An Effective Approach to Long-Term Optimal Operation of Large-Scale Reservoir Systems: Case Study of the Three Gorges System

A new approach for optimization of long-term operation of large-scale reservoirs is presented, incorporating Incremental Dynamic Programming (IDP) and Genetic algorithm (GA) . The immense storage capacity of the large scale reservoirs enlarges feasible region of the operational decision variables, which leads to invalidation of traditional random heuristic optimization algorithms. Besides, long term raised problem dimension, which has a negative impact on reservoir operational optimization because of its non-linearity and non-convexity. The hybrid IDP-GA approach proposed exploits the validity of IDP for high dimensional problem with large feasible domain by narrowing the search space with iterations, and also takes the advantage of the efficiency of GA in solving highly non-linear, non-convex problems. IDP is firstly used to narrow down the search space with discrete d variables. Within the sub search space provided by IDP, GA searches the optimal operation scheme with continuous variables to improve the optimization precision. This hybrid IDP-GA approach was applied to daily optimization of the Three Gorges Project-Gezhouba cascaded hydropower system for annual evaluation from the year of 2004 to 2008. Contrast test shows hybrid IDP-GA approach outperforms both the univocal IDP and the classical GA. Another sub search space determined by actual operational data is also compared, and the hybrid IDP-GA approach saves about 10 times of computing resources to obtain similar increments. It is shown that the hybrid IDP GA approach would be a promising approach to dealing with long-term optimization problems of large-scale reservoirs.     

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.     

改进的粒子群算法在水库优化调度中应用

针对水库优化调度中存在的规模庞大、结构复杂,涉及大量的决策变量和复杂的约束条件,呈现出高维度、非线性、强约束特性,传统的优化方法难以直接求解或者计算效率低,存在早熟等问题。为了提高粒子群算法全局搜索能力和收敛性能,把下山搜索策略引入到粒子群智能算法中,提出了改进的粒子群算法。函数测试证明该方法改进了算法的鲁棒性,提高了算法求解效率。上述优化算法应用于水库优化调度模型求解中,计算结果表明:该方法易于实现,求解效率高,为水库优化调度模型求解提供了新的途径。     

耦合KL理论与调度特征的大规模水电站群优化调度降维方法

大规模水电站群优化调度计算效率是水电及电力系统运行面临的最棘手问题之一,是突破超百座水电站高维复杂系统求解的理论和技术障碍。本文提出一种耦合KL理论与调度特征的水电优化调度降维方法,通过对水电站群长系列调度样本进行主成分分析,识别调度过程中的库水位变化特征值与其对应的特征函数,采用KL理论将库水位描述为多个水位变化特征项的组合函数,引入Kullback-Leibler散度以根据问题特点确定调度特征项随机系数的概率分布及初始值;构建了两阶段逐步迭代寻优策略,通过动态搜索水位特征项的随机系数实现大规模水电站群优化调度的高效求解。提出的方法以云南电网超百座水电站群调度问题进行了验证,通过不同算例对方法的有效性、高效性、随机系数概率分布和参数敏感性进行了分析,与经典动态规划及其改进算法相比,KL方法在有效保持结果精度的条件下显著提高了计算效率。     

A Memetic Multi-objective Immune Algorithm for Reservoir Flood Control Operation

Reservoir flood control operation (RFCO) is a challenging optimization problem with multiple conflicting decision goals and interdependent decision variables. With the rapid development of multi-objective optimization techniques in recent years, more and more research efforts have been devoted to optimize the conflicting decision goals in RFCO problems simultaneously. However, most of these research works simply employ some existing multi-objective optimization algorithms for solving RFCO problem, few of them considers the characteristics of the RFCO problem itself. In this work, we consider the complexity of the RFCO problem in both objective space and decision space, and develop an immune inspired memetic algorithm, named M-NNIA2, to solve the multi-objective RFCO problem. In the proposed M-NNIA2, a Pareto dominance based local search operator and a differential evolution inspired local search operator are designed for the RFCO problem to guide the search towards the and along the Pareto set respectively. On the basis of inheriting the good diversity preserving in immune inspired optimization algorithm, M-NNIA2 can obtain a representative set of best trade-off scheduling plans that covers the whole Pareto front of the RFCO problem in the objective space. Experimental studies on benchmark problems and RFCO problem instances have illustrated the superiority of the proposed algorithm.     

A Genetic Algorithm Parallel Strategy for Optimizing the Operation of Reservoir with Multiple Eco-environmental Objectives

Optimizing the operation of reservoir involving ecological and environmental (eco-environmental) objectives is challenging due to the often competing social-economic objectives. Non-dominated Sorting Genetic Algorithm-II is a popular method for solving multi-objective optimization problems. However, within a complex search space, the NSGA-II population (i.e., a group of candidate solutions) may be trapped in local optima as the population diversity is progressively reduced. This study proposes a computational strategy that operates several parallel populations to maintain the diversity of the candidate solutions. An improved version of the NSGA-II, called c-NSGA-II is implemented by incorporating multiple recombination operators. The parallel strategy is then coupled into the routine of the c-NSGA-II and applied to the operation of the Qingshitan reservoir (Southwest of China) which includes three eco-environmental and two social-economic objectives. Three metrics (convergence, diversity, and hyper volume index) are used for evaluating the optimization performances. The results show that the proposed parallel strategy significantly improves the solution quality in both convergence and diversity. Two characteristic schemes are identified for the operation of the Qingshitan reservoir for trade-off between the eco-environmental and social-economic objectives.     

Multi-Colony Ant Algorithm for Continuous Multi-Reservoir Operation Optimization Problem

Ant Colony Optimization (ACO) algorithms are basically developed for discrete optimization and hence their application to continuous optimization problems require the transformation of a continuous search space to a discrete one by discretization of the continuous decision variables. Thus, the allowable continuous range of decision variables is usually discretized into a discrete set of allowable values and a search is then conducted over the resulting discrete search space for the optimum solution. Due to the discretization of the search space on the decision variable, the performance of the ACO algorithms in continuous problems is poor. In this paper a special version of multi-colony algorithm is proposed which helps to generate a non-homogeneous and more or less random mesh in entire search space to minimize the possibility of loosing global optimum domain. The proposed multi-colony algorithm presents a new scheme which is quite different from those used in multi criteria and multi objective problems and parallelization schemes. The proposed algorithm can efficiently handle the combination of discrete and continuous decision variables. To investigate the performance of the proposed algorithm, the well-known multimodal, continuous, nonseparable, nonlinear, and illegal (CNNI) Fletcher–Powell function and complex 10-reservoir problem operation optimization have been considered. It is concluded that the proposed algorithm provides promising and comparable solutions with known global optimum results.     

基于DPSA 的梯级水库群优化调度

动态规划法是一种求解多阶段决策优化问题的常用方法,在水库优化调度计算中应用广泛。该方法最大的缺陷就是用于水库群优化调度时易出现"维数灾"问题。逐次逼近动态规划法(DPSA)可以有效克服这一问题,它采用逐次迭代逼近的思想,将一个多维问题分解为多个一维问题求解。本文以水库运行模拟模型为基础,建立了基于DPSA的梯级水库群中长期优化调度模型,以汉江上游梯级水库群为研究对象,选取发电量最大为目标,对各水库库容进行离散,从而求解水库优化运行过程,其结果对于水库优化调度运行具有指导意义。     

Multi-objective Cultured Differential Evolution for Generating Optimal Trade-offs in Reservoir Flood Control Operation

Reservoir flood control operation (RFCO) is a complex problem because it needs to consider multiple objectives and a large number of constraints. Traditional methods usually convert multiple objectives into a single objective to solve, using weighted methods or constrained methods. In this paper, a new approach named multi-objective cultured differential evolution (MOCDE) is proposed to deal with RFCO. MOCDE takes cultural algorithm as its framework and adopts differential evolution (DE) in its population space. Considering the features of DE and multi-objective optimization, three knowledge structures are defined in belief space to improve the searching efficiency of MOCDE. MOCDE is first tested on several benchmark problems and compared with some well known multi-objective optimization algorithms. On achieving satisfactory performance for test problems, MOCDE is applied to a case study of RFCO. It is found that MOCDE provides decision makers many alternative non-dominated schemes with uniform coverage and convergence to true Pareto optimal solutions in a short time. The results obtained show that MOCDE can be a viable alternative for generating optimal trade-offs in reservoir multi-objective flood control operation.     

基于改进萤火虫算法的梯级水库优化调度研究

梯级水电站水库群联合调度问题具有复杂的约束条件,受到发电、供水、防洪等目标的制约。作为多目标非线性优化调度问题,为了解决传统算法中存在结果受初值参数影响较大、容易陷入局部最优解、收敛速度不理想等问题,首次尝试将萤火虫算法引入梯级水库优化调度研究中。在传统萤火虫算法模仿自然界萤火虫捕食求偶行为的基础上,对其进行优化与改进,引入目标空间中解的Pareto支配关系比较萤火虫荧光亮度,比较其优化解,采用轮盘赌法确定萤火虫每次更新过程中的移动路径,利用精英保留策略建立多目标萤火虫模型。通过典型的梯级水电站进行仿真计算,研究结果表明,改进的多目标萤火虫算法在优化过程中具有较强的寻优能力,能更好地进行全局搜索和局部搜索,计算过程中具有良好的稳定性,并且计算效率较高,优于遗传算法(GA)、粒子群算法(PSO)和蚁群算法(ACO),为多阶段、多约束的梯级水电站水库群中长期优化调度问题提供了新的途径和新方法。     

面向梯级水库多目标优化调度的进化算法研究

实际工程中以梯级水库多目标优化调度为代表的大规模高维多目标优化问题,其优化难度是一般方法所难以应对的。为此本文提出一种新型的多目标粒子群算法LMPSO,其包含了基于超体积指标Ihk的适应值分配方法与基于问题变换的搜索空间降维策略,以有效处理问题的高维目标向量与大规模决策变量。将该算法应用于溪洛渡-向家坝梯级水库的中长期多目标优化调度中,并与4种知名算法的计算结果进行对比分析,验证LMPSO在求解该类问题上的卓越性能。由此为多目标优化调度高质量非劣解集的获取提供一种可靠的方法,并为下一步的多目标调度决策提供有力的数据支持。     

Reference Point Based Multi-Objective Optimization of Reservoir Operation: a Comparison of Three Algorithms

Traditional multi-objective evolutionary algorithms treat each objective equally and search randomly in all solution spaces without using preference information. This might reduce the search efficiency and quality of solutions preferred by decision makers, especially when solving problems with complicated properties or many objectives. Three reference point based algorithms which adopt preference information in optimization progress, e.g., R-NSGA-II, r-NSGA-II and g-NSGA-II, have been shown to be effective in finding more preferred solutions in theoretical test problems. However, more efforts are needed to test their effectiveness in real-world problems. This study conducts a comparison of the above three algorithms with a standard algorithm NSGA-II on a reservoir operation problem to demonstrate their performance in improving the search efficiency and quality of preferred solutions. Under the same calculation times of the objective functions, Pareto optimal solutions of the four algorithms are used in the empirical comparison in terms of the approximation to the preferred solutions. Three performance indicators are then adopted for further comparison. Results show that R-NSGA-II and r-NSGA-II can improve the search efficiency and quality of preferred solutions. The convergence and diversity of their solutions in the concerned region are better than NSGA-II, and the closeness degree to the reference point can be increased by 42.8%, and moreover the number of preferred solutions can be increased by more than 3 times when part of objectives are preferred. By contrast, g-NSGA-II shows worse performance. This study exhibits the performance of three reference point based algorithms and provides insights in algorithm selection for multi-objective reservoir optimization problems.

     

Large scale reservoir operation by Constrained Particle Swarm Optimization algorithms

In this paper two adapted versions of Particle Swarm Optimization (PSO) algorithm are presented for the efficient solution of large scale reservoir operation problems with release volumes taken as the decision variables of the problem. In the first version, exploiting the sequential nature of the solution building procedure of the PSO, the continuity equation is used at each period to define a new set of bounds for the decision variable of the next period which satisfies storage volume constraints of the problem. Particles of the swarm are, therefore, forced to fly in the feasible region of the search space except for very rare cases and hence the name of the Partially Constrained Particle Swarm Optimization (PCPSO) algorithm. In the second, the periods of the operations are treated in a reverse order prior to the PCPSO search to define a new set of bounds for each storage volume such that partially constrained particles are not given any chance of producing infeasible solutions and, hence, the name of Fully Constrained Particle Swarm Optimization (FCPSO) algorithm. These methods are used here to solve two problems of water supply and hydropower operation of “Dez” reservoir in Iran and the results are presented and compared with those of the conventional unconstrained PSO and a genetic algorithm. Three cases of short, medium and long-term operations are considered to illustrate the efficiency and effectiveness of the proposed methods for the solution of large scale operation problems. The methods are shown to be superior to the original PSO and genetic algorithm in locating near optimal solutions and convergence characteristics. Proposed algorithms are also shown to be relatively insensitive to the swarm size and initial swarm compared to the original unconstrained PSO and genetic algorithm.     

FS-DDDP方法及其在水库群优化调度中的应用

可行搜索-离散微分动态规划(FS-DDDP)方法是在考虑水库运行的综合利用要求的前提下,利用正向搜索和逆向搜索相结合的方式寻找水库优化调度过程的大量可行轨迹,以目标函数较大的几个可行轨迹作为DDDP方法的初始轨迹分别进行再寻优计算的优化算法.该方法可进行单库优化计算,也可进行库群优化计算.黄河上游梯级水库数量较多,综合利用要求复杂.文中以该梯级为例,说明FS-DDDP方法可在满足该梯级水库群的河流生态用水、防凌用水、灌溉用水、发电用水等综合利用要求的前提下,以水库群发电效益最大为目标,求得水库群优化调度的较好解.     

水库多目标优化调度技术比较研究

多目标智能优化算法种类繁多,不断涌现,在水库优化调度中得到了广泛应用,但多目标智能优化技术仍然是目前水库群综合利用优化调度研究中的热点和难点之一。已有的研究算法大多是关于水库优化调度中适用性的应用研究,且实际问题简化多,在算法算子的选择、算法性能的探讨和比较、特别是多目标优化等方面还不够深入。为此,选择应用较为广泛的NSGA-Ⅱ和DEMO算法,从变量规模、约束处理技术等方面,对其在水库多目标优化调度中的应用效果进行初步分析、比较和评估,为水库多目标优化调度算法的选择提供了参考。     

XI World Water Congress of IWRA “Water Resources Management in the 21st Century”

Abstract

Stochastic Dynamic Programming and Deterministic Dynamic Programming techniques are used in this study to optimize a reservoir system under a max-min type of objective function to maximize the on-peak firm energy generation. This paper shows that SDP is not appropriate for the optimization as it significantly overestimates the firm energy targets while DDP resulted in very reasonable on-peak firm energy targets. An advantage of this objective function under DDP optimization is that it facilitates the sequential optimization of complex reservoir systems and successfully avoids the problem of dimensionality. The local optimum achieved by the sequential optimization is comparable with the global optimum. Implicit stochastic schemes are used to incorporate the stochastic behavior of the system in optimization. Simulation of the system with the optimum on-peak firm energy targets and synthetic flow series have resulted in high reliabilities for targets from DDP while those from SDP are very low.     

基于Fork/Join多核并行框架的梯级水库群优化调度

为了满足大规模梯级水库群优化调度精细化管理需求,解决决策计算耗时长及求解效率低等困难,提出了基于Fork/Join多核并行框架的梯级水库群优化调度并行求解方法,并以离散微分动态规划方法并行化为例,给出了梯级水库群优化调度方法在Fork/Join框架下的并行化实现方式。红水河大规模梯级水库群长期发电优化调度测试结果表明,并行计算能够充分发挥多核处理器的加速性能,有效缩短计算耗时,提高求解效率;选择合理的Fork/Join框架规模控制阈值是充分发挥并行优势的关键因素。     

基于可行空间搜索遗传算法的梯级水库群调度规则研究

以梯级水库群系统多年平均发电量和旬出力保证率最大为目标函数,以梯级水库群内各水库拐点式调度图为决策变量,建立梯级水库群联合发电调度模型,并采用可行空间搜索遗传算法进行求解。为了避免模型求解过程中对不可行解的过多处理,有针对性地对可行解进行优化。最后,以汉江流域梯级水库群为例,对模型和算法的有效性进行了验证。     

Flood Control Operation of Reservoir Group Using Yin-Yang Firefly Algorithm

Flood control operation (FCO) of a reservoir is a complex optimization problem with a large number of constraints. With the rapid development of optimization techniques in recent years, more and more research efforts have been devoted to optimizing FCO problems. However, for solving large-scale reservoir group optimization problem, this is still a challenging task. In this work, a reservoir group FCO model is established with minimum flood volume stored in each reservoir and minimum peak flow of downstream control point during the dispatch process. At the same time, a flood forecast model for FCO of a reservoir group is developed by coupling Yin-Yang firefly algorithm (YYFA) with ε constrained method. As a case study, the proposed model is applied to a three-reservoir flood control system in Luanhe River Basin consisting of reservoirs, river channels, and downstream control points. Results show that optimal operation of three reservoirs systems can efficiently reduce the occupied storage capacity for flood control and flood peaks at downstream control point of the basin. The proposed method can be extended to FCO of other reservoir groups with similar conditions.

     

随机约束线性规划在水库综合利用中的应用

由于水库入流的不确定性，各用水目标的基本要求（目标放水量）将体现在年内各时期水库放水的随机约束上，配合水库线民生蓄泄水决策规则，将全部随机约束进行确定性等效转换，得到线性规划模型，经多次解析，就可得到水主加容量一定情况下的最优运行规则，针对大型水资源工程综合利用的多目标要求，研究建立了随机约束线性规划模型，以求解水库最优运行规划的方法，并以西南地区某大型综合利用水库为例，对模型进行求解，该方法随机