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.     

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.     

混沌差分算法在确定河流水质模型参数中的应用

将混沌寻优思想引入到差分优化算法形成混沌差分算法,并将其应用于确定河流水质模型参数的函数优化问题.数值实验结果表明:应用混沌差分算法求解此参数问题无论是在精度还是时间上都优于差分优化算法.它将混沌寻优的遍历性和随机性思想引入到差分优化算法中,在每次差分进化寻得的最优位置附近进行混沌细搜索,并配合特殊的迭代终止准则进行寻优.其明显缩短了混沌搜索计算时间和克服了差分优化算法后期早熟的缺陷,提高模型求解的收敛速度和精度.     

混沌差分进化算法在水库优化调度中的应用研究

针对差分进化算法在求解水库调度等复杂优化问题时,算法初始种群的随机性导致其在解空间中的代表性不足,算法的贪婪选择策略又极易导致种群迅速趋同而"早熟"收敛。提出初始种群的混沌生成策略,利用混沌因子的遍历性提高算法初始种群的代表性。同时,以动态概率接受适应值较差的个体作为子代个体参与进化,从而提高算法跳出局部最优解的能力。将改进的差分进化算法模拟乌江梯级电站优化调度问题,模拟计算结果表明,改进的差分进化算法具有较高全局搜索能力,大幅提高了求解的精度,适合求解水库优化调度等问题。     

基于多目标混沌优化算法的水资源配置研究

本文将多目标混沌优化算法,应用于水资源优化配置中,该方法将多目标属性与混沌遍历性耦合起来,将混沌序列放大到优化变量的取值范围进行迭代寻优,避免了搜索过程陷入局部极小点,克服了要求目标函数和约束条件连续、可微的困难.经过实例计算,证明了算法的有效性.     

混沌粒子群优化算法在马斯京根模型参数优化中的应用

针对目前马斯京根模型参数率定中存在的求解复杂、精度不高等问题,本文将混沌搜索机制引入粒子群优化算法中,构建混沌粒子群优化算法对马斯京根模型参数进行率定。这种方法利用混沌运动的遍历性,改善了粒子群优化算法的全局寻优能力,避免算法陷入局部极值,使得粒子群体的进化速度加快,提高了算法的收敛速度和精度。通过实例应用表明,混沌粒子群优化算法可以有效地估算出马斯京根模型参数,优化效果明显优于粒子群优化算法及试错法,因此该算法具有很好的实用性。     

混沌粒子群优化算法在确定含水层参数中的应用

以泰斯公式为例,将混沌粒子群优化算法应用于求解分析抽水试验数据,解决含水层参数的函数优化问题.通过在粒子群算法的初始化粒子位置及后续的细搜索过程中加入混沌序列,提高了算法的收敛速度和精度.数值实验结果表明:混沌粒子群算法能够有效地应用于求解含水层参数计算问题;粒子数的增多对混沌粒子群算法收敛性的影响不明显;待估导水系数选取不同的倍数均体现出混沌粒子群算法的收敛性明显优于粒子群优化算法.混沌粒子群算法应用于确定含水层参数是可行的.     

Parameter Identification of Nonlinear Muskingum Model with Backtracking Search Algorithm

Nonlinear Muskingum model is a popular approach widely used for flood routing in hydraulic engineering. An improved backtracking search algorithm (BSA) is proposed to estimate the parameters of nonlinear Muskingum model. The orthogonal designed initialization population strategy and chaotic sequences are introduced to improve the exploration and exploitation ability of BSA. At the same time, a selection strategy based individual feasibility violation is developed to ensure that the computed outflows are non-negative in the evolutionary process. Finally, three examples are employed to demonstrate the performance of the improved BSA. The comparison between the results of routing outflows and those of Wilcoxon signed ranks test shows that the improved BSA outperforms particle swarm optimization, genetic algorithm, differential evolution and other algorithms reported in the literature in terms of solution quality. Therefore, it is reasonable to draw the conclusion that the proposed BSA is a satisfactory and efficient choice for parameter estimation of nonlinear Muskingum model.     

基于多目标遗传算法的水资源优化配置

文章基于进化计算思想提出了水资源优化配置的多目标遗传算法,建立了基于并列选择多目标遗传算法的水资源优化配置模型.并结合实例分析,求出水资源优化配置问题的Pareto最优解.优化结果表明,该算法应用在水资源优化配置中是合理、有效的.     

A Novel Multi-Objective Shuffled Complex Differential Evolution Algorithm with Application to Hydrological Model Parameter Optimization

Practice experience suggests that the traditional calibration of hydrological models with single objective cannot properly measure all of the behaviors of the hydrological system. To circumvent this problem, in recent years, a lot of studies have looked into calibration of hydrological models with multi-objective. In this paper, we propose a novel multi-objective evolution algorithm entitled multi-objective shuffled complex differential evolution (MOSCDE) algorithm, which is an extension of the famous single objective algorithm, shuffled complex evolution (SCE-UA) algorithm, to the multi-objective framework. This new proposed algorithm replaces the simplex search used in SCE-UA with the differential evolution (DE) algorithm and can more thoroughly utilize the information of the individuals in the evolutionary population and improve the search ability of the algorithm. Meanwhile, the Cauchy mutation (CM) operator is employed to prevent the algorithm from falling into the local optimal region of the feasible space. Moreover, two types of archive sets are employed to further improve the performance of the algorithm. The efficacy of the MOSCDE algorithm is first tested on five benchmark problems. After achieving satisfactory performance on the test problems, the MOSCDE is applied to multi-objective parameter optimization of a hydrological model for daily runoff forecasting. The results show that the MOSCDE algorithm can be a viable alternative for multi-objective parameter optimization of hydrological model.     

梯级水库生态调度多目标混合蛙跳差分算法研究

提出多目标混合蛙跳差分算法求解梯级水库多目标生态调度模型。该算法结合混沌理论生成初始解以提高初始解群体质量,构建基于动态更新机制的外部归档集引导种群进化,提高算法的收敛性与非劣解的多样性,引入自适应差分算法加快子种群个体寻优,提高算法收敛速度。对L河梯级水库多目标生态调度进行实例研究,计算结果表明:本文所提出的算法能够计算得到收敛性与分布性较好的调度方案集,对比典型调度方案下泄径流与物种生态适宜径流,表明生态调度能够较好满足物种的生态需水,生态效益显著。     

水电站水库优化调度的改进混沌遗传算法

针对水电站水库优化调度问题,提出了将改进遗传算法和混沌优化相耦合的改进混沌遗传算法。该算法将混沌变量映射到优化变量的取值范围中,对混沌变量进行编码,表示成染色体,然后对其进行选择、交叉和变异,通过增加混沌扰动,不断进化收敛得到最优解。实例计算并与其他方法比较表明,该算法在求解水电站优化调度这样的复杂非线性优化问题时,搜索效率高,收敛性能好,能以较快的速度收敛于全局最优解,为水电站水库优化调度模型求解提供了一种新方法。     

Optimization of Multireservoir Systems by Genetic Algorithm

Application of optimization techniques for determining the optimal operating policy of reservoirs is a major issue in water resources planning and management. As an optimization Genetic Algorithm, ruled by evolution techniques, have become popular in diversified fields of science. The main aim of this study is to explore the efficiency and effectiveness of genetic algorithm in optimization of multi-reservoirs. A computer code has been constructed for this purpose and verified by means of a reference problem with a known global optimum. Three reservoirs in the Colorado River Storage Project were optimized for maximization of energy production. Besides, a real-time approach utilizing a blend of online and a posteriori data was proposed. The results obtained were compared to the real operational data and genetic algorithm was found to be effective and can be utilized as an alternative technique to other traditional optimization techniques.     

混沌变异粒子群算法在水库供水调度规则制定中的应用

本文针对基于调度图规则的水库供水调度问题,建立了以水库供水保证率高且缺水量少为目标的优化调度模型。同时应用混沌变异减缓粒子群算法收敛速度,当算法进化停滞步数大于停滞步数阀值时,随机选取其中20%的粒子进行混沌变异操作,将原本聚集的粒子群"驱散开来",达到增加种群多样性、避免算法早熟收敛的目的,并将该算法引入到调度图的获取中。并以白石水库为例,得到了满足各项用水保证率的水库调度图,验证了该方法的可行性。     

基于不同优化算法的土壤水分特征曲线模型模拟性能分析

土壤水分特征曲线反映了包气带土壤孔隙中水分质量与能量之间的基本关系,同时也间接反映出土壤内部的孔隙情况。土壤水分特征曲线模型对实测土壤持水数据的拟合效果不仅取决于所选用的模型,还依赖于对拟合算法的选取。基于UNSODA 2.0数据库中世界各地实测土壤持水数据,采用多种高效拟合算法(遗传算法、粒子群算法、模拟退火算法、差分演化算法)对4种应用广泛的土壤水分特征曲线模型(Brooks-Corey模型、van Genuchten模型、Kosugi模型、Biexponential模型)进行研究,旨在获取最适宜拟合土壤水分特征曲线的模型与拟合算法。结果表明:van Geunchten模型对较细和较粗质地土壤的实测持水数据拟合效果较好; Biexponential模型在中等质地土壤类型下的拟合效果较好;而Brooks-Corey模型拟合效果整体较差;粒子群算法与差分演化算法对土壤水分特征曲线的拟合效果最佳;模拟退火算法在运算效率上高于其他算法,当需处理的数据量较大时使用该算法可显著缩短运算时间。研究成果可以为农田水利、生态水文等研究中土壤水力参数的选取提供指导和参考。     

Multi-Objective Differential Evolution-Chaos Shuffled Frog Leaping Algorithm for Water Resources System Optimization

A multi-objective differential evolution-chaos shuffled frog leaping algorithm (MODE-CSFLA) is proposed for water resources system optimization to overcome the shortcomings of easily falling into local minima and premature convergence in SFLA. The performance of MODE-CSFLA in solving benchmark problems is compared with that of non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimization (MOPSO). At last, the proposed MODE-CSFLA is used to optimize the water resources allocation plan of the East Route of the South-to-North Water Transfer Project in the normal, dry, and extremely dry years. The results reveal that MODE-CSFLA performs better than NSGA-II and MOPSO under all conditions. Compared with shuffled frog leaping algorithm (SFLA), MODE-CSFLA can result in a 29.39, 27.47 and 22.55% increase in water supply when the single objective is to minimize the water pumpage; and a 41.01, 39.63 and 30.94% decrease in total pumpage when the single objective is to maximize the water supply in the normal, dry, and extremely dry conditions, respectively. Thus, MODE-CSFLA has the potential to be used for solving complex optimization problems of water resources systems.     

自适应混沌差分进化算法在梯级水库优化调度中的应用

介绍了一种基于自适应混沌映射的差分进化算法,该算法采用混沌映射的方式产生初始种群,并综合考虑算法迭代进度和个体进化程度两个因素,对缩放因子进行动态调整以促进算法全局搜索和局部寻优的平衡。同时,在算法进化的不同阶段采取不同尺度的扰动策略,进一步提高算法的再搜索能力。将该算法应用于某梯级水库发电调度的研究中,通过实例计算,并与基本差分进化算法、模拟退火算法相比,得到了更优的全局最优解,验证了该算法的可靠性和实用性。     

Multi-objective reservoir operation using particle swarm optimization with adaptive random inertia weights

Based on conventional particle swarm optimization(PSO), this paper presents an efficient and reliable heuristic approach using PSO with an adaptive random inertia weight(ARIW) strategy, referred to as the ARIW-PSO algorithm, to build a multi-objective optimization model for reservoir operation. Using the triangular probability density function, the inertia weight is randomly generated, and the probability density function is automatically adjusted to make the inertia weight generally greater in the initial stage of evolution, which is suitable for global searches. In the evolution process, the inertia weight gradually decreases, which is beneficial to local searches. The performance of the ARIWPSO algorithm was investigated with some classical test functions, and the results were compared with those of the genetic algorithm(GA), the conventional PSO, and other improved PSO methods. Then, the ARIW-PSO algorithm was applied to multi-objective optimal dispatch of the Panjiakou Reservoir and multi-objective flood control operation of a reservoir group on the Luanhe River in China, including the Panjiakou Reservoir, Daheiting Reservoir, and Taolinkou Reservoir. The validity of the multi-objective optimization model for multi-reservoir systems based on the ARIW-PSO algorithm was verified.     

混沌优化方法及其在水文水资源中的应用研究进展

混沌优化方法是解决非线性问题的一种新颖而有效的方法。本文介绍了混沌优化方法的基本原理及其优点,并且分别对两类混沌优化方法——完全混沌优化方法和混合混沌优化方法的国内外研究发展现状及其在水文水资源领域中的应用情况做了较为详细的介绍。同时,也提出了目前在混沌优化理论研究过程中存在的一些问题。最后,对混沌优化理论未来的发展前景进行了展望。     

Parameter study of differential evolution based optimal scheduling of hydrothermal systems

Differential evolution (DE) has been proved to be a powerful evolutionary algorithm for global optimization in many real-world problems. The performance of evolutionary algorithms is heavily dependent on the setting of control parameters. Proper selection of the control parameters is very important for the success of the algorithm. Optimal settings of control parameters of differential evolution depend on the specific problem under consideration. In this paper, a study of control parameters on differential evolution based optimal scheduling of hydrothermal systems with cascaded reservoir is conducted empirically. A multi-reservoir cascaded hydrothermal system with non-linear relationship between water discharge rate, power generation and net head is considered for the present study. The water transport delay between connected reservoirs is also taken into account. Several equality and non-equality constraints on thermal plants such as maximum and minimum generation capacity and effect of valve point loading are also considered. The results of the effect of the variations of the parameters are presented systematically and it is observed that the search algorithm may fail in finding the optimal value if the parameter selection is not done with proper attention.