Water Resources Management and Planning under Uncertainty: an Inexact Multistage Joint-Probabilistic Programming Method

In this study, an inexact multistage joint-probabilistic programming (IMJP) method is developed for tackling uncertainties presented as interval values and joint probabilities. IMJP improves upon the existing multistage programming and inexact optimization approaches, which can help examine the risk of violating joint-probabilistic constraints. Moreover, it can facilitate analyses of policy scenarios that are associated with economic penalties when the promised targets are violated within a multistage context. The developed method is applied to a case study of water-resources management within a multi-stream, multi-reservoir and multi-period context, where mixed integer linear programming (MILP) technique is introduced into the IMJP framework to facilitate dynamic analysis for decisions of surplus-flow diversion. The results indicate that reasonable solutions for continuous and binary variables have been generated. They can be used to help water resources managers to identify desired system designs against water shortage and for flood control, and to determine which of these designs can most efficiently accomplish optimizing the system objective under uncertainty.     

Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSP) method was developed for water resources management under uncertainty. As a new extension of mathematical programming methods, the developed ITSSP approach has advantages in uncertainty reflection and policy analysis. In order to better account for uncertainties, the ITSSP approach is expressed with discrete intervals, functional intervals and probability density functions. The ITSSP method integrates the two-stage stochastic programming (TSP), interval programming (IP) and semi-infinite programming (SIP) within a general optimization framework. The ITSSP has an infinite number of constraints because it uses functional intervals with time (t) being an independent variable. The different t values within the range [0, 90] lead to different constraints. At same time, ITSSP also includes probability distribution information. The ITSSP method can incorporate pre-defined water resource management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a water resource management system with three users and four periods (corresponding to winter, spring, summer and fall, respectively). Solutions of the ITSSP model provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable interval solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flow. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system reliability criteria.     

Identifying Optimal Water Resources Allocation Strategies through an Interactive Multi-Stage Stochastic Fuzzy Programming Approach

In this study, an interactive multi-stage stochastic fuzzy programming (IMSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact multi-stage stochastic programming framework. IMSFP can deal with dual uncertainties expressed as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints. Moreover, IMSFP is capable of reflecting dynamics of uncertainties and the related decision processes through constructing a set of representative scenarios within a multi-stage context. A management problem in terms of water resources allocation has been studied to illustrate applicability of the proposed approach. The results indicate that a set of solutions under different feasibility degrees (i.e., risk of constraint violation) has been generated for planning the water resources allocation. They can not only help quantify the relationship between the objective-function value and the risk of violating the constraints, but also enable decision makers (DMs) to identify, in an interactive way, a desired compromise between two factors in conflict: satisfaction degree of the goal and feasibility degree of constraints. Besides, a number of decision alternatives have been generated under different policies for water resources management, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised water-allocation targets are violated, and thus help DMs to identify desired water-allocation schemes under uncertainty.     

Multi-Objective Optimization of the Proposed Multi-Reservoir Operating Policy Using Improved NSPSO

Severe water shortage is unacceptable for water-supply reservoir operation. For avoiding single periods of catastrophic water shortage, this paper proposes a multi-reservoir operating policy for water supply by combining parametric rule with hedging rule. In this method, the roles of parametric rule and hedging rule can be played at the same time, which are reducing the number of decision variables and adopting an active reduction of water supply during droughts in advance. In order to maintain the diversity of the non-dominated solutions for multi-objective optimization problem and make them get closer to the optimal trade-off surfaces, the multi-population mechanism is incorporated into the non-dominated sorting particle swarm optimization (NSPSO) algorithm in this study to develop an improved NSPSO algorithm (I-NSPSO). The performance of the I-NSPSO on two benchmark test functions shows that it has a good ability in finding the Pareto optimal set. The water-supply multi-reservoir system located at Taize River basin in China is employed as a case study to verify the effect of the proposed operating policy and the efficiency of the I-NSPSO. The operation results indicate that the proposed operating policy is suitable to handle the multi-reservoir operation problem, especially for the periods of droughts. And the I-NSPSO also shows a good performance in multi-objective optimization of the proposed operating policy.     

Deriving Optimal Operating Rules of a Multi-Reservoir System Considering Incremental Multi-Agent Benefit Allocation

Joint multi-reservoir operation is one of the most efficient measures to meet the demand for increasing economic benefits. Operating rules have been widely used in long-term reservoir operations. However, reservoirs belong to multiple agents in most cases, which imposes difficulties on benefit allocation. This motivated us to derive optimal operating rules for a multi-reservoir system, considering incremental benefit allocation among multiple agents. Fairness of incremental benefits for multiple agents is proposed as one of the objective functions, and then optimal joint operating rules with fairness are derived. The optimal joint operating rules with fairness are compared with conventional, optimal individual, and joint operating rules. The Three Gorges (Three Gorges and Gezhouba) and Qing River (Shuibuya, Geheyan and Gaobazhou) cascade reservoirs are selected for case study. The optimal joint operating rules with fairness not only encourage agents to participate in joint operation, but also increase average annual hydropower generation and the assurance rate of hydropower generation relative to those of the conventional operating rules. Furthermore, the proposed optimal operating rules with fairness are easier to implement in practice than the optimal joint rules. This indicates that the proposed method has potential for improving operating rules of a multi-reservoir system.     

Simulation-optimization model of reservoir operation based on target storage curves

This paper proposes a new storage allocation rule based on target storage curves. Joint operating rules are also proposed to solve the operation problems of a multi-reservoir system with joint demands and water transfer-supply projects. The joint operating rules include a water diversion rule to determine the amount of diverted water in a period, a hedging rule based on an aggregated reservoir to determine the total release from the system, and a storage allocation rule to specify the release from each reservoir. A simulation-optimization model was established to optimize the key points of the water diversion curves, the hedging rule curves, and the target storage curves using the improved particle swarm optimization （IPSO） algorithm. The multi-reservoir water supply system located in Liaoning Province, China, including a water transfer-supply project, was employed as a case study to verify the effectiveness of the proposed join operating rules and target storage curves. The results indicate that the proposed operating rules are suitable for the complex system. The storage allocation rule based on target storage curves shows an improved performance with regard to system storage distribution.     

An Inexact Two-Stage Water Resources Allocation Model for Sustainable Development and Management Under Uncertainty

In this study, an inexact two-stage water resources allocation (ITWR) model is put forward for supporting sustainable development and management of water resources in Sanjiang Plain, China, which is in such a situation, with multi-water source, multi-water supply subarea, multi-water user and multi-planning goal. The costs of net system, water supply and recourse are analyzed. The developed ITWR model, which shows a strong ability in tacking with various uncertain factors in probability distributions and discrete interval numbers, mixes the techniques of interval-parameter programming (IPP) and two-stage stochastic programming (TSP) within a general optimization framework. And it also has formed an effective link in such a conflict between the policy scenarios and the associated various levels of economic penalties, when the pre-allocation targets of water resources are violated. Based on this model, a series of scenarios under different levels of pre-allocation water is done and different degrees of water surplus and shortage are obtained correspondingly. The results indicate that the reasonable distribution plans with maximum system benefit and minimum system-failure risk have been generated. And these results are valuable for saving water resources to realize its sustainable development and mitigating the penalty to gain economic benefits maximum, and thus some desired results are provided for decision makers in tackling with a complex and uncertain water-resource system.     

Chaotic Evolutionary Algorithms for Multi-Reservoir Optimization

The water sharing dispute in a multi-reservoir river basin forces the water resources planners to have an integrated operation of multi-reservoir system rather than considering them as a single reservoir system. Thus, optimizing the operations of a multi-reservoir system for an integrated operation is gaining importance, especially in India. Recently, evolutionary algorithms have been successfully applied for optimizing the multi-reservoir system operations. The evolutionary optimization algorithms start its search from a randomly generated initial population to attain the global optimal solution. However, simple evolutionary algorithms are slower in convergence and also results in sub-optimal solutions for complex problems with hardbound variables. Hence, in the present study, chaotic technique is introduced to generate the initial population and also in other search steps to enhance the performance of the evolutionary algorithms and applied for the optimization of a multi-reservoir system. The results are compared with that of a simple GA and DE algorithm. From the study, it is found that the chaotic algorithm with the general optimizer has produced the global optimal solution (optimal hydropower production in the present case) within lesser generations. This shows that coupling the chaotic algorithm with evolutionary algorithm will enrich the search technique by having better initial population and also converges quickly. Further, the performances of the developed policies are evaluated for longer run using a simulation model to assess the irrigation deficits. The simulation results show that the model satisfactorily meets the irrigation demand in most of the time periods and the deficit is very less.     

跨流域水库群最优调供水过程耦合研究

为了有效描述和求解跨流域水库群最优调供水过程,本文建立了基于0-1规划方法的水库群最优化调度模型,统一考虑并最终确定了最优调供水过程。为减少模型单次求解的变量数目,同时增加算法全局搜索的能力,本文借用逐步优化算法思想,对传统粒子群进行改进,提出了逐步优化粒子群算法(PRA-PSO)对模型进行求解。最后,通过中国北方某大型跨流域调水工程的实例研究分析了模型的合理性和有效性。最优调供水过程的确定不仅可为采用隐随机优化方法确定跨流域水库群调水规则和供水规则提供最优化样本过程,而且对跨流域调水工程调度运行评价具有重要意义。     

跨流域供水水库群联合调度规则研究

针对跨流域供水水库群联合调度存在的主从递阶结构,提出了调水规则和供水规则相结合的跨流域供水水库群联合调度规则。其中,调水规则由一组基于各水库蓄水量的调水控制线表示,根据其间的相对位置关系,决定是否调水,调水量如何分配等;供水规则由各库供水调度图表示,对应于不同用水户的限制供水线将水库的兴利库容分为若干调度区。建立了适合于主从递阶结构的水库群联合调度二层规划模型,采用并行种群混合进化的粒子群算法对模型进行求解。中国北方某大型跨流域调水工程的实例研究证明了模型的合理性和有效性。     

跨流域水库群最优调供水过程耦合研究

为了有效描述和求解跨流域水库群最优调供水过程,本文建立了基于0-1规划方法的水库群最优化调度模型,统一考虑并最终确定了最优调供水过程。为减少模型单次求解的变量数目,同时增加算法全局搜索的能力,本文借用逐步优化算法的思想,对传统粒子群进行改进,提出了逐步优化粒子群算法（PRA-PSO）对模型进行求解。最后,通过中国北方某大型跨流域调水工程的实例研究分析了模型的合理性和有效性。最优调供水过程的确定不仅可为采用隐随机优化方法确定跨流域水库群调水规则和供水规则提供最优化样本过程,而且对跨流域调水工程调度运行评价具有重要意义。     

A Fuzzy Stochastic Dynamic Nash Game Analysis of Policies for Managing Water Allocation in a Reservoir System

In this paper a fuzzy dynamic Nash game model of interactions between water users in a reservoir system is presented. The model represents a fuzzy stochastic non-cooperative game in which water users are grouped into four players, where each player in game chooses its individual policies to maximize expected utility. The model is used to present empirical results about a real case water allocation from a reservoir, considering player (water user) non-cooperative behavior and also same level of information availability for individual players. According to the results an optimal allocation policy for each water user can be developed in addition to the optimal policy of the reservoir system. Also the proposed model is compared with two alternative dynamic models of reservoir optimization, namely Stochastic Dynamic Programming (SDP) and Fuzzy-State Stochastic Dynamic programming (FSDP). The proposed modeling procedures can be applied as an appropriate tool for reservoir operation, considering the interaction among the water users as well as the water users and reservoir operator.     

A Conditional Value-at-Risk Based Inexact Water Allocation Model

A conditional value-at-risk (CVaR) based inexact two-stage stochastic programming (CITSP) model was developed in this study for supporting water resources allocation problems under uncertainty. A CITSP model was formulated through incorporating a CVaR constraint into an inexact two-stage stochastic programming (ITSP) framework, and could be used to deal with uncertainties expressed as not only probability distributions but also discrete intervals. The measure of risks about the second-stage penalty cost was incorporated into the model, such that the trade-off between system economy and extreme expected loss could be analyzed. The developed model was applied to a water resources allocation problem involving a reservoir and three competing water users. The results indicated that the CITSP model performed better than the ITSP model in its capability of reflecting the economic loss from extreme events. Also, it could generate interval solutions within which the decision alternatives could be selected from a flexible decision space. Overall, the CITSP model was useful for reflecting the decision maker’s attitude toward risk aversion and could help seek cost-effective water resources management strategies under complex uncertainties.     

应用线性二次高斯控制进行灌区调度

本文研究了随机环境下灌区调度问题，建立了一个水库和田间配水整合随机调度模型。文中引入土壤水库的概念，把灌区调度的问题转化成水库群调度的问题，采用线性二次高斯控制(Linear Quadratic Gaussion control，LQG)对模型进行求解，解决了此类研究中的求解技术难题，从而克服了前人模型中仿真性能不好的问题。此外，本文还对水库群调度中的LQG方法进行了改进。实例计算表明，本文建立的模型能取得良好的效益，LQG算法稳定、计算速度快。     

Development of a Dynamic Long-Term Water Allocation Model for Agriculture and Industry Water Demands

Demands growth and water resources limitation, enforce water sector policy makers to integrate water supply–demand interactions in a coherent framework for efficient water allocation. Water supply–demand interaction, changes long-term trend of water demands, which in turn has a substantial influence on water allocation. Researches on water allocation modeling lack adequate projection of relationship between water supply and demand. Socio-economic factors representing water allocation stakeholders’ benefits, account for the main share of water supply–demand interaction. Identification, representation and consideration of these factors in a water allocation model, is the main limitation of researches on this issue. In this paper a new long-term water allocation model at basin level is developed and introduced. This model considers water supply–demand interaction in agriculture and industry sectors, by use of socio-economic parameters; such as, production, cultivated land area, revenue and employment. The model main advantage is its ability to reflect the interrelationship between essential hydro-system and supply–demand components. It can explore both socio-economic and water allocation consequences of various policy choices. The model is used to assess two different development policies at basin level. The first one is fourth 5-year development plan of Iran, which fixes predefined growth rate for different sectors. The second one assumes the present state continues up to the end of planning horizon. A typical multi-reservoir water basin is modeled and analyzed for two policies. Indices that summarize long-term state of hydro-system and stakeholders are defined and used in policies assessment and decision making. Results of these assessments show fourth 5-year development policy provides opportunities for substantial improvement in water allocation and stakeholders’ benefits.     

Coupled Operating Rules for Optimal Operation of Multi-Reservoir Systems

Due to the complexity of multi-reservoir system operation problems, researchers usually prefer to assume lumped demands located downstream of such systems. Consequently, distributed local demands through the system are neglected or supplied completely (e.g. using Standard operating policy, SOP), in order to simplify the problem. In this study, Coupled Operating Rules (COR) as a simple and suitable operating policy is applied for optimal operation of multi-reservoir systems with local demands. The applied policy includes two types of linear rules, which are defined to determine total releases and local water allocations in decision points. This policy is adopted within a simulation-optimization approach to optimally operate a three-reservoir system in the Karkheh river basin. Obtained results indicate that the proposed strategy reduces the intensity of demand deficits and distributes the occurred shortages throughout the system properly. Moreover, the system losses are managed appropriately and big unbalanced local shortages are prevented. Although COR strategy decreases the reliability of local demands compared to SOP, it is a reasonable operating policy for systems with distributed local demand sites. Moreover, in this study an effective Improved Melody Search (IMeS) algorithm is proposed to achieve the optimum values of operating rules’ parameters. The efficiency of the optimization method is compared to the results achieved by other selected well-known heuristic search methods. Based on the experimental results, it is revealed that the proposed algorithm is more effective in finding precise solutions over a long-term period, comparing with the other conventional algorithms.     

西北诸河水资源供需分析与配置格局

西北诸河地域广大,不同地区水资源及其开发利用情况差异明显。针对西北诸河各地区各流域特点,在对河流水资源情况、开发利用状况、承载能力分析的基础上,按照水资源三次平衡的分析方法,基于深入挖潜节水、多渠道开源、适时调水的总体思路进行水资源供需分析和合理配置。通过水资源合理配置,可基本实现水资源的供需平衡,支撑区域经济社会的快速发展和生态环境的良性维持。     

Policy Options to Improve Water Allocation Efficiency: Analysis on Egypt and Morocco

Abstract

Because of political risk, economic feasibility, and cultural concerns, it has been a great challenge for economists to provide palatable remedies to governments to promote water allocation efficiency. Considering the limitation of water pricing to irrigation water, this research addresses questions of which strategic policy alternatives to water pricing might improve irrigation water allocation efficiency. An empirical framework is provided to compare irrigation policies for allocating scarce water to agricultural production in Egypt and Morocco. Partial-equilibrium agricultural sector models specific to Egypt and Morocco were employed for policy tests. Consumer and producer surplus from agricultural based commodities is maximized subject to various resources, technical, and policy constraints. Positive Mathematical Programming (PMP) was used to calibrate the model. Water pricing policy, water complementary input factor tax policy, and output tax policy are tested using these two agricultural sector models. Results suggest that effective policy depends on the social, economic, and environmental contexts of specific regions. For countries like Egypt where most agricultural land is irrigated, taxes on Nitrogen (N) fertilizer and energy and output tax on water-intensive and low profit crop production may be more effective than others. For the Moroccan case, taxation on crop inputs and outputs not only affect water use in the public irrigation sector, but also private irrigation sector and rain-fed as a whole. Water pricing and output tax policies are better suited and effective than water complementary input factor taxation. Findings from Morocco might be generalized to other countries with similar irrigation characteristics and diversity in irrigated (public and private) and rain-fed land. The results for both countries demonstrate that some of the strategic irrigation policies can work towards directing cropping decisions to less water intensive crops and also generating revenues for governments in situations where governments choose not to price water.     

IFTSQP: An Inexact Optimization Model for Water Resources Management under Uncertainty

Abstract

An interval-fuzzy two-stage quadratic programming (IFTSQP) method is developed for water resources management under uncertainty. The methodincorporates techniques of interval-parameter programming, two-stage stochastic programming, and fuzzy quadratic programming within a general optimization framework to tackle multiple uncertainties presented as intervals, fuzzy sets and probability distributions. In the model formulation, multiple control variables are adopted to handle independent uncertainties in the model's right-hand sides; fuzzy quadratic terms are used in the objective function to minimize the variation in satisfaction degrees among the constraints. Moreover, the method can support the analysis of policy scenarios that are associated with economic penalties when the promised targets are violated. The developed method is then applied to a case study of water resources management planning. The results indicate that reasonable solutions have been obtained. They can help provide bases for identifying desired water-allocation plans with a maximized system benefit and a minimized constraint-violation risk.     

有外调水源的库群联合供水调度方法的改进

针对有外调水源的库群联合供水调度常规方法存在的不足,在调水规则和共同供水任务分配方面进行了改进。在调水规则方面,提出了一种调水过程控制的双调水控制线法,该方法在调度图中引入上下两条调水控制线,两线之间形成一个调水启闭的"缓冲区",有效克服了单调水控制线法调水启闭频次过多的缺陷,易于实际应用。在成员水库共同供水任务分配方面,提出了一种附加调节系数的动态分水方法,通过与成员水库蓄水状态相关的调节系数对共同供水任务进行"二次分配",与常规分水方法相比,供水任务分配更加合理,有效降低了供水成本。在大连市供水系统中的应用实例,验证了改进方法的有效性与合理性。