An application of Karmarkar's interior-point linear programming algorithm for multi-reservoir operations optimization

Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.     

A parallel dynamic programming algorithm for multi-reservoir system optimization

This paper develops a parallel dynamic programming algorithm to optimize the joint operation of a multi-reservoir system. First, a multi-dimensional dynamic programming (DP) model is formulated for a multi-reservoir system. Second, the DP algorithm is parallelized using a peer-to-peer parallel paradigm. The parallelization is based on the distributed memory architecture and the message passing interface (MPI) protocol. We consider both the distributed computing and distributed computer memory in the parallelization. The parallel paradigm aims at reducing the computation time as well as alleviating the computer memory requirement associated with running a multi-dimensional DP model. Next, we test the parallel DP algorithm on the classic, benchmark four-reservoir problem on a high-performance computing (HPC) system with up to 350 cores. Results indicate that the parallel DP algorithm exhibits good performance in parallel efficiency; the parallel DP algorithm is scalable and will not be restricted by the number of cores. Finally, the parallel DP algorithm is applied to a real-world, five-reservoir system in China. The results demonstrate the parallel efficiency and practical utility of the proposed methodology.     

Stochastic differential dynamic programming for multi-reservoir system control

: As with all dynamic programming formulations, differential dynamic programming (DDP) successfully exploits the sequential decision structure of multi-reservoir optimization problems, overcomes difficulties with the nonconvexity of energy production functions for hydropower systems, and provides optimal feedback release policies. DDP is particularly well suited to optimizing large-scale multi-reservoir systems due to its relative insensitivity to state-space dimensionality. This advantage of DDP encourages expansion of the state vector to include additional multi-lag hydrologic information and/or future inflow forecasts in developing optimal reservoir release policies. Unfortunately, attempts at extending DDP to the stochastic case have not been entirely successful. A modified stochastic DDP algorithm is presented which overcomes difficulties in previous formulations. Application of the algorithm to a four-reservoir hydropower system demonstrates its capabilities as an efficient approach to solving stochastic multi-reservoir optimization problems. The algorithm is also applied to a single reservoir problem with inclusion of multi-lag hydrologic information in the state vector. Results provide evidence of significant benefits in direct inclusion of expanded hydrologic state information in optimal feedback release policies.     

Stochastic differential dynamic programming for multi-reservoir system control

: As with all dynamic programming formulations, differential dynamic programming (DDP) successfully exploits the sequential decision structure of multi-reservoir optimization problems, overcomes difficulties with the nonconvexity of energy production functions for hydropower systems, and provides optimal feedback release policies. DDP is particularly well suited to optimizing large-scale multi-reservoir systems due to its relative insensitivity to state-space dimensionality. This advantage of DDP encourages expansion of the state vector to include additional multi-lag hydrologic information and/or future inflow forecasts in developing optimal reservoir release policies. Unfortunately, attempts at extending DDP to the stochastic case have not been entirely successful. A modified stochastic DDP algorithm is presented which overcomes difficulties in previous formulations. Application of the algorithm to a four-reservoir hydropower system demonstrates its capabilities as an efficient approach to solving stochastic multi-reservoir optimization problems. The algorithm is also applied to a single reservoir problem with inclusion of multi-lag hydrologic information in the state vector. Results provide evidence of significant benefits in direct inclusion of expanded hydrologic state information in optimal feedback release policies.     

A practical estimation of Clark IUH parameters using root selection and linear programming

The values of the parameters of the Clark instantaneous unit hydrograph (IUH) are often relying on the subjective decision of the researcher, which leads to large variations of their values. Therefore, an objective method minimizing the subjective judgement in the IUH modelling procedure while providing a reduced range of acceptable values is proposed. The proposed method uses a basin average IUH to mitigate the robustness problem of the Clark IUH parameters. Using linear system theory, the z‐transform is applied to the average IUH and then the IUH polynomial is factored into the recession and time‐area curve (TAC) components based on a convolution relation between the Clark IUH parameters. During this calculation, the root selection method was adopted to verify the storage coefficient R from the recession component and a linear programming technique was applied for determining the TAC for the basin of interest. The Wi River basin was used to test the applicability of the proposed method. The results showed that the components of a single reservoir and the TAC for Clark IUH were separated effectively, and acceptable values for the parameters were obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty

In this study, an interval-parameter multi-stage stochastic linear programming (IMSLP) method has been developed for water resources decision making under uncertainty. The IMSLP is a hybrid methodology of inexact optimization and multi-stage stochastic programming. It has three major advantages in comparison to the other optimization techniques. Firstly, it extends upon the existing multi-stage stochastic programming method by allowing uncertainties expressed as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. Secondly, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. Thirdly, it cannot only handle uncertainties through constructing a set of scenarios that is representative for the universe of possible outcomes, but also reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. The developed IMSLP method is applied to a hypothetical case study of water resources management. The results are helpful for water resources managers in not only making decisions of water allocation but also gaining insight into the tradeoffs between environmental and economic objectives.     

An improved shuffled frog leaping algorithm and its application in the optimization of cascade reservoir operation

ABSTRACT

A new improved shuffled frog leaping algorithm (SFLA), the chaos catfish effect SFLA (CCESFLA), is proposed by coupling a local “refine search” mechanism and a “global incentive adjustment” mechanism. Chaotic technology is introduced in the local “refine search” mechanism to improve local search ability, by implementing more refined local search around the optimal individuals. The catfish effect mechanism is adopted in the “global incentive adjustment” mechanism to improve global convergence, by motivating the frogs to “jump out” of the local steady state. The operation optimization by the CCESFLA is carried out taking the Li Xianjiang cascade reservoirs in China as an example. Compared with SFLA, particle swarm optimization, immune SFLA and cloud SFLA, the average annual power generation using the CCESFLA can be increased by 6.7, 7.5, 3.0 and 0.8%, respectively. The convergence process of the CCESFLA is more stable, and its execution time is the least of the three improved SFLAs.     

Development of operating rules for a complex multi-reservoir system by coupling genetic algorithms and network optimization

Abstract

An alternative procedure for assessment of reservoir Operation Rules (ORs) under drought situations is proposed. The definition of ORs for multi-reservoir water resources systems (WRSs) is a topic that has been widely studied by means of optimization and simulation techniques. A traditional approach is to link optimization methods with simulation models. Thus the objective here is to obtain drought ORs for a real and complex WRS: the Júcar River basin in Spain, in which one of the main issues is the resource allocation among agricultural demands in periods of drought. To deal with this problem, a method based on the combined use of genetic algorithms (GA) and network flow optimization (NFO) is presented. The GA used was PIKAIA, which has previously been used in other water resources related fields. This algorithm was linked to the SIMGES simulation model, a part of the AQUATOOL decision support system (DSS). Several tests were developed for defining the parameters of the GA. The optimization of various ORs was analysed with the objective of minimizing short-term and long-term water deficits. The results show that simple ORs produce similar results to more sophisticated ones. The usefulness of this approach in the assessment of ORs for complex multi-reservoir systems is demonstrated.

Citation Lerma, N., Paredes-Arquiola, J., Andreu, J., and Solera, A., 2013. Development of operating rules for a complex multi-reservoir system by coupling genetic algorithms and network optimization. Hydrological Sciences Journal, 58 (4), 797–812.     

An integrated optimization algorithm for parameter structure identification in groundwater modeling

The inverse problem of parameter structure identification in a distributed parameter system remains challenging. Identifying a more complex parameter structure requires more data. There is also the problem of over-parameterization. In this study, we propose a modified Tabu search for parameter structure identification. We embed an adjoint state procedure in the search process to improve the efficiency of the Tabu search. We use Voronoi tessellation for automatic parameterization to reduce the dimension of the distributed parameter. Additionally, a coarse-fine grid technique is applied to further improve the effectiveness and efficiency of the proposed methodology. To avoid over-parameterization, at each level of parameter complexity we calculate the residual error for parameter fitting, the parameter uncertainty error and a modified Akaike Information Criterion. To demonstrate the proposed methodology, we conduct numerical experiments with synthetic data that simulate both discrete hydraulic conductivity zones and a continuous hydraulic conductivity distribution. Our results indicate that the Tabu search allied with the adjoint state method significantly improves computational efficiency and effectiveness in solving the inverse problem of parameter structure identification.     

A set of linked optimization models for an inter-basin water transfer

ABSTRACT

A set of linked optimization models was used to evaluate planning and operation of the proposed Pamba-Achankovil-Vaippar (PAV) water transfer project in India. The shortage of water for irrigation in the Vaippar basin has led to the need for water import. The project consists of three reservoirs. The models were applied at three levels. At Level-1, the projections of water requirement for irrigation in the Vaippar basin at Reservoir-1 were estimated using an LP model. Level-2 was operated at three sub-levels: the first was the determination of the export requirements from the Pamba basin (Reservoir-2) to the Achankovil basin (Reservoir-1); the second was determining the capability of Reservoir-2 to export and sizing of the three reservoirs to meet the above targets was the third sub-level. Integrated reservoir operation and canal irrigation water distribution were done at Level-3. DP models were employed at levels-2 and 3. The linked LP, DP and simulation models were found effective for planning water transfers.     

2D多尺度混合优化地球物理反演方法及其应用(英文)

局部优化和全局优化方法广泛应用到地球物理反演,但是两者各有其优缺点。将两类方法结合起来可以取长补短。将退火遗传算法（SAGA）和单纯形算法相结合,得到了一种高效、健全的2D非线性混合地震走时反演方法。首先,利用SAGA进行大范围的全局搜索,然后由单纯形方法进行快速局部搜索。为了降低层析成像的多解性,我们采用了多尺度逐次逼近的技巧。把速度场划分为不同的空间尺度,定义网格节点上的速度作为待反演参数,采用双三次样条函数模型参数化,正问题采用有限差分走时计算方法,反问题采用多尺度混合反演方法。一个低速度异常体的数值模拟试验和抗走时扰动试验表明该方法是有效和健全的。我们将该方法应用到青藏高原东北缘阿尼玛卿rlet,Meyer,Marr,缝合带东段上部地壳速度结构研究中。数字模型试验和实际资料的应用表明了方法的有效性和健全性。     

Genetic algorithm for seismic topology optimization of lifeline network systems

Lifeline systems, such as water distribution and gas supply networks, usually cover large areas. For these systems, seismic design is always a difficult problem because of the complexity of large‐scale networks. In this paper, a topology optimization technology for lifeline networks is established. Firstly, in order to speed up the convergence of optimization process, an element investment importance analysis is carried out to evaluate the importance of components to the lifeline network. Then a topology optimization model is established. The aim of the model is to find the least‐cost network topology while the seismic reliability between the sources and each terminal satisfies prescribed reliability constraints. For this optimization problem, a genetic algorithm, which takes network topologies as the individuals of its population, is used to search for the optimal solutions by suitable operators, including selection, crossover and mutation operators. The capacity of the proposed algorithm is illustrated by its applications to a simple example network consisting of 10 nodes and an actual network with 391 nodes located in a large city of China. Copyright © 2008 John Wiley & Sons, Ltd.     

地震反射波反演二阶优化方法及其应用

常规地震数据大都缺乏低频成分与长炮检距信号,经典的全波形反演方法不易获取中、深层弹性参数模型的长波长分量,波动方程反射波形反演作为替代方法近来受到极大关注.然而,现有的反射波形反演方法几乎都采用梯度类的一阶优化算法,收敛性和精度都有待提高.本文在二阶优化理论框架下,推导弹性参数背景与扰动模型的反射波敏感核、泛函梯度以及海森算子,揭示海森矩阵对泛函梯度的去模糊化作用和改善反演的工作机制.推覆体模型合成数据实验表明,相比于常用的共轭梯度法,利用近似海森矩阵的高斯-牛顿法明显提升了反射波形反演的收敛性与宽谱建模能力.在东海实例中,本文方法超越常用的反射走时层析技术,通过改善中、深层偏移速度建模,支撑逆时偏移高分辨率刻画长江坳陷内部复杂的断裂系统,改善了深部基底的成像质量.

     

An approach for evaluating the hydrological effects of urbanization and its application

This study focuses mainly on observing urban development in Taiwan's Wu‐Tu watershed from the perspective of urban hydrological theory. An approach is proposed for developing a method for incorporating available meteorological data to define the degree of change in a runoff hydrograph for urbanizing basins. The mean rainfall was estimated using the Kriging method. For calibration, two methods of calculating the effective rainfall (the Φ‐index method and the non‐linear‐programming (NLP) method) were used as model inputs, and the optimal global parameters of the linear reservoir model were then obtained from the shuffled complex evolution (SCE) algorithm. Twenty‐six (1966–1991) and eight (1994–1997) rainfall–runoff events were used for calibration and verification, respectively. The NLP method yielded better results than the Φ‐index method, especially for multipeak rainfall–runoff events. The regression equation determined the relationship between the parameters of the model and impervious areas. A comparison based on the results of the instantaneous unit hydrograph of the study area revealed that three decades of urbanization had increased the peak flow by 27%, and the time to peak was decreased by 4 h. The study simply describes the results of the impact of imperviousness on hydrological modelling. Copyright © 2002 John Wiley & Sons, Ltd.     

Building more realistic reservoir optimization models using data mining - A case study of Shelbyville Reservoir

In this paper, we promote a novel approach to develop reservoir operation routines by learning from historical hydrologic information and reservoir operations. The proposed framework involves a knowledge discovery step to learn the real drivers of reservoir decision making and to subsequently build a more realistic (enhanced) model formulation using stochastic dynamic programming (SDP). The enhanced SDP model is compared to two classic SDP formulations using Lake Shelbyville, a reservoir on the Kaskaskia River in Illinois, as a case study. From a data mining procedure with monthly data, the past month’s inflow (Q_t−1), current month’s inflow (Q_t), past month’s release (R_t−1), and past month’s Palmer drought severity index (PDSI_t−1) are identified as important state variables in the enhanced SDP model for Shelbyville Reservoir. When compared to a weekly enhanced SDP model of the same case study, a different set of state variables and constraints are extracted. Thus different time scales for the model require different information. We demonstrate that adding additional state variables improves the solution by shifting the Pareto front as expected while using new constraints and the correct objective function can significantly reduce the difference between derived policies and historical practices. The study indicates that the monthly enhanced SDP model resembles historical records more closely and yet provides lower expected average annual costs than either of the two classic formulations (25.4% and 4.5% reductions, respectively). The weekly enhanced SDP model is compared to the monthly enhanced SDP, and it shows that acquiring the correct temporal scale is crucial to model reservoir operation for particular objectives.     

地震波时域数值优化研究及应用

将最小二乘拟合法与单自由度地震动力反应递归法相结合来解决地震观测和人工模拟地震波过程中速度、位移的基线漂移问题。首先以3次多项式来拟合加速度的均值线(一次优化);再对一次优化后的积分速度、位移时程仍存在的长周期基线波动问题,运用单自由度地震动力反应递归法进行二次优化。文中通过3个数值算例体现出优化算法的优越性,并将优化后的地震波加速度时程应用到江坪河水电站溢洪道控制段三维有限元动力计算分析中。结果表明,该算法消除了积分基线漂移影响,具有较好的可行性、数值稳定性和易操作性。     

Using a hybrid genetic algorithm–simulated annealing algorithm for fuzzy programming of reservoir operation

We present a novel approach for optimizing reservoir operation through fuzzy programming and a hybrid evolution algorithm, i.e. genetic algorithm (GA) with simulated annealing (SA). In the analysis, objectives and constraints of reservoir operation are transformed by fuzzy programming for searching the optimal degree of satisfaction. In the hybrid search procedure, the GA provides a global search and the SA algorithm provides local search. This approach was investigated to search the optimizing operation scheme of Shihmen Reservoir in Taiwan. Monthly inflow data for three years reflecting different hydrological conditions and a consecutive 10‐year period were used. Comparisons were made with the existing M‐5 reservoir operation rules. The results demonstrate that: (1) fuzzy programming could effectively formulate the reservoir operation scheme into degree of satisfaction α among the users and constraints; (2) the hybrid GA‐SA performed much better than the current M‐5 operating rules. Analysis also found the hybrid GA‐SA conducts parallel analyses that increase the probability of finding an optimal solution while reducing computation time for reservoir operation. Copyright © 2007 John Wiley & Sons, Ltd.     

Snoke震源机制求解方法应用研究

通过2003年青海德令哈M_L 6.7地震序列的主震和3个不同震级的余震震源机制解测定实例,展示了Snoke(2003)震源机制求解方法的应用过程和结果,提出了应用该方法需注意的问题。将同时利用了P波和S波初动方向及振幅比数据的测定结果与仅用P波初动方向数据的结果作了对比研究,说明仅用P波初动方向常常不能有效约束震源机制解,而Snoke方法增加使1用的SH波和SV波的初动方向以及SH波、SV波与P波的观测振幅比数据,使解答得到了更有效的约束,提高了解答的可信度。本试验研究说明,基于区域性的宽频带数字地震记录,利用Snoke震源机制求解方法,有可能测定出比较可靠的中、小地震的震源机制解。     

土层地震反应等效线性化方法综述

当前土层地震反应分析所用的主要方法是一维等效线性化波动方法。简单阐述了等效线性化方法的基本原理,总结了其发展历程和现状。根据其原理和多年的应用实践,指出了其优点和缺点。其优点主要是概念简单明确,计算量较小,便于工程应用。其缺点主要是该方法本身不能反应地震波在土体传播的真实过程,在工程实践中处理软弱土层和强震动输入时所表现出的一些不合理的地方。并对这些优缺点的机理进行了简要地分析。     

Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

Abstract

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naïve approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Teegavarapu, R.S.V., 2012. Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records. Hydrological Sciences Journal, 57 (3), 383–406.