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

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

Optimal Reservoir Operation Using Multi-Objective Evolutionary Algorithm

This paper presents a Multi-objective Evolutionary Algorithm (MOEA) to derive a set of optimal operation policies for a multipurpose reservoir system. One of the main goals in multi-objective optimization is to find a set of well distributed optimal solutions along the Pareto front. Classical optimization methods often fail in attaining a good Pareto front. To overcome the drawbacks faced by the classical methods for Multi-objective Optimization Problems (MOOP), this study employs a population based search evolutionary algorithm namely Multi-objective Genetic Algorithm (MOGA) to generate a Pareto optimal set. The MOGA approach is applied to a realistic reservoir system, namely Bhadra Reservoir system, in India. The reservoir serves multiple purposes irrigation, hydropower generation and downstream water quality requirements. The results obtained using the proposed evolutionary algorithm is able to offer many alternative policies for the reservoir operator, giving flexibility to choose the best out of them. This study demonstrates the usefulness of MOGA for a real life multi-objective optimization problem.     

改进的遗传算法在水库调度中的应用

为了改善遗传算法在水库优化调度中的应用效果,采用自适应遗传算法和广度变异模块相结合的分层收敛算法:第一层采用广度变异和外部存档的方式改善种群的多样性;第二层嵌套广度变异模块,并采用自适应遗传算法进行全局搜索。通过比较自适应遗传算法和分层进化算法,结果显示:基于遗传算法的分层算法具有高效的全局搜索能力,避免了自适应遗传算法陷入局部最优的缺陷,在一定收敛条件下得到了更接近全局最优的目标值。     

Improved Reservoir Operation Using Hybrid Genetic Algorithm and Neurofuzzy Computing

A hybrid genetic and neurofuzzy computing algorithm was developed to enhance efficiency of water management for a multipurpose reservoir system. The genetic algorithm was applied to search for the optimal input combination of a neurofuzzy system. The optimal model structure is modified using the selection index (SI) criterion expressed as the weighted combination of normalized values of root mean square error (RMSE) and maximum absolute percentage of error (MAPE). The hybrid learning algorithm combines the gradient descent and the least-square methods to train the genetic-based neurofuzzy network by adjusting the parameters of the neurofuzzy system. The applicability of this modeling approach is demonstrated through an operational study of the Pasak Jolasid Reservoir in Pasak River Basin, Thailand. The optimal reservoir releases are determined based on the reservoir inflow, storage stage, sideflow, diversion flow from the adjoining basin, and the water demand. Reliability, vulnerability and resiliency are used as indicators to evaluate the model performance in meeting objectives of satisfying water demand and maximizing flood prevention. Results of the performance evaluation indicate that the releases predicted by the genetic-based neurofuzzy model gave higher reliability for water supply and flood protection compared to the actual operation, the releases based on simulation following the current rule curve, and the predicted releases based on other approaches such as the fuzzy rule-based model and the neurofuzzy model. Also the predicted releases based on the newly developed approach result in the lowest amount of deficit and spill indicating that the developed modeling approach would assist in improved operation of Pasak Jolasid Reservoir.     

水电站水库汛期洪水退水段优化调度研究

有防洪任务的水电站水库,洪水退水段的调度对发电非常重要,退水段调度好坏直接影响水库全年兴利效益。以北方某水电站水库为例,在预测退水段径流过程的条件下,建立了退水段发电量最大模型,并利用遗传算法对该模型进行求解。遗传算法与常规调度结果的对比结果表明,前者能获得更优的调度结果。该方法对指导水电站水库汛期洪水退水段的调度,有较强的实用价值。     

Genetic Algorithm for Optimal Operating Policy of a Multipurpose Reservoir

This paper presents a Genetic Algorithm (GA) model for finding the optimal operating policy of a multi-purpose reservoir, located on the river Pagladia, a major tributary of the river Brahmaputra. A synthetic monthly streamflow series of 100 years is used for deriving the operating policy. The policies derived by the GA model are compared with that of the stochastic dynamic programming (SDP) model on the basis of their performance in reservoir simulation for 20 years of historic monthly streamflow. The simulated result shows that GA-derived policies are promising and competitive and can be effectively used for reservoir operation.     

蜜蜂进化型遗传算法在水库优化调度中的应用

提出了一种基于蜜蜂进化型遗传算法的水库优化调度问题的求解方法,并通过实例对蜜蜂进化型遗传算法和标准遗传算法的性能做了比较.结果表明,在进化代数相同的条件下,由于蜜蜂进化型遗传算法在配种选择算子上使用种群的最优个体作为蜂王,提高了种群收敛速度;再者,在代进化过程中引入一个随机种群,保持了群体的多样性,提高了算法的勘测能力.     

基于改进遗传算法的生态友好型水库调度

以锦屏梯级水库为案例,从系统工程论的角度出发,将梯级水库作为物理系统,以年发电量为目标函数,建立了梯级水库调度优化模型。为减少水库调度对河道生态系统的影响,在鱼类栖息地模拟的研究基础上,引入目标物种的生态需水过程对调度模型进行动态约束,并采用改进的遗传算法进行求解。研究得到了满足目标鱼类生态需水条件下发电量最大的梯级水库调度策略,并对生态流量满足程度与工程效益损失之间的定量响应关系进行了研究,提出了折中方案选择的基本原则。     

遗传模拟退火和小生境遗传算法在水库优化调度中的比较

根据溪洛渡水库的具体情况,建立了以发电量最大为目标的水库优化调度非线性数学模型,并利用遗传模拟退火算法(GSA)和小生境遗传算法(NGA)分别求解模型.结果表明,GSA和NGA的收敛速度和计算结果都明显优于基本遗传算法;且两者相比,GSA的收敛性更强,但计算时间较长.而在求解水库长系列优化调度问题时,各遗传算法占用机时太多,且收敛能力较差.     

Optimizing Hydropower Reservoir Operation Using Hybrid Genetic Algorithm and Chaos

Genetic algorithms (GA) have been widely applied to solve water resources system optimization. With the increase of the complexity and the larger problem scale of water resources system, GAs are most frequently faced with the problems of premature convergence, slow iterations to reach the global optimal solution and getting stuck at a local optimum. A novel chaos genetic algorithm (CGA) based on the chaos optimization algorithm (COA) and genetic algorithm (GA), which makes use of the ergodicity and internal randomness of chaos iterations, is presented to overcome premature local optimum and increase the convergence speed of genetic algorithm. CGA integrates powerful global searching capability of the GA with that of powerful local searching capability of the COA. Two measures are adopted in order to improve the performance of the GA. The first one is the adoption of chaos optimization of the initialization to improve species quality and to maintain the population diversity. The second is the utilization of annealing chaotic mutation operation to replace standard mutation operator in order to avoid the search being trapped in local optimum. The Rosenbrock function and Schaffer function, which are complex and global optimum functions and often used as benchmarks for contemporary optimization algorithms for GAs and Evolutionary computation, are first employed to examine the performance of the GA and CGA. The test results indicate that CGA can improve convergence speed and solution accuracy. Furthermore, the developed model is applied for the monthly operation of a hydropower reservoir with a series of monthly inflow of 38 years. The results show that the long term average annual energy based CGA is the best and its convergent speed not only is faster than dynamic programming largely, but also overpasses the standard GA. Thus, the proposed approach is feasible and effective in optimal operations of complex reservoir systems.     

Development of 3-D Optimal Surface for Operation Policies of a Multireservoir in Fuzzy Environment Using Genetic Algorithm for River Basin Development and Management

A Multi objective, Multireservoir operation model for maximization of irrigation releases and maximization of hydropower production is proposed using Genetic Algorithm. These objectives are fuzzified and are simultaneously maximized by defining and then maximizing level of satisfaction (λ). In the present study a multireservoir system in Godavari River sub basin in Maharashtra State, India is considered. Problem is formulated with four reservoirs and a barrage. A monthly Multi Objective Genetic Algorithm Fuzzy Optimization (MOGAFUOPT) model for the present study is developed in ‘C’ Language. The optimal operation policy for maximization of irrigation releases, maximization of hydropower production and maximization of level of satisfaction is presented for existing demand in command area. The entire range of optimal operation policies, for different levels of satisfaction i.e. λ (ranging from 0 to 1), are determined. From the relationships developed amongst irrigation releases, hydropower production and level of satisfaction, a three dimensional (3-D) surface covering the whole range of policies has been developed. This solution surface can be the basis for decision makers for implementing the policies. Considering the future requirements in the command area, both the irrigation and hydropower demands are increased by 10 and 20%. The optimal operation policy for maximization of irrigation releases, maximization of hydropower production and maximization of level of satisfaction is also presented for these cases. The 3-D solution surface is also developed in these cases.     

遗传算法在水库(群)优化调度研究中的应用综述

介绍了遗传算法在水库(群)优化调度中的应用背景及算法的收敛性,讨论了水库(群)优化调度中遗传算法的基本应用步骤以及存在的问题,给出了算法的各种改进方法,并对遗传算法的应用前景进行了展望.     

Water Supply Reservoir Operation by Combined Genetic Algorithm – Linear Programming (GA-LP) Approach

Multi-reservoir operation planning is a complex task involving many variables, objectives, and decisions. This paper applies a hybrid method using genetic algorithm (GA) and linear programming (LP) developed by the authors to determine operational decisions for a reservoir system over the optimization period. This method identifies part of the decision variables called cost reduction factors (CRFs) by GA and operational variables by LP. CRFs are introduced into the formulation to discourage reservoir depletion in the initial stages of the planning period. These factors are useful parameters that can be employed to determine operational decisions such as optimal releases and imports, in response to future inflow predictions. A part of the Roadford Water Supply System, UK, is used to demonstrate the performance of the GA-LP method in comparison to the RELAX algorithm. The proposed approach obtains comparable results ensuring non zero final storages in the larger reservoirs of the Roadford Hydrosystem. It shows potential for generating operating policy in the form of hegging rules without a priori imposition of their form.     

结合广度搜索的遗传算法在水库调度中的应用

为了改善遗传算法在水库优化调度中的应用效果,采用自适应遗传算法和广度搜索算子结合的算法,同时为保证水库优化调度搜索全局最优提供了一定保障。针对遗传算法容易陷入局部最优的缺点,引入正弦函数取随机数的广度搜索与遗传算法相结合的算法。通过分析比较单独使用自适应遗传算法或者广度搜索算法以及结合算法在实际水库优化调度中效果,结果显示,优化结果要比自适应遗传算法以及广度算法的结果更理想。充分证明了结合算法的高效全局搜索能力,避免了自适应遗传算法陷入局部最优,同时在一定程度上克服了广度搜索很难收敛的缺点,在一定收敛条件下得到了更接近全局最优的结果。