Irrigation Planning Under Uncertainty—A Multi Objective Fuzzy Linear Programming Approach

The problem of irrigation planning becomes more complex by considering an uncertainty. The uncertainties can be tackled by formulating the problem of irrigation planning as Fuzzy Linear Programming (FLP). FLP models can incorporate the scenario of real world problem. In the present study, Multi Objective Fuzzy Linear Programming (MOFLP) irrigation planning model is formulated for deriving the optimal cropping pattern plan for the case study of Jayakwadi project in the Godavari river sub basin in Maharashtra State, India. Four conflicting objectives are considered such as Net Benefits (NB), Crop/Yield Production (CP), Employment Generation/Labour Requirement (EG) and Manure Utilization (MU). Four different cases are considered to incorporate the uncertainty in MOFLP model. To include the uncertainty in irrigation planning problem only objectives are taken as fuzzy and constraints are crisp in nature in Case-I. To consider the uncertainty involved in availability of resources, in Case-II the stipulations are fuzzy. The technological coefficients are fuzzy in Case-III. The Case-IV includes both technological coefficients and stipulations fuzzy. The level of satisfaction (λ) works out to be 0.58, 0.50, 0.50 and 0.28 respectively for Case-I to IV. The results obtained in Case-IV are more realistic and promising as it involves the uncertainty in technological coefficients and stipulations simultaneously.     

Multi Objective Sustainable Irrigation Planning with Decision Parameters and Decision Variables Fuzzy in Nature

This paper presents the Multi Objective Fuzzy Linear Programming (MOFLP) model, which deals with the fuzziness in resources and decision variables, closer to the real world situation. The MOFLP model is developed and applied to the Jayakwadi Project Stage-I built across the river Godavari in the State of Maharashtra, India. It focuses on the four objectives namely maximization of Net Benefits, maximization of Crop Production, maximization of Employment Generation and maximization of Manure Utilization. The level of satisfaction ???=?0.625 is worked out for compromised solution for four conflicting objectives under fuzzy environment. The MOFLP model compromised solution for irrigation planning provides Net Benefits 1522.75 (Million Rupees), Crop Production 322504.40 (Tons), Employment Generation 29.27 (Million Man Days) and Manure Utilization 147229.40 (Tons) respectively and irrigation intensity 68.50?%. The results obtained are promising for sustainable development in irrigation sector and closer to the true picture of the real world problem as it incorporates the fuzziness in both resources and decision variables simultaneously.     

Integrated Sustainable Irrigation Planning with Multiobjective Fuzzy Optimization Approach

Multiobjective fuzzy methodology is applied to a case study of Khadakwasla complex irrigation project located near Pune city of Maharashtra State, India. Three objectives, namely, maximization of net benefits, crop production and labour employment are considered. Effect of reuse of wastewater on the planning scenario is also studied. Three membership functions, namely, nonlinear, hyperbolic and exponential are analyzed for multiobjective fuzzy optimization. In the present study, objective functions are considered as fuzzy in nature whereas inflows are considered as dependable. It is concluded that exponential and hyperbolic membership functions provided similar cropping pattern for most of the situations whereas nonlinear membership functions provided different cropping pattern. However, in all the three cases, irrigation intensities are more than the existing irrigation intensity.     

Multiobjective Multireservoir Operation in Fuzzy Environment

In this paper, the operation of a complex system of multireservoirs with multiple objectives is being demonstrated. The multireservoir system includes uncertainties of inflows, demands to the large extent. Fuzzy set theory has been proved as a robust theory where these kinds of uncertainties have major role. In this study, the fuzzy linear programming method is used to get the better policy for the system operation with the uncertainty in various parameters i.e. resources, technological coefficients, objective function coefficients. A four reservoir system (a compound parallel and series) is taken as a case study and the fuzzification of all parameters is tried on the system. The effect of fluctuations in irrigation demand and release, power demand and release and available storage volume are considered. The consequences on the objectives i.e. maximization of returns from irrigation release, maximization of returns from power releases are also examined. The operation policies thus evolved give a better understanding of the problem and the intricate complexities associated and there effects. With this the policy makers (a decision maker) can have a wide range of options at his disposal for suitable action.     

A multiobjective fuzzy linear programming model for sustainable integrated operation of a multireservoir system

Irrigated agriculture is the largest consumer of water, with high significance in India as the majority of its people depend on it. Rainfall uncertainties, and uneven distribution of utilizable water over space and time, have presented a serious challenge to irrigation water management and crop production. Surface water reservoirs play a major role in supplying irrigation water and also addressing uneven water distribution to some degree. Varying water requirements for different crops under multiple canals, however, requires that planners develop an optimal crop planning for the efficient operation of a multireservoir irrigation system. The spatial and temporal water transfer within a multireservoir irrigation system necessitates integrated operation of all the involved reservoirs. Thus, integrated operation of a multireservoir system is a fundamental requirement for efficient irrigation water management, and also become a key issue for sustainable agricultural development. This study derived an optimal crop plan for the integrated operation of a complex multireservoir system with intrabasin water transfer, using a multiobjective fuzzy linear programming (MOFLP) approach. The MOFLP model resulted in a level of satisfaction of 0.46, with an irrigation intensity of 102.18%, and a total crop area of 149 232.10 ha. The optimal policies were furthermore assessed with various statistical indicators with a simulation model, indicating they are performing well, with high reliability and resilience for longer periods.     

Irrigation Planning using Genetic Algorithms

The present study deals with the application of Genetic Algorithms(GA) for irrigation planning. The GA technique is used to evolve efficient cropping pattern for maximizing benefits for an irrigation project in India. Constraints include continuity equation, land and water requirements, crop diversification and restrictions on storage. Penalty function approach is used to convert constrained problem into an unconstrained one. For fixing GA parameters the model is run for various values of population, generations, cross over and mutation probabilities. It is found that the appropriate parameters for number of generations, population size, crossover probability, and mutation probability are 200, 50, 0.6 and 0.01 respectively for the present study. Results obtained by GA are compared with Linear Programming solution and found to be reasonably close. GA is found to be an effective optimization tool for irrigation planning and the results obtained can be utilized for efficient planning of any irrigation system.     

基于模糊RES-云模型的坝基岩体可灌性评价研究

岩体可灌性分析与评价是大坝基岩灌浆的重点和难点,科学合理的可灌性评价对保证灌浆效果具有重要理论与工程意义。目前涉及坝基岩体可灌性的研究中缺乏多影响因素下的岩体可灌性分析,同时亦未能够考虑评价过程中的不确定性问题。针对上述问题,提出基于模糊RES(岩石工程系统Rock Engineering System)-云模型的坝基岩体可灌性综合评价方法。首先,在系统分析影响岩体可灌性的相关因素的基础上,选取地质条件、浆液性质以及灌浆工艺等方面的12个因素构建评价指标体系;其次,基于RES理论从系统的角度科学合理地确定评价因子的重要性程度,并引入模糊理论克服RES方法中对主观因素的依赖,获取指标权重;再者,利用云模型考虑岩体可灌性评价过程中的随机性和模糊性的特点实现可灌性等级与评价指标值之间的不确定映射;最后,将基于模糊RES-云模型的综合评价方法应用于国内某大型水电工程,结果表明该方法具有较高的准确性和可靠性。     

基于模糊优选模型的水资源可持续利用评价

模糊优选模型是进行水资源可持续利用评价的一种有效方法,由于影响区域水资源可持续利用的因素是多方面的,而每一类因素所占的地位及其对它们的评价都伴随着明显的模糊性,利用模糊优选模型进行水资源可持续利用评价获得了较好的结果,可为地区水资源可持续利用管理提供较为科学的依据。     

Integrated irrigation development planning by multi‐objective optimization

A multi‐objective linear‐programming‐based planning model for irrigation development, incorporating the integrated use of surface and groundwater resources, is presented. Applicability of the model is illustrated by a case study of the Bagmati River Basin, Nepal. Alternative plans for irrigation development are identified by analysing trade‐offs between the specified objectives of maximizing total net economic benefits from agriculture (economic efficiency) and total irrigated cropped area (balanced regional development). Evaluation of the alternatives by compromise programming is carried out in order to indicate the optimal scale of development, cropping plans, system design capacities and water allocation policies.     

Fuzzy Stochastic Genetic Algorithm for Obtaining Optimum Crops Pattern and Water Balance in a Farm

This paper is concerned with multi-objective fuzzy stochastic model for determination of optimum cropping patterns with water balance for the next crop season. The objective functions of the model is to study the effect of various cropping patterns on crop production subject to total water supply in a small farm. The decision variables are the cultivated area of different crops at the farm. The water requirement of the crops follows fuzzy uniform distribution and yields in the objective functions are taken as a fuzzy numbers. The model is solved by using fuzzy stochastic simulation based genetic algorithm without deriving the deterministic equivalents.     

Optimal multiobjective reservoir operation with fuzzy decision variables and resources: A compromise approach

Imprecision is often involved in reservoir-systems operation, as these systems are too complex to be defined in precise terms. Fuzzy programming has an essential role in fuzzy modeling, which can formulate uncertainty in the actual environment. In this study, a multipurpose, single-reservoir operation model is developed by assuming triangular fuzzy-number distribution of the parameters. The applicability of the model is demonstrated through the case study of the Jayakwadi reservoir stage II, Maharashtra State, India. The reservoir-operation model considers two objectives: maximization of the releases for irrigation and maximization of the releases for hydropower generation. The model is solved for a vector of a triangular fuzzy-number by giving a priority to each objective. By individual optimization, the fuzzy optimal solution is obtained for each objective in the form of a triangular fuzzy-number distribution. This solution is defuzzified to obtain the crisp values, which are further used to develop a fuzzy-compromised model. The compromised model is solved for the maximization of the degree of satisfaction (λ) by simultaneously optimizing both of the objectives. The degree of satisfaction (λ) achieved is 0.67, and the corresponding values for irrigation releases and hydropower releases are equal to the 388.54 Mm³ and 195.19 Mm³, respectively.     

基于模糊数学和极限平衡法的滑坡稳定性评价

滑坡的稳定性评价中存在着模糊性,如力学参数的模糊性、影响因素的模糊性以及评价标准的模糊性等,这就需要运用不确定分析方法中的模糊数学方法来分析评价滑坡的稳定性。但模糊数学方法确定的隶属函数及权重分配具有主观性,是定性评价,而极限平衡法是通过建立稳定性系数表达式进行定量评价。将两种方法结合起来,既可通过模糊综合评判方法的定性评价体现出滑坡稳定性中的模糊性,又可通过极限平衡方法的定量评价反映滑坡稳定状态的本质。研究表明,两种方法得到的结果与工程实际相符合,并且互为补充使评价结果更加合理。     

A Fuzzy Variable Least Core Game for Inter-basin Water Resources Allocation Under Uncertainty

In this paper, a new solution concept, called Fuzzy Variable Least Core (FVLC), is developed for fuzzy cooperative games. The FVLC is able to incorporate fuzzy input variables and result in fuzzy benefit shares of players participating in a coalition. This solution concept is used for water and benefit allocation to water users in inter-basin water transfer systems considering the uncertainties associated with their benefit coefficients. In the proposed water allocation methodology, an Integrated Stochastic Dynamic Programming (ISDP) model is developed to obtain the water rights of players and economic water allocation policies. In the next step, the total net fuzzy benefit of the system is reallocated to water users in an equitable and rational way using a FVLC-based model. In this model, a new algorithm is proposed for converting a multilateral cooperative game with fuzzy variables to some fuzzy bilateral cooperative games, which are solved using the FLVC solution concept. The applicability and efficiency of the proposed methodology is examined by applying it to a large scale inter-basin water transfer project in Iran.     

三角模糊数随机模拟的防洪工程联系数风险评价模型

针对受多种不确定性因素综合作用的流域防洪工程体系风险评价问题，提出用防洪工程体系风险评价指标样本与评价标准等级之间的多元联系数定量描述样本与标准等级之间隶属关系的层次性和模糊性，用三角模糊数和多元联系数理论相结合的方法处理风险评价中以区间数形式表示的评价等级标准的模糊性，用三角模糊数定量表示联系数的差异度系数的连续变化过程和各指标权重的不确定性，再通过随机模拟三角模糊数的方法建立了三角模糊数随机模拟的防洪工程联系数风险评价模型（CN-SSTFN）。研究结果表明：CN-SSTFN综合利用了流域防洪工程体系风险评价过程的各种主客观不确定性评价信息，以置信区间形式表示的评价结果比现有方法提供了评价结果可靠性方面的更多重要信息，能反映受多种不确定性因素综合影响的流域防洪工程体系风险评价的客观实际情况；CN-SSTFN的计算方法简便、通用，在各种系统风险等级评价问题中具有推广应用价值，有利于促进集对分析和可变模糊集理论的进一步发展。     

基于组合赋权的岩质边坡安全稳定性综合评价模型

针对岩质边坡安全稳定性评价的层次性与模糊性等不确定性问题,将岩质边坡安全稳定性评价作为一个模糊系统,充分考虑地质现状、工程现状、环境条件及监测表现4个方面及其影响因素,构建了包括目标层、准则层、指标层多个层次的岩质边坡安全稳定性评价指标体系;将主成分分析法与改进层次分析法相结合,提出了一种能同时顾及主、客观权重的赋权方法,可提高指标权重的合理性与准确性;运用模糊理论构造隶属度函数,进而建立岩质边坡安全稳定性的多层次模糊综合评价模型。实例应用表明,该模型可行,操作简便,结果符合实际,为岩质边坡安全稳定性评价提供了一条新途径。     

Comparison of Policies Derived from Stochastic Dynamic Programming and Genetic Algorithm Models

A comprehensive Genetic Algorithm (GA) model has been developed and applied to derive optimal operational strategies of a multi-purpose reservoir, namely Perunchani Reservoir, in Kodaiyar Basin in Tamil Nadu, India. Most of the water resources problem involves uncertainty, in order to see that the GA model takes care of uncertainty in the input variable, the result of the GA model is compared with the performance of a detailed Stochastic Dynamic Programming (SDP) model. The SDP models are well established and proved that it takes care of uncertainty in-terms of either implicit or explicit approach. In the present study, the objective function of the models is set to minimize the annual sum of squared deviation from desired target release and desired storage volume. In the SDP model the optimal policies are derived by varying the state variables from 3 to 9 representative class intervals, and then the cases are evaluated for their performance using a simulation model for longer length of inflow data, generated using a Thomas–Fiering model. From the performance of the SDP model policies, it is found that the system encountered irrigation deficit, whereas GA model satisfied the demand to a greater extent. The sensitivity analysis of the GA model in selecting optimal population, optimal crossover probability and the optimal number of generations showed the values of 150, 0.76 and 175 respectively. On comparing the performance of SDP model policy with GA model, it is found that GA model has resulted in a lesser irrigation deficit. Thus based on the present case study, it may be concluded that the GA model performs better than the SDP model.     

An Entropy-Based Approach to Fuzzy Multi-objective Optimization of Reservoir Water Quality Monitoring Networks Considering Uncertainties

In this study, a new fuzzy methodology for a multi-objective optimization of reservoir Water Quality Monitoring Stations (WQMS) was developed, based on Transinformation Entropy (TE), the IRanian Water Quality Index (IRWQI), and fuzzy social choice considering uncertainties. The approach was utilized in the Karkheh Dam reservoir in Iran. The objective functions were: 1) minimizing costs, 2) minimizing redundant information and uncertainties, and 3) maximizing the spatial coverage of the network. A CE-QUAL-W2 model was used for the simulation of water quality variables. The IRWQI was computed to reveal a complete picture of the reservoir water quality. The TE quantities were calculated for each pair of potential stations. The TE values were plotted against the spatial distances among potential WQMS to obtain the TE–Distance (TE–D) curve, and minimize redundant information among stations, while providing coverage of the entire network. A multi-objective Genetic Algorithm (NSGA-II) was applied to obtain Pareto-optimal solutions taking stakeholder preference into account. The most preferred solution was then obtained using fuzzy social choice approaches to achieve a consensus. The fuzziness embedded in the decision-making procedure, the uncertainty in the value of mutual information, and the uncertainty in identifying the optimal distance among WQMS were also investigated. Results indicated that the three fuzzy social choice approaches (Borda Count, Minimax, and Approval Voting) led to the same number of optimized WQMS in each fuzzy alpha-cut. Based on the fuzzy linguistic quantifiers method, the number of optimized WQMS was increased.     

集对分析多元模糊模型在灌区评价中的应用

灌区水利现代化综合评价涉及经济、社会、技术、资源与生态环境等多方面,影响因素多样化、关系非线性化、不确定性复杂化.应用集对分析多元模糊评价模型( MFSPAFM),选择农村经济发展水平、安全保障水平、灌溉排水生产条件、水利科技现代化水平、农村生活用水指标、农村生态环境指标和管理队伍及管理现代化水平等7个指标,对2008...     

Conjunctive Water Use Planning in an Irrigation Command Area

In the present study, an integrated soil water balance algorithm was coupled to a non-linear optimization model in order to carry out water allocation planning in complex deficit agricultural water resources systems based on an economic efficiency criterion. The LINGO 10.0, optimization package has been used to evolve at optimal allocation plan of surface and ground water for irrigation of multiple crops. The proposed model was applied for Qazvin Irrigation Command Area, a semi-arid region in Iran. Various scenarios of conjunctive use of surface and ground water along-with current and proposed cropping pattern have been explored. Some deficit irrigation practices were also investigated. The results indicate that conjunctive use practices are feasible and can be easily implemented in the study area, which would enhance the overall benefits from cropping activities. The study provides various possible operational scenarios of the branch canals of the command area in the common and dry condition, which can help managers in decision making for the optimum allocation plans of water resources within the different irrigation districts. The findings demonstrate that for deficit irrigation options, the mining allowance of ground water value of the command area is greatly reduced and ground water withdrawal may be also restricted to the recharge to maintain the river–aquifer equilibrium.     

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.