day reservoir inflow data collected during the growth season (3 months) of the first paddy crop, we first conduct the optimization search of reservoir operation by using the non-dominated sorting genetic algorithm-II (NSGA-II) in consideration of agricultural and public water demands simultaneously. The simulation method is used as a comparative model to the NSGA-II. Results demonstrate that the NSGA-II can suitably search the optimal water allocation series and obtain much lower seasonal water shortage rates than those of the simulation method. Then seasonal water shortage rates in response to future water demands for both sectors are estimated by using the adaptive network fuzzy inference system (ANFIS). The back-propagation neural network (BPNN) is adopted as a comparative model to the ANFIS. During model construction, future water demands, predicted monthly inflows (or seasonal inflow) of the reservoir in the next coming quarter and historical initial reservoir storages configure the input patterns while the optimal seasonal water shortage rates obtained from the NSGA-II serve as output targets (training targets) for both neural networks. Results indicate that the ANFIS and the BPNN models produce almost equally good performance in estimating water shortage rates, yet the ANFIS model produces even better stability. The reliability of the proposed scheme is further examined by scenario analysis. The scenario analysis indicates that an increase in public water demand or a decrease in agricultural water demand would bring more impacts of water supply on agricultural sectors than public sectors. Similarly, a bigger decrease in inflow amount would obviously bring more influence on agricultural sectors than public one. Consequently, given predicted inflow, decision makers can pre-experience the possible outcomes in response to competing water demands through the estimation models in order to determine adequate water supply as well as preparedness measures, if needed, for drought mitigation.     

Bi-objective analysis of waste load allocation using fuzzy linear programming

Because of its complexity from both a legal and economic standpoint, the problem of optimal waste load allocation is multiobjective by nature and should be treated accordingly. To perform this task, an optimization technique known as fuzzy linear programming is utilized in solving a multiple-discharge, two-objective waste load allocation problem. The two objectives considered are: (1) the maximization of waste discharge and (2) the minimization of the largest difference in equity measure between the various dischargers. Results from this study reveal that fuzzy linear programming is a valuable tool for solving the multiple-objective water quality management problems. Moreover, it is shown that the selection of a linear or logistic membership function in providing preference criteria between the two objects, has no effect on the best compromising solution.     

Multi-Objective Optimal Model for Conjunctive Use Management Using SGAs and NSGA-II Models

The widespread investigations on water resources management has become an essential issue because due to lack of sufficient research and inattention to planning and management of conjunctive use of surface and groundwater. The conjunctive management is a suitable alternative for imbalanced water resources distribution and related constraints in using of surface water. In this paper, a multi-objective model is developed to maximize the minimum reliability of system as well as minimize the costs due to water supply, aquifer reclamation and violation of the reservoir capacity in operation and allocation priority. The non-dominated sorting genetic algorithm (NSGA-II) is used to present the optimal trade-off between the objectives. The sequential genetic algorithms is also applied (SGA) in order to be compared with the NSGA-II model. The results show that the NSGA-II model can considerably reduce the computation burden of the conjunctive use models in comparison with the SGA optimization model. The obtained trade-off curve shows that a little increase in reliability leads to much more system costs. The weighted single objective SGA model results verify optimal trade-off obtained from NSGA-II model and show the optimality of allocated discharges.