A Hybrid Fuzzy-Based Multi-Objective PSO Algorithm for Conjunctive Water Use and Optimal Multi-Crop Pattern Planning

This paper focuses on extracting an optimal multi-crop pattern plan through multi-objective conjunctive surface-ground water use management. Minimizing shortages in meeting irrigation demands, maximizing groundwater resources sustainability and maximizing agricultural net benefits are the three main goals of the multi-objective optimization problem solved in this paper. A new robust fuzzy-based multi-objective PSO algorithm called f-MOPSO is adopted and modified to solve a three-objective real-world conjunctive use management problem presented in this paper after testing on standard test problems revealed f-MOPSO superiority as compared to the well-known multi-swarm vector evaluated PSO (VEPSO) algorithm. The f-MOPSO benefits from a well-organized Sugeno fuzzy inference system (SFIS) designed for handling multi-objective nature of the optimization problems. The unique performance of f-MOPSO is not only presenting the better final solutions, but also aggregating the capabilities for measurement of dominance and diversity of the solutions in one stage by one index named comprehensive dominance index, in contrast to a wide range of multi-objective algorithms that evaluate dominance and diversity in two separate stages resulting in excessive computational burden. The optimization model is carried out on a 10-year long-term simulation period, resulting in increasing irrigation efficiency i.e. decreasing water losses, decreasing water consumption per unit cultivated area and increasing water productivity compared to those similar criteria observed in actual operation in the study area. The wheat and rice crops were identified as the dominant crops, while the optimization model was the least interested to onion cultivation, assigning the least average cultivation area to this crop over the whole planning period.     

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.     

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.     

A Multiobjective Optimisation Model for Groundwater Remediation Design at Petroleum Contaminated Sites

This study proposes a fuzzy multi-objective model for groundwater remediation in petroleum-contaminated aquifers. The optimisation system is designed based on the PAT technology, and includes two objectives (i.e. total pumping rate and average post-remedial contaminant concentration). The relationship between pumping rates and contamination concentrations at all monitoring wells after remediation are determined by a proxy model, which integrates simulation, inference, and optimisation technologies and is composed of intercept, linear, interactive, and quadratic options. Fuzzy algorithms are used to solve the formulated multi-objective optimisation problem to find optimal solutions. The model is then applied to a petroleum-contaminated aquifer in western Canada. The trade-off and λ analyses of the results indicate that the fuzzy multi-objective model has great potential in groundwater remediation applications as it can: (1) provide reliable groundwater remediation strategies, (2) reduce computational costs in the optimization processes, and (3) balance the trade-off between remediation costs and remediation outcomes.     

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.     

Application of Artificial Neural Networks for Identifying Optimal Groundwater Pumping and Piping Network Layout

The simulation-optimization approach is often used to solve water resource management problem although repeated use of the simulation model enhances the computational load. In this study, Artificial Neural Network (ANN) and Bagged Decision Trees (BDT) models were developed as an approximator for Analytic Element Method (AEM) based groundwater flow model. Developed ANN and BDT models were coupled with Particle Swarm Optimization (PSO) model to solve the well-field management problem. The groundwater flow model was developed for the study area and used to generate the dataset for the training and testing of the ANN & BDT models. These coupled ANN-PSO & BDT-PSO models were employed to find the optimal design and cost of the new well-field system by optimizing discharge & co-ordinate of wells along with the cost effective layout of piping network. The Minimum Spanning Tree (MST) based model was used to find out the optimal piping network layout and checking the hydraulic constraints in the piping network. The results show that the ANN & BDT models are good approximators of AEM model and they can reduce the computational burden significantly although ANN model performs better than BDT model. The results show that the coupling of piping network model with simulation-optimization model is very significant for finding the cost effective and realistic design of the new well-field system.     

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.     

Distributed Simulation‐optimization Model for Conjunctive Use of Groundwater and Surface Water Under Environmental and Sustainability Restrictions

Evolving optimal management strategies are essential for the sustainable development of water resources. A coupled simulation-optimization model that links the simulation and optimization models internally through a response matrix approach is developed for the conjunctive use of groundwater and surface water in meeting irrigation water demand and municipal water supply, while ensuring groundwater sustainability and maintaining environmental flow in river. It incorporates the stream-aquifer interactions, and the aquifer response matrix is generated from a numerical groundwater model. The optimization model is solved by using MATLAB. The developed model has been applied to the Hormat-Golina valley alluvial stream-aquifer system, Ethiopia, and the optimal pumping schedules were obtained for the existing 43 wells under two different scenarios representing with and without restrictions on stream flow depletion, and satisfying the physical, operational and managerial constraints arising due to hydrological configuration, sustainability and ecological services. The study reveals that the total annual optimal pumping is reduced by 19.75?% due to restrictions on stream flow depletion. It is observed that the groundwater pumping from the aquifer has a significant effect on the stream flow depletion and the optimal conjunctive water use plays a great role in preventing groundwater depletion caused by the extensive pumping for various purposes. The groundwater contribution in optimal conjunctive water use is very high having a value of 92?% because of limited capacity of canal. The findings would be useful to the planners and decision makers for ensuring long-term water sustainability.

     

基于分段粒子群算法的梯级水库多目标优化调度模型研究

提出了约束破坏向量、分段粒子群算法以及多目标分段粒子群算法,有效解决了在时间步长较小、计算时段数目较多时,传统智能优化算法解水库优化调度问题的寻优效率低下甚至无可行解的问题。该方法基于粒子群算法框架,引入约束破坏向量、分段操作和特殊变异操作来增强进化过程中的种群质量,从而提高算法的计算效率。闽江流域金溪梯级水库多目标优化调度的实例分析表明,在解时间步长较小、计算时段数目较多的水库优化调度问题时,分段粒子群算法、多目标分段粒子群算法相对其他算法具有明显优势。     

Stochastic and Robust Multi-Objective Optimal Management of Pumping from Coastal Aquifers Under Parameter Uncertainty

Combined simulation-optimization approaches have been used as tools to derive optimal groundwater management strategies to maintain or improve water quality in contaminated or other aquifers. Surrogate models based on neural networks, regression models, support vector machies etc., are used as substitutes for the numerical simulation model in order to reduce the computational burden on the simulation-optimization approach. However, the groundwater flow and transport system itself being characterized by uncertain parameters, using a deterministic surrogate model to substitute it is a gross and unrealistic approximation of the system. Till date, few studies have considered stochastic surrogate modeling to develop groundwater management methodologies. In this study, we utilize genetic programming (GP) based ensemble surrogate models to characterize coastal aquifer water quality responses to pumping, under parameter uncertainty. These surrogates are then coupled with multiple realization optimization for the stochastic and robust optimization of groundwater management in coastal aquifers. The key novelty in the proposed approach is the capability to capture the uncertainty in the physical system, to a certain extent, in the ensemble of surrogate models and using it to constrain the optimization search to derive robust optimal solutions. Uncertainties in hydraulic conductivity and the annual aquifer recharge are incorporated in this study. The results obtained indicate that the methodology is capable of developing reliable and robust strategies for groundwater management.     

Chance Constrained Optimal Design of Composite Channels Using Meta-Heuristic Techniques

Optimal design of irrigation channels has an important role in planning and management of irrigation projects. The input parameters used in design of irrigation channels are prone to uncertainty and may result in failure of channels. To improve the overall reliability and cost effectiveness, optimal design of composite channels is performed as a chance constrained problem in this study. The models are developed to minimize the total cost, while satisfying the specified probability of the channel capacity being greater than the design flow. The formulated model leads to a highly non-linear and non-convex optimization problem having multimodal behavior. In this paper, the usefulness of two meta-heuristic search algorithms such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) are investigated to obtain the optimal solutions. Two site specific cases of restricted top width and restricted flow depth are also analyzed. It is found that both the algorithms performing quite well in giving optimal solutions and handling the additional constraints.     

Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies.     

Algorithm for Increasing the Speed of Evolutionary Optimization and its Accuracy in Multi-objective Problems

Optimization algorithms are important tools for the solution of combinatorial management problems. Nowadays, many of those problems are addressed by using evolutionary algorithms (EAs) that move toward a near-optimal solution by repetitive simulations. Sometimes, such extensive simulations are not possible or are costly and time-consuming. Thus, in this study a method based on artificial neural networks (ANN) is proposed to reduce the number of simulations required in EAs. Specifically, an ANN simulator is used to reduce the number of simulations by the main simulator. The ANN is trained and updated only for required areas in the decision space. Performance of the proposed method is examined by integrating it with the non-dominated sorting genetic algorithm (NSGAII) in multi-objective problems. In terms of density and optimality of the Pareto front, the hybrid NSGAII-ANN is able to extract the Pareto front with much less simulation time compared to the sole use of the NSGAII algorithm. The proposed NSGAII-ANN methodology was examined using three standard test problems (FON, KUR, and ZDT1) and one real-world problem. The latter addresses the operation of a reservoir with two objectives (meeting demand and flood control). Thus, based on this study, use of the NSGAII-ANN integrative algorithm in problems with time-consuming simulators reduces the required time for optimization up to 50 times. Results of the real-world problem, despite lower computational-time requirements, show a performance similar to that achieved in the aforementioned test problems.     

Pumping Optimization of Coastal Aquifers Assisted by Adaptive Metamodelling Methods and Radial Basis Functions

The application of metamodelling frameworks is a popular approach to handle the computational cost arising from complex computer simulations and global optimization algorithms in simulation-optimization routines. In this paper, Radial Basis Functions (RBF) are used as metamodels for the computationally expensive variable-density flow and salt transport numerical simulations, in a pumping optimization problem of coastal aquifers. While RBF metamodels have been fairly utilized in many engineering optimization problems, their use is very limited in coastal aquifer management. Two adaptive metamodelling frameworks are employed, that is, the adaptive-recursive approach and the metamodel-embedded evolution strategy. In both frameworks, cubic RBF models are used to approximate the constraint functions imposed on the coastal aquifer pumping optimization problem. The optimal pumping rates are first calculated based on the variable-density and salt transport numerical models of seawater intrusion. The resulting optimal solutions and the computational times are set as benchmark values in order to assess the performance of the metamodelling optimization strategies. Results indicate that the metamodel-embedded evolution framework outperformed in terms of computational efficiency the adaptive-recursive approach while it successfully located the region of the global optimum. Furthermore, with the metamodel-embedded evolution strategy the computational time of the variable-density-based optimization was reduced by 96 %.     

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.     

Simulation and optimization of an experimental membrane wastewater treatment plant using computational intelligence methods

The optimization of relaxation and filtration times of submerged microfiltration flat modules in membrane bioreactors used for municipal wastewater treatment is essential for efficient plant operation. However, the optimization and control of such plants and their filtration processes is a challenging problem due to the underlying highly nonlinear and complex processes. This paper presents the use of genetic algorithms for this optimization problem in conjunction with a fully calibrated simulation model, as computational intelligence methods are perfectly suited to the nonconvex multi-objective nature of the optimization problems posed by these complex systems. The simulation model is developed and calibrated using membrane modules from the wastewater simulation software GPS-X based on the Activated Sludge Model No.1 (ASM1). Simulation results have been validated at a technical reference plant. They clearly show that filtration process costs for cleaning and energy can be reduced significantly by intelligent process optimization.     

A Probabilistic Multiperiod Simulation–Optimization Approach for Dynamic Coastal Aquifer Management

Combined simulation–optimization (CSO) schemes are common in the literature to solve different groundwater management problems, and CSO is particularly well-established in the coastal aquifer management literature. However, with a few exceptions, nearly all previous studies have employed the CSO approach to derive static groundwater management plans that remain unchanged during the entire management period, consequently overlooking the possible positive impacts of dynamic strategies. Dynamic strategies involve division of the planning time interval into several subintervals or periods, and adoption of revised decisions during each period based on the most recent knowledge of the groundwater system and its associated uncertainties. Problem structuring and computational challenges seem to be the main factors preventing the widespread implementation of dynamic strategies in groundwater applications. The objective of this study is to address these challenges by introducing a novel probabilistic Multiperiod CSO approach for dynamic groundwater management. This includes reformulation of the groundwater management problem so that it can be adapted to the multiperiod CSO approach, and subsequent employment of polynomial chaos expansion-based stochastic dynamic programming to obtain optimal dynamic strategies. The proposed approach is employed to provide sustainable solutions for a coastal aquifer storage and recovery facility in Oman, considering the effect of natural recharge uncertainty. It is revealed that the proposed dynamic approach results in an improved performance by taking advantage of system variations, allowing for increased groundwater abstraction, injection and hence monetary benefit compared to the commonly used static optimization approach.

     

多级串联明渠调水工程多目标水位预测控制模型研究

针对传统的明渠水位预测控制模型无法考虑闸门调控次数限制的问题,本文在以往的预测控制目标中加入了流量调整惩罚量,构造了多目标渠池水位预测控制模型;并采用带有精英排序策略的遗传算法来进行复杂优化问题的求解。将此模型应用于南水北调中线干线工程最后6级渠池的虚拟仿真模型中对模型可靠性进行分析,结果表明在两种测试工况中,本文的多目标预测控制模型相比于传统预测控制模型,能在保持相似的水位控制效果同时使得闸控次数降低43%和52%;而且采用遗传算法求解能考虑闸门死区带来的流量最小变幅约束问题,在需要提前进行流量微调的情况下生成更加合理的调控方案。本文结果也表明,基于水位状态预测模型构造多目标预测控制模型,并采用启发式算法进行优化问题求解,这一思路具有一定可行性。     

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。     

Design of optimal environmental flow regime at downstream of reservoirs using wetted perimeter-optimization method

Conflict between water demand and environmental flow requirements is a challenging aspect in the reservoir management. Hence, optimizing environmental flow regime is one of the most important tasks at downstream of the large dams. The present study proposes a coupled simulation–optimization method based on the wetted perimeter method as an assessment method of the environmental flow and optimization of the reservoir operation to minimize difference between habitat loss and water demand loss using different metaheuristic algorithms. Moreover, the fuzzy TOPSIS as the decision-making system was applied for ranking the optimization algorithms. Indices including reliability index, vulnerability index, root mean square error and mean absolute error were utilized as criteria to measure the system performance and to select the best algorithm. Based on the results, gravity search algorithm (GSA) was the best method to optimize environmental flow regime at downstream of the reservoir in the case study. The proposed method is able to optimize environmental flow to minimize conflicts between human’s needs and aquatic’s needs considering storage constraints in the reservoir management. The proposed method might minimize negotiations between environmental managers and stakeholders. Furthermore, it should be noted that original wetted perimeter method is not able to provide optimal environmental flow regime based on a balance between users and constraints in the reservoir management such as storage constraints. The proposed method converts wetted perimeter method from an assessment method to a simulation–optimization method for optimizing environmental flow at downstream of the reservoirs.