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.     

Extracting Optimal Policies of Hydropower Multi-Reservoir Systems Utilizing Enhanced Differential Evolution Algorithm

Deriving the optimal policies of hydropower multi-reservoir systems is a nonlinear and high-dimensional problem which makes it difficult to achieve the global or near global optimal solution. In order to optimally solve the problem effectively, development of optimization methods with the purpose of optimizing reservoir operation is indispensable as well as inevitable. This paper introduces an enhanced differential evolution (EDE) algorithm to enhance the exploration and exploitation abilities of the original differential evolution (DE) algorithm. The EDE algorithm is first applied to minimize two benchmark functions (Ackley and Shifted Schwefel). In addition, a real world two-reservoir hydropower optimization problem and a large scale benchmark problem, namely ten-reservoir problem, were considered to indicate the effectiveness of the EDE. The performance of the EDE was compared with the original DE to solve the three optimization problems. The results demonstrate that the EDE would have a powerful global ability and faster convergence than the original DE to solve the two benchmark functions. In the 10-reservoir optimization problem, the EDE proved to be much more functional to reach optimal or near optimal solution and to be effective in terms of convergence rate, standard deviation, the best, average and worst values of objective function than the original DE. Also, In the case of two-reservoir system, the best values of the objective function obtained 93.86 and 101.09 for EDE and DE respectively. Based on the results, it can be stated that the most important reason to improve the performance of the EDE algorithm is the promotion of local and global search abilities of the DE algorithm using the number of novel operators. Also, the results of these three problems corroborated the superior performance, the high efficiency and robustness of the EDE to optimize complex and large scale multi-reservoir operation problems.     

Shuffled complex evolution coupled with stochastic ranking for reservoir scheduling problems

This paper introduces an optimization method(SCE-SR) that combines shuffled complex evolution(SCE) and stochastic ranking(SR) to solve constrained reservoir scheduling problems,ranking individuals with both objectives and constrains considered.A specialized strategy is used in the evolution process to ensure that the optimal results are feasible individuals.This method is suitable for handling multiple conflicting constraints,and is easy to implement,requiring little parameter tuning.The search properties of the method are ensured through the combination of deterministic and probabilistic approaches.The proposed SCE-SR was tested against hydropower scheduling problems of a single reservoir and a multi-reservoir system,and its performance is compared with that of two classical methods(the dynamic programming and genetic algorithm).The results show that the SCE-SR method is an effective and efficient method for optimizing hydropower generation and locating feasible regions quickly,with sufficient global convergence properties and robustness.The operation schedules obtained satisfy the basic scheduling requirements of reservoirs.     

基于灰色关联度与理想点法的梯级水电站多目标优化调度方法

针对梯级水电站群调度目标间的协调问题,建立了多目标优化调度模型,提出了基于灰色关联度法与熵权理想点法相结合的迭代计算方法。应用灰色关联度法将多目标优化模型转换成多个单目标优化模型,并采用逐步优化算法求解,得到多目标优化数学模型的非劣解集,以熵权理想点法从非劣解集中选择最优解。澜沧江流域梯级水电站群的实例研究表明,该方法较好地处理了不同目标间、不同目标权重组合方案间双重多目标优化问题,为协调长期优化调度多目标间的矛盾提供了一种可行方法。     

水库群系统发电调度的合作博弈研究

水资源的竞争性和非排他性导致水库管理者基于个体利益进行发电调度,使得水库在满足个体利益的同时往往忽略了系统的整体效益。为了在保证个体利益的基础上实现系统总效益的最大化,建立了梯级水库群发电调度合作博弈模型;采用改进后的水循环算法对模型进行分层求解。以金沙江两库与三峡梯级构成的梯级水库群为研究对象,选取典型年进行实例计算。计算结果表明：梯级水库群发电调度的合作博弈模型在获得系统最大效益的同时使得个体利益达到Pareto最优状态,实现水库群总效益和单库个体效益的双赢,既优于联合优化调度模型又优于单库优化调度模型。该合作博弈模型及其新解法可为水库群调度决策分析开创一种新思路。     

Optimal Operation of Hydropower Reservoir Systems Using Weed Optimization Algorithm

The optimal hydropower operation of reservoir systems is known as a complex nonlinear nonconvex optimization problem. This paper presents the application of invasive weed optimization (IWO) algorithm, which is a novel evolutionary algorithm inspired from colonizing weeds, for optimal operation of hydropower reservoir systems. The IWO algorithm is used to optimally solve the hydropower operation problems for both cases of single reservoir and multi reservoir systems, over short, medium and long term operation periods, and the results are compared with the existing results obtained by the two most commonly used evolutionary algorithms, namely, particle swam optimization (PSO) and genetic algorithm (GA). The results show that the IWO is more efficient and effective than PSO and GA for both single reservoir and multi reservoir hydropower operation problems.     

水库群防洪系统优化调度模型及应用

本文以澧水流域中上游江垭、皂市及宜冲桥3个水库及其下游河道防洪系统联合优化调度问题为背景，建立了基于河道洪水演进方程与多目标离散微分动态规划的水库群防洪系统多目标优化调度模型，给出了一种离散微分动态规划与马斯京根洪水演进相结合多目标优化算法.经计算分析，结果满意.     

Application of an Interior-Point Algorithm For Optimization of a Large-Scale Reservoir System

Optimization of a multi-reservoir system operation is challenging due to the non-linearity, stochasticity, and dimensionality involved in such a problem. In this research, a long-term planning model is presented for optimizing the operation of Iranian Karoon-Dez reservoir system using an interior-point algorithm. The system is the largest multi-purpose reservoir system in Iran with hydropower generation, water supply, and environmental objectives. The focus is on resolving the dimensionality of this problem while considering hydropower generation and water supply objectives. The weighting and constraints methods of multi-objective programming are used to assess the trade-off between water supply and hydropower objectives so as to find noninferior solutions. The computational efficiency of the proposed approach is demonstrated using historical data taken from Karoon-Dez reservoir system.     

梯级水电站群短期联合优化调度研究

遗传算法是一种简单、适用的搜索方法,经常用于解决非线性复杂的问题。水库群的最优调度问题,就是利用搜索算法根据水库群进出水和综合利用情况,把水电站水库看作一个系统,把系统的各元素,输入／输出参数等简化和假设后建立简化通用的数学模型,用搜索算法对该数学模型进行优化仿真,得出最优解。     

梯级水电站群中长期优化调度的离散梯度逐步优化算法

充分利用现有水电资源,进行库群中长期优化调度是构建清洁低碳、安全高效的现代能源体系的重要措施。逐步优化算法(POA)将多阶段问题转化为多个两阶段子优化问题,是求解中长期库群优化调度较为广泛且有效的一种方法。但随着水库数目的增加,POA仍会面临严重的"维数灾"问题。本文以梯度下降法为基础,提出离散梯度的概念及离散梯度逐步优化算法(DGPOA),该方法在不直接求导的情况下充分利用局部离散梯度信息确定最优搜索方向,可以快速获得优化结果。最后将该算法应用到澜沧江流域五水库梯级系统中,在不同离散精度和来水条件下,利用POA、POA-DPSA和DGPOA算法对梯级水库进行优化计算。结果表明,在不显著降低全局搜索能力的情况下,DGPOA的计算速度分别达到了POA-DPSA算法的8~12倍,POA算法的50~250倍,是一种解决梯级水库站群中长期优化调度中"维数灾"问题的有效方法。     

长江上游控制性水库群联合调度及水资源影响分析

针对长江上游控制性水库群联合调度问题,建立了大规模混联水库群联合优化调度模型,并提出离散微分动态规划(DDDP)和逐步优化算法(POA)相结合的混合方法,实现大规模混联梯级水库群联合优化调度问题的高效求解。在此基础上,结合流域长系列历史径流资料,进行了长江上游控制性梯级水库群调度模拟,分析了联合调度的发电效益;并在此基础上,结合相关研究成果,探究并分析了梯级水库群建成投运后,联合调度对流域水资源的影响。成果表明,梯级水库群的建成及联合调蓄对于长江中下游枯水期的流量补偿效益十分明显,供水、航运以及压咸补淡等综合效益十分显著。     

Identifying Explicit Formulation of Operating Rules for Multi-Reservoir Systems Using Genetic Programming

Operating rules have been widely used to handle the inflows uncertainty for reservoir long-term operations. Such rules are often expressed in implicit formulations not easily used by other operators and/or reservoirs directly. This study presented genetic programming (GP) to derive the explicit nonlinear formulation of operating rules for multi-reservoir systems. Steps in the proposed method include: (1) determining the optimal operation trajectory of the multi-reservoir system using the dynamic programming to solve a deterministic long-term operation model, (2) selecting the input variables of operating rules using GP based on the optimal operation trajectory, (3) identifying the formulation of operating rules using GP again to fit the optimal operation trajectory, (4) refining the key parameters of operating rules using the parameterization-simulation-optimization method. The method was applied to multi-reservoir system in China that includes the Three Gorges cascade hydropower reservoirs (Three Gorges and Gezhouba reservoirs) and the Qing River cascade hydropower reservoirs (Shuibuya, Geheyan and Gaobazhou reservoirs). The inflow and storage energy terms were selected as input variables for total output of the aggregated reservoir and for decomposition. It was shown that power energy term could more effectively reflect the operating rules than water quantity for the hydropower systems; the derived operating rules were easier to implement for practical use and more efficient and reliable than the conventional operating rule curves and artificial neural network (ANN) rules, increasing both average annual hydropower generation and generation assurance rate, indicating that the proposed GP formulation had potential for improving the operating rules of multi-reservoir system.     

Optimal Allocation of Flood Control Capacity for Multi-Reservoir Systems Using Multi-Objective Optimization Approach

Operation of multi-reservoir systems during flood periods is of great importance in the field of water resources management. This paper proposes a multi-objective optimization model with new formulation for optimal operation of multi-reservoir systems. In this model, the release rate and the flood control capacity of each reservoir is considered as decision variable and the resulting nonlinear non-convex multi-objective optimization problem is solved with ε-constraint method through the mixed integer linear programming (MILP). Objective functions of the model are minimizing the flood damage at downstream sites and the loss of hydropower generation. The developed model is used to determine optimal operating strategies for Karkheh multi-reservoir system in southwestern Iran. For this purpose, the model is executed in two scenarios based on “two-reservoir” and “six-reservoir” systems and for floods with return periods of 25 and 50 years. The results show that in two-reservoir system, flood damage is at least about 114 million dollars and cannot be mitigated any further no matter how hydropower generation is managed. But, in the case of developing all six reservoirs, optimal strategies of coordinated operation can mitigate and even fully prevent flood damage.     

Robust Diversity-based Sine-Cosine Algorithm for Optimizing Hydropower Multi-reservoir Systems

Hydropower energy generation depends on the available water resources. Therefore, planning and operation of the water resource systems are paramount tasks for energy management. Since reservoirs are one of the important components of water resources systems, extracting optimal operating policies for proper management of energy generated from these systems is an imperative step. Optimizing reservoir system operation (ORSO) is a non-linear, large-scale, and non-convex problem with a large number of constraints and decision variables. To solve ORSO problem effectively, a robust diversity-based, sine-cosine algorithm (RDB-SCA) is developed in the present study by introducing several strategies to balance the global exploration and local exploitation ability and to achieve accurate and reliable solutions. An efficient linear operation rule is coupled with the RDB-SCA to maximize the energy generation. The proposed method is then applied to a real-world, multi-reservoir system to extract optimal operational policies and, consequently, maximize the energy production. It is shown that the RDB-SCA is able to generate 24, 14, and 6% more energy than the original SCA, respectively for 2-, 3-, and 4-reservoir systems. The present findings are useful to suggest guidelines for efficient operation of hydropower multi-reservoir systems. This paper is supported by https://imanahmadianfar.com/codes.

     

Multi-Objective Differential Evolution for Design of Cascade Hydropower Reservoir Systems

After Paris Agreement and obligation made by various countries to decrease greenhouse gases, generation of clean energy with low carbon was taken into consideration. Hydropower plant is considered as a clean, cheap and renewable energy source for generating electrical energy. Through the construction of the multipurpose dams and their optimal planning and management, we may decrease the potential losses sustained by aquatic ecosystem in addition to supplying the energy and fulfilling the industrial, agricultural and drinking water demands. In the present study, a multi-objective optimization model was proposed for determination of design parameters in cascade hydropower multi-purpose reservoir systems. Considering the significant number of constraints and decision variables and non-convex form of the objective functions and constraints, particularly in multi-reservoir systems, a multi-objective evolutionary algorithm (MOEA) known as non-dominated sorting differential evolution (NSDE) was developed to solve the problem and reduce the computational costs. Karkheh River basin was selected as a case study in order to make an assessment on the capabilities and strength of the model. This basin is capable of generating hydropower energy and agricultural development with high environmental considerations due to Hurolazim International Wetland. Based on the results, we may supply various demands such as environmental demands of the aquatic ecosystem with high reliability as well as generating firm hydropower energy through optimal design of cascade hydropower reservoirs.     

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.     

Partially and Fully Constrained Ant Algorithms for the Optimal Solution of Large Scale Reservoir Operation Problems

This paper presents a constrained formulation of the ant colony optimization algorithm (ACOA) for the optimization of large scale reservoir operation problems. ACO algorithms enjoy a unique feature namely incremental solution building capability. In ACO algorithms, each ant is required to make a decision at some points of the search space called decision points. If the constraints of the problem are of explicit type, then ants may be forced to satisfy the constraints when making decisions. This could be done via the provision of a tabu list for each ant at each decision point of the problem. This is very useful when attempting large scale optimization problem as it would lead to a considerable reduction of the search space size. Two different formulations namely partially constrained and fully constrained version of the proposed method are outlined here using Max-Min Ant System for the solution of reservoir operation problems. Two cases of simple and hydropower reservoir operation problems are considered with the storage volumes taken as the decision variables of the problems. In the partially constrained version of the algorithm, knowing the value of the storage volume at an arbitrary decision point, the continuity equation is used to provide a tabu list for the feasible options at the next decision point. The tabu list is designed such that commonly used box constraints for the release and storage volumes are simultaneously satisfied. In the second and fully constrained algorithm, the box constraints of storage volumes at each period are modified prior to the main calculation such that ants will not have any chance of making infeasible decision in the search process. The proposed methods are used to optimally solve the problem of simple and hydropower operation of “Dez” reservoir in Iran and the results are presented and compared with the conventional unconstrained ACO algorithm. The results indicate the ability of the proposed methods to optimally solve large scale reservoir operation problems where the conventional heuristic methods fail to even find a feasible solution.     

Optimization of Multi-Reservoir Operating Rules for a Water Supply System

To obtain the optimal releases of the multi-reservoir system, two sets of joint operating rules (JOR-I and JOR-II) are presented based on the aggregation-disaggregation approach and multi-reservoir approach respectively. In JOR-I, all reservoirs are aggregated to an equivalent reservoir, the operating rules of which, the release rule of the system is optimized following operating rule curves coupled with hedging rules. Then the system release is disaggregated into each reservoir according to water supply priorities and the dynamic demand partition approach. In JOR-II, a two-stage demand partition approach is applied to allocate the different demand priorities to determine the release from each reservoir. To assess the reliability and effectiveness of the joint operating rules, the proposed rules are applied to a multi-reservoir system in Liaoning province of China. Results demonstrate that JOR-I is suitable for high-dimensional multi-reservoir operation problems with large-scale inflow data, while JOR-II is suitable for low-dimensional multi-reservoir operation problems with small-scale inflow data, and JOR-II performs better than JOR-I but requires more computation time. The research provides guidelines for the management of multi-reservoir system.     

Improving Optimization Efficiency for Reservoir Operation Using a Search Space Reduction Method

Reservoir operation problems are challenging to efficiently optimize because of their high-dimensionality, stochasticity, and non-linearity. To alleviate the computational burden involved in large-scale and stringent constraint reservoir operation problems, we propose a novel search space reduction method (SSRM) that considers the available equality (e.g., water balance equation) and inequality (e.g., firm output) constraints. The SSRM can effectively narrow down the feasible search space of the decision variables prior to the main optimization process, thus improving the computational efficiency. Based on a hydropower reservoir operation model, we formulate the SSRM for a single reservoir and a multi-reservoir system, respectively. To validate the efficiency of the proposed SSRM, it is individually integrated into two representative optimization techniques: discrete dynamic programming (DDP) and the cuckoo search (CS) algorithm. We use these coupled methods to optimize two real-world operation problems of the Shuibuya reservoir and the Shuibuya-Geheyan-Gaobazhou cascade reservoirs in China. Our results show that: (1) the average computational time of SSRM-DDP is 1.81, 2.50, and 3.07 times less than that of DDP when decision variables are discretized into 50, 100, and 500 intervals, respectively; and (2) SSRM-CS outperforms CS in terms of its capability of finding near-optimal solutions, convergence speed, and stability of optimization results. The SSRM significantly improves the search efficiency of the optimization techniques and can be integrated into almost any optimization or simulation method. Therefore, the proposed method is useful when dealing with large-scale and complex reservoir operation problems in water resources planning and management.     

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.