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.     

Model for Optimal Operation of Water Distribution Pumps with Uncertain Demand Patterns

An optimization model is presented for pump operation based upon minimizing operation costs and indirectly the maintenance costs of pumps considering uncertainty of specified demand (load) curves. The purpose of this model is to determine pump operation to meet the uncertain demands as well as to satisfy the pressure requirements in the water distribution system. In addition, constraints on the number of pump (‘on-off’) switches are included as a surrogate to indirectly minimizing the maintenance costs. This model is a mixed integer nonlinear programming (MINLP) problem using a chance constraint formulation of the uncertain demand constraint. The optimization model was solved using the LocalSolver option in A Mathematical Programming Language (AMPL). The model was first applied to the operation of an example pumping system for an urban water distribution system (WDS) illustrating a reduction in operation costs using the optimization model. The optimization model with the chance-constraint for demand was applied for a range of demand satisfaction uncertainties. A decrease in the operation costs was observed with an increased uncertainty in demand satisfaction, which shows that the model further optimizes the operations considering the relaxed constraints. Model application could be extended to operations of pumping systems during emergencies and contingencies such as droughts, component failures etc.     

Conjunctive Use of Surface and Groundwater with Inter-Basin Transfer Approach: Case Study Piranshahr

Disregarding water as a key sustainable development has led to the water crisis in Iran. This problem is the biggest factor for marginalizing the planning and long-term management of water. The sustainable development policies in water resources management of IRAN require consideration of the different aspects of management that each of them demands the scientific integrated programs. Optimal use of inter-basin surface and groundwater resources and transfer of surplus water to adjacent basins are important from different aspects. The purpose of this study is to develop an efficient optimization model based on inter-basin water resources and restoration of outer-basin water resources. In the proposed model the three different objectives are as follow supplying inter-basin water demand, reducing the amount of water output of the boundary of IRAN and increasing water transfer to adjacent basins (Urmia Lake basin) are considered. In this model, water allocation is done based on consumption and resources priorities and groundwater table level constraints. In this research, the non-dominate sorting genetic algorithm is used for performing the developed model regarding the complexity and nonlinearity of the objectives and the decision variables. The optimal allocation of each water resources and water transfer to adjacent basin can be determined by using of proposed model. Optimal allocation policy presented based on optimal value and planning horizon. The results show that we can transfer considerable volume of water resources within the basin for restoration the outside basin and prevent the great flow of water by the border rivers applying the optimal operation policy.     

Multi-objective Planning for Conjunctive Use of Surface and Subsurface Water Using Genetic Algorithm and Dynamics Programming

The consideration of fixed cost and time-varying operating cost associated with the simultaneous conjunctive use of surface and subsurface water should be treated as a multi-objective problem due to the conflicting characteristics of these two objectives. In order to solve this multi-objective problem, a novel approach is developed herein by integrating the multi-objective genetic algorithm (MOGA), constrained differential dynamic programming (CDDP) and the groundwater simulation model ISOQUAD. A MOGA is used to generate the various fixed costs of reservoirs’ scale, generate a pattern of pumping/recharge, and estimate the non-inferior solutions set. A groundwater simulation model ISOQUAD is directly embedded to handle the complex dynamic relationship between the groundwater level and the generated pumping/recharge pattern. The CDDP optimization model is then adopted to distribute the optimal releases among reservoirs provided that reservoir capacities are known. Finally, the effectiveness of our proposed integrated model is verified by solving a water resources planning problem for the conjunctive use of surface and subsurface water in southern Taiwan.     

Comparative Evaluation of Genetic Programming and Neural Network as Potential Surrogate Models for Coastal Aquifer Management

Determining the optimal rates of groundwater extraction for the sustainable use of coastal aquifers is a complex water resources management problem. It necessitates the application of a 3D simulation model for coupled flow and transport simulation together with an optimization algorithm in a linked simulation-optimization framework. The use of numerical models for aquifer simulation within optimization models is constrained by the huge computational burden involved. Approximation surrogates are widely used to replace the numerical simulation model, the widely used surrogate model being Artificial Neural Networks (ANN). This study evaluates genetic programming (GP) as a potential surrogate modeling tool and compares the advantages and disadvantages with the neural network based surrogate modeling approach. Two linked simulation optimization models based on ANN and GP surrogate models are developed to determine the optimal groundwater extraction rates for an illustrative coastal aquifer. The surrogate models are linked to a genetic algorithm for optimization. The optimal solutions obtained using the two approaches are compared and the advantages of GP over the ANN surrogates evaluated.     

Planning of Groundwater Supply Systems Subject to Uncertainty Using Stochastic Flow Reduced Models and Multi-Objective Evolutionary Optimization

The typical modeling approach to groundwater management relies on the combination of optimization algorithms and subsurface simulation models. In the case of groundwater supply systems, the management problem may be structured into an optimization problem to identify the pumping scheme that minimizes the total cost of the system while complying with a series of technical, economical, and hydrological constraints. Since lack of data on the subsurface system most often reflects upon the development of groundwater flow models that are inherently uncertain, the solution to the groundwater management problem should explicitly consider the tradeoff between cost optimality and the risk of not meeting the management constraints. This work addresses parameter uncertainty following a stochastic simulation (or Monte Carlo) approach, in which a sufficiently large ensemble of parameter scenarios is used to determine representative values selected from the statistical distribution of the management objectives, that is, minimizing cost while minimizing risk. In particular, the cost of the system is estimated as the expected value of the cost distribution sampled through stochastic simulation, while the risk of not meeting the management constraints is quantified as the expected value of the intensity of constraint violation. The solution to the multi-objective optimization problem is addressed by combining a multi-objective evolutionary algorithm with a stochastic model simulating groundwater flow in confined aquifers. Evolutionary algorithms are particularly appropriate in optimization problems characterized by non-linear and discontinuous objective functions and constraints, although they are also computationally demanding and require intensive analyses to tune input parameters that guarantee optimality to the solutions. In order to drastically reduce the otherwise overwhelming computational cost, a novel stochastic flow reduced model is thus developed, which practically allows for averting the direct inclusion of the full simulation model in the optimization loop. The computational efficiency of the proposed framework is such that it can be applied to problems characterized by large numbers of decision variables.     

GASAPF方法在徐州市裂隙岩溶水资源管理模型中的应用

本文首次将GASAPF(基于遗传算法的模拟退火罚函数方法)应用于求解条件复杂的、大面积的徐州市裂隙岩溶水资源管理模型。徐州市是以裂隙岩溶水作为主要供水水源的工业城市，针对徐州市地下水长期无节制开采和管理不善而引起的多种环境地质问题，建立了研究区裂隙岩溶水资源的管理模型，并运用GASAPF方法求解，为今后合理开采研究区裂隙岩溶地下水资源提供了科学依据。同时通过分析优化结果的合理性，进一步证明GASAPF方法适用于条件复杂的大面积地下水资源的优化管理，完善和验证了GASAPF方法的实用性。最后，根据本次研究经验指出了GASAPF方法求解复杂系统管理模型时需要注意的问题。     

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.     

Hybrid Leakage Management for Water Network Using PSF Algorithm and Soft Computing Techniques

Reduction of leakages in water distribution system (WDS) is one of the major concerns for water industries. This paper presents a hybrid leakage reduction model using pressure management technique, performed by optimizing water storage level in the tank, along with optimized control and localization of pressure reducing valve (PRV) in water distribution system. Pattern Sequence-based Forecasting (PSF) algorithm is used for prediction of flow rate (demand) from the tank for next 48 h, to calibrate the future desire water storage level in the tank. A mathematical tank and pump simulation algorithm is proposed for optimization of water storage level in the tank. A modified reference pressure algorithm is proposed for efficient localization of pressure reducing valve. Multiobjective genetic algorithm (NSGA-II) is used for finding out the optimized operational control setting of the pressure reducing valve for leakage minimization. The proposed algorithm leads to better leakage reduction of 20.81% in modified benchmark WDS, with a reduced number of the pressure reducing valves. Constraints such as maintaining lower hydraulic failure index (<0.01), emergency water storage, etc. is also considered. It can be concluded that the proposed hybrid leakage reduction technique provides efficient as well as cost-effective solution for leakage control.     

Applying Genetic Algorithm and Neural Network to the Conjunctive Use of Surface and Subsurface Water

The conjunctive use of surface and subsurface water is one of the most effective ways to increase water supply reliability with minimal cost and environmental impact. This study presents a novel stepwise optimization model for optimizing the conjunctive use of surface and subsurface water resource management. At each time step, the proposed model decomposes the nonlinear conjunctive use problem into a linear surface water allocation sub-problem and a nonlinear groundwater simulation sub-problem. Instead of using a nonlinear algorithm to solve the entire problem, this decomposition approach integrates a linear algorithm with greater computational efficiency. Specifically, this study proposes a hybrid approach consisting of Genetic Algorithm (GA), Artificial Neural Network (ANN), and Linear Programming (LP) to solve the decomposed two-level problem. The top level uses GA to determine the optimal pumping rates and link the lower level sub-problem, while LP determines the optimal surface water allocation, and ANN performs the groundwater simulation. Because the optimization computation requires many groundwater simulations, the ANN instead of traditional numerical simulation greatly reduces the computational burden. The high computing performance of both LP and ANN significantly increase the computational efficiency of entire model. This study examines four case studies to determine the supply efficiencies under different operation models. Unlike the high interaction between climate conditions and surface water resource, groundwater resources are more stable than the surface water resources for water supply. First, results indicate that adding an groundwater system whose supply productivity is just 8.67 % of the entire water requirement with a surface water supply first (SWSF) policy can significantly decrease the shortage index (SI) from 2.93 to 1.54. Second, the proposed model provides a more efficient conjunctive use policy than the SWSF policy, achieving further decrease from 1.54 to 1.13 or 0.79, depending on the groundwater rule curves. Finally, because of the usage of the hybrid framework, GA, LP, and ANN, the computational efficiency of proposed model is higher than other models with a purebred architecture or traditional groundwater numerical simulations. Therefore, the proposed model can be used to solve complicated large field problems. The proposed model is a valuable tool for conjunctive use operation planning.     

Conjunctive Use of Surface Water and Groundwater: Application of Support Vector Machines (SVMs) and Genetic Algorithms

Combined simulation-optimization models have been widely used to address the management of water resources issues. This paper presents a simulation-optimization model for conjunctive use of surface water and groundwater at a basin-wide scale, the Zayandehrood river basin in west central Iran. In the Zayandehrood basin, in the past 10 years, a historical low rainfall in the head of the basin, combined with growing demand for water, has triggered great changes in water management at basin and irrigation system level. The conjunctive use model that coupled numerical simulation with nonlinear optimization is used to minimize shortages of water in meeting irrigation demands for four irrigation systems. Constraints guarantee the maximum/minimum cumulative groundwater drawdown and maximum capacity of irrigation systems. A support vector machines (SVMs) model is developed as a simulator of surface water and groundwater interaction model while a genetic algorithm (GA) is used as the optimization model. Conjunctive use model runs for three scenarios. Results show that the accuracy of SVMs as a simulator for surface water and groundwater interaction model is good and that it is possible to decrease the water shortage for irrigation systems with application of proposed SVMs-GA model.     

Optimization of Pump Scheduling Program in Water Supply Systems Using a Self-Adaptive NSGA-II; a Review of Theory to Real Application

The operation of pumps imposes significant costs on a water distribution system for energy supply and pumps maintenance. To derive an optimum pumps scheduling program, this study presents a multiobjective optimization problem with the objective functions of 1- energy cost and 2- the number of pump switches. The optimization of both objective functions together leads to a multiobjective constrained optimization problem. To solve the problem, the Non-Dominated Sorting Genetic Algorithm, version II, (NSGA-II) is coupled to the EPANET hydraulic simulation model. For constraint handling, some modifications are introduced to the standard NSGA-II to make it self-adaptive through which all constraints of the problem are automatically satisfied. Application of the model to a test example and a real pipe network verifies that the proposed scheme is computationally efficient and reliable. Also, optimization of the real pipe network reveals that by a careful pump scheduling program the total number of pump switches even in optimum operations could be decreased by 69% while the energy cost increases at most by 10%.     

基于并行遗传算法的新安江模型参数优化率定方法

本文结合新安江模型参数的特点，以洪峰流量、峰现时间和洪水总量的合格率为评价目标，定义了评价洪水性能目标的模糊合格率，提出了新安江模型参数率定的并行遗传算法，并在微机集群环境下，利用JAVA语言进行了算法编程。串行和并行遗传算法计算结果的比较表明，本文提出的并行遗传算法可以大大缩短优化过程的时间，得到较为稳定的模型参数。     

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.     

Simulation and Multi-Objective Management of Coastal Aquifers in Semi-Arid Regions

Groundwater is the main water resource in many semi-arid coastal regions and water demand, especially in summer months, can be very high. Groundwater withdrawal for meeting this demand often causes seawater intrusion and degradation of water quality of coastal aquifers. In order to satisfy demand, a combined management plan is proposed and is under consideration for the island of Santorini. The plan involves: (1) desalinization (if needed) of pumped water to a potable level using reverse osmosis and (2) injection into the aquifer of biologically-treated waste water. The management plan is formulated in a multi-objective, optimization framework, where simultaneous minimization of economic and environmental costs is desired, subject to a constraint so that cleaned water satisfies demand. The decision variables concern the well locations and the corresponding pumping and recharging rates. The problem is solved using a computationally efficient, multi-objective, genetic algorithm (NSGAII). The constrained multi-objective, optimization problem is transformed to an unconstrained one using a penalty function proportional to constraint violation. This extends the definition of the objective function outside the domain of feasibility. The impact of prolonged droughts on coastal aquifers is investigated by assuming various scenarios of reduced groundwater recharge. Water flow and quality in the coastal aquifer is simulated using a three-dimensional, variable density, finite difference model (SEAWAT). The method is initially applied to a test aquifer and the trade-off curves (Pareto fronts) are determinedl for each drought scenario. The trade-off curves indicate an increase on the economic and environmental cost as groundwater recharge reduces due to climate change.     

Improving Consumer Satisfaction in Water Distribution Networks Through Optimal Use of Auxiliary Tanks (A Case Study of Kashan City,Iran)

Temporal and spatial variations in pressure may lead to consumer dissatisfaction and distrust of water distribution networks when it comes to reliable performance. Pressure management is a set of programs and operations conducted in water distribution networks to adjust the pressure. Constructing new auxiliary tanks in proper locations at the best height for the area they serve minimizes the pressure fluctuations. Additionally, chlorine is often injected in the reservoirs and tanks to improve the water quality. The goal of this research was to improve the condition of the network by adding auxiliary tanks with appropriate locations, heights and chlorine concentration. An optimization model is prepared to optimize consumer satisfaction, water quality and the relevant costs as objective functions. The performance of the models are evaluated by a selected case study; and the objectives are optimized in three scenarios. Using the proposed model in a water distribution network, a trade-off diagram of reliability and costs is obtained, that lets the decision makers select the proper options considering the available fund. A new indicator, the consumer satisfaction index, is also proposed as a way to evaluate the performance of water distribution networks.     

Simulation-Optimization Modeling for Sustainable Groundwater Development: A Moroccan Coastal Aquifer Case Study

A transient simulation model characterizing groundwater flow in the coastal aquifer of Rhis-Nekor was constructed and calibrated. The flow model was then used in conjunction with a genetic algorithm based optimization model to explore the optimal pumping schemes that meet current and future water demands while minimizing the risks for several adverse environmental impacts, such as saltwater intrusion prevention, avoiding excessive drawdown, as well as controlling waterlogging and salinity problems. Modeling results demonstrate the importance of this combined simulation-optimization methodology for solving groundwater management problems associated with the Rhis-Nekor plain.     

引江济淮工程（河南段）多目标水量优化调度

引江济淮工程（河南段）涉及河道、闸泵、管道和调蓄水库,约束条件复杂,常规的优化调度算法难以搜索可行解,求解效率低。选用受水区缺水率平均值最小、泵站总抽水量最小和受水区缺水率标准差最小作为目标函数,从供水保障、供水成本和公平性角度构建多目标水量优化调度模型。基于可行搜索思路,结合逆序演算和顺序演算过程对约束条件进行处理,引入决策系数,通过映射关系使搜索空间保持在可行域中,结合多目标非支配排序遗传算法（non-dominated sorting genetic algorithms,NSGA-II）进行求解,得到Pareto最优解集,并采用熵权法进行方案优选。结果表明,基于可行搜索的NSGA-II算法能够有效求解复杂调度系统的多目标优化问题,综合考虑多个目标的最优方案相对单目标方案更加合理,结果可为引江济淮工程（河南段）运行管理提供决策支撑。     

Joint optimization scheduling for water conservancy projects in complex river networks

In this study, we simulated water flow in a water conservancy project consisting of various hydraulic structures, such as sluices, pumping stations, hydropower stations, ship locks, and culverts, and developed a multi-period and multi-variable joint optimization scheduling model for flood control, drainage, and irrigation. In this model, the number of sluice holes, pump units, and hydropower station units to be opened were used as decision variables, and different optimization objectives and constraints were considered. This model was solved with improved genetic algorithms and verified using the Huaian Water Conservancy Project as an example. The results show that the use of the joint optimization scheduling led to a 10% increase in the power generation capacity and a 15% reduction in the total energy consumption. The change in the water level was reduced by 0.25 m upstream of the Yundong Sluice, and by 50% downstream of pumping stations No. 1, No. 2, and No. 4. It is clear that the joint optimization scheduling proposed in this study can effectively improve power generation capacity of the project, minimize operating costs and energy consumption, and enable more stable operation of various hydraulic structures. The results may provide references for the management of water conservancy projects in complex river networks.     

Well Field Management Using Multi-Objective Optimization

Efficient management of groundwater resources is important because groundwater availability is limited and, locally, groundwater quality has been impaired because of contamination. Here we present a multi-objective optimization framework for improving the management of a water works that operates with infiltration basins, injection wells and abstraction wells. The two management objectives are to minimize the amount of water needed for infiltration and to minimize the risk of getting contaminated water into the drinking water wells. The management is subject to a daily demand fulfilment constraint. Two different optimization methods are tested. Constant scheduling where decision variables are held constant during the time of optimization, and sequential scheduling where the optimization is performed stepwise for daily time steps. The latter is developed to work in a real-time situation. Case study optimization results are presented for the Hardhof water works in Zurich, Switzerland. It is found that both methods perform better than the historical management. The constant scheduling performs best in fairly stable conditions, whereas the sequential optimization performs best in extreme situations with heavy rainfall or large changes in water demand.