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.     

High efficient parallel numerical surface wave model based on an irregular quasi-rectangular domain decomposition scheme

To achieve high parallel efficiency for the global MASNUM surface wave model, the algorithm of an irregular quasi-rectangular domain decomposition and related serializing of calculating points and data exchanging schemes are developed and conducted, based on the environment of Message Passing Interface (MPI). The new parallel version of the surface wave model is tested for parallel computing on the platform of the Sunway BlueLight supercomputer in the National Supercomputing Center in Jinan. The testing involves four horizontal resolutions, which are 1°×1°, (1/2)°×(1/2)°, (1/4)°×(1/4)°, and (1/8)°×(1/8)°. These tests are performed without data Input/Output (IO) and the maximum amount of processors used in these tests reaches to 131072. The testing results show that the computing speeds of the model with different resolutions are all increased with the increasing of numbers of processors. When the number of processors is four times that of the base processor number, the parallel efficiencies of all resolutions are greater than 80%. When the number of processors is eight times that of the base processor number, the parallel efficiency of tests with resolutions of 1°×1°, (1/2)°×(1/2)° and (1/4)°×(1/4)° is greater than 80%, and it is 62% for the test with a resolution of (1/8)°×(1/8)° using 131072 processors, which is the nearly all processors of Sunway BlueLight. When the processor’s number is 24 times that of the base processor number, the parallel efficiencies for tests with resolutions of 1°×1°, (1/2)°×(1/2)°, and (1/4)° ×(1/4)° are 72%, 62%, and 38%, respectively. The speedup and parallel efficiency indicate that the irregular quasi-rectangular domain decomposition and serialization schemes lead to high parallel efficiency and good scalability for a global numerical wave model.     

Solving nonlinear water management models using a combined genetic algorithm and linear programming approach

Gradient-based nonlinear programming (NLP) methods can solve problems with smooth nonlinear objectives and constraints. However, in large and highly nonlinear models, these algorithms can fail to find feasible solutions, or converge to local solutions which are not global. Evolutionary search procedures in general, and genetic algorithms (GAs) specifically, are less susceptible to the presence of local solutions. However, they often exhibit slow convergence, especially when there are many variables, and have problems finding feasible solutions in constrained problems with “narrow” feasible regions. In this paper, we describe strategies for solving large nonlinear water resources models management, which combine GAs with linear programming. The key idea is to identify a set of complicating variables in the model which, when fixed, render the problem linear in the remaining variables. The complicating variables are then varied by a GA. This GA&LP approach is applied to two nonlinear models: a reservoir operation model with nonlinear hydropower generation equations and nonlinear reservoir topologic equations, and a long-term dynamic river basin planning model with a large number of nonlinear relationships. For smaller instances of the reservoir model, the CONOPT2 nonlinear solver is more accurate and faster, but for larger instances, the GA&LP approach finds solutions with significantly better objective values. The multiperiod river basin model is much too large to be solved in its entirety. The complicating variables are chosen here so that, when they are fixed, each period's model is linear, and these models can be solved sequentially. This approach allows sufficient model detail to be retained so that long-term sustainability issues can be explored.     

On open boundary conditions for three dimensional primitive equation ocean circulation models

Abstract

An open boundary condition is constructed for three dimensional primitive equation ocean circulation models. The boundary condition utilises dominant balances in the governing equations to assist calculations of variables at the boundary. The boundary condition can be used in two forms. Firstly as a passive one in which there is no forcing at the boundary and phenomena generated within the domain of interest can propagate outwards without distorting the interior. Secondly as an active condition where a model is forced by the boundary condition. Three simple idealised tests are performed to verify the open boundary condition, (1) a passive condition to test the outflow of free Kelvin waves, (2) an active condition during the spin up phase of an ocean, (3) finally an example of the use of the condition in a tropical ocean.     

基于区域分解法的海洋可控源电磁三维正演模拟研究

为准确刻画复杂海底地质结构中电磁场变化特征,有效处理大规模海洋可控源电磁三维正演模拟问题,本文将基于矢量有限元的 FETI-DP(Dual-Primal Finite-Element Tearing and Interconnecting)区域分解法引入到海洋电磁三维正演模拟中 该方法首先利用非结构四面体网格对海洋地电...     

Parallel finite element algorithm with domain decomposition for three-dimensional magnetotelluric modelling

We present a new finite element (FE) method for magnetotelluric modelling of three-dimensional conductivity structures. Maxwell's equations are treated as a system of first-order partial differential equations for the secondary fields. Absorbing boundary conditions are introduced, minimizing undesired boundary effects and allowing the use of small computational domains. The numerical algorithm presented here is an iterative, domain decomposition procedure employing a nonconforming FE space. It does not use global matrices, therefore allowing the modellization of large and complicated structures. The algorithm is naturally parallellizable, and we show results obtained in the IBM SP2 parallel supercomputer at Purdue University. The accuracy of the numerical method is verified by checking the computed solutions with the results of COMMEMI, the international project on the comparison of modelling methods for electromagnetic induction.     

线性拉东域预测反褶积在海洋多次波去除中的应用

海洋多次波是海洋地震资料处理中最难去除的噪声,目前时空域预测反褶积、SRME、高精度拉冬切除等方法均能有效衰减部分多次波,但对于强反射界面(如硬海底,海底以下高速层等)产生的多次波,单独采用以上方法仍会产生能量较强的残余多次波,针对该问题,根据多次波与一次波周期性差异在线性拉东域比时空域更为明显且有利于压制长周期多次波的特点,可以将线性拉东域预测反褶积技术作为SRME、高精度拉东切除技术的补充,取长补短,联合应用消除深水海底多次波.本文对线性拉东域预测反褶积的基本原理进行了阐述,讨论了如何选取参数,并对其应用范围进行了分析.将线性拉东域预测反褶积应用于南海某凹陷海洋资料的多次波衰减处理中,有效的消除了残余海底多次波,验证了该方法的实用性.     

Dynamic model of mesoscale eddies. Eddy parameterization for coarse resolution ocean circulation models

In the framework of the eddy dynamic model developed in two previous papers (Dubovikov, M.S., Dynamical model of mesoscale eddies, Geophys. Astophys. Fluid Dyn., 2003, 97, 311–358; Canuto, V.M. and Dubovikov, M.S., Modeling mesoscale eddies, Ocean Modelling, 2004, 8, 1–30 referred as I–II), we compute the contribution of unresolved mesoscale eddies to the large-scale dynamic equations of the ocean. In isopycnal coordinates, in addition to the bolus velocity discussed in I–II, the mesoscale contribution to the large scale momentum equation is derived. Its form is quite different from the traditional down-gradient parameterization. The model solutions in isopycnal coordinates are transformed to level coordinates to parameterize the eddy contributions to the corresponding large scale density and momentum equations. In the former, the contributions due to the eddy induced velocity and to the residual density flux across mean isopycnals (so called Σ-term) are derived, both contributions being shown to be of the same order. As for the large scale momentum equation, as well as in isopycnal coordinates, the eddy contribution has a form which is quite different from the down-gradient expression.     

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.     

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.     

On the developments of spectral wave models: numerics and parameterizations for the coastal ocean

The development of numerical wave models for coastal applications, including coupling with ocean circulation models, has spurred an ongoing effort on theoretical foundations, numerical techniques, and physical parameterizations. Some important aspects of this effort are reviewed here, and results are shown in the case of the French Atlantic and Channel coast using version 4.18 of the WAVEWATCH III ^R model. Compared to previous results, the model errors have been strongly reduced thanks to, among other things, the introduction of currents, coastal reflection, and bottom sediment types. This last item is described here for the first time, allowing unprecedented accuracy at some sites along the French Atlantic Coast. The adequate resolution, necessary to represent strong gradients in tidal currents, was made possible by the efficiency brought by unstructured grids. A further increase in resolution, necessary to resolve surf zones and still cover vast regions,will require further developments in numerical methods.     

基于CEP的重力自适应并行EKF匹配算法

针对现有惯性/重力/重力梯度组合导航EKF匹配算法滤波状态方程存在模型误差以及惯性导航系统定位存在累积误差而造成的滤波失准乃至发散问题, 提出一种基于CEP(Circular Error Probable, 圆概率误差)的自适应并行EKF匹配算法.该算法首先通过自适应因子调节状态预测信息的权重, 削弱预设动力学模型不准确产生的误差; 同时利用惯性导航系统圆概率误差半径构建基于CEP的移动窗口分层模型, 然后根据滤波量测值与窗口坡度等信息, 对移动窗口范围进行约束; 最后组建分层窗口并行滤波器, 得到最优匹配结果.南海海域实验结果表明, 基于CEP的自适应并行EKF匹配算法相较于传统EKF算法和自适应EKF算法的水下重力匹配导航定位精度分别提升了74.0%和49.8%.该算法能够在一定程度上克服惯性导航系统由于时间推移误差积累的缺陷, 提高系统导航定位精度, 增加匹配算法的鲁棒性.

     

基于遗传算法的大地电磁阻抗张量分解方法研究

本文针对Groom-Bailey分解法在消除地表电性不均匀体对MT数据的畸变效应时存在的问题引入遗传算法,对基于传统线性最优化方法的GB分解算法进行改进,提出基于遗传算法的大地电磁阻抗张量分解方法.通过对理论合成数据以及三维/二维模型正演数据的分解试验,并且对青藏高原北缘阿尔金断裂地区实际MT数据进行分解处理,证明了基于遗传算法的GB分解能够更加有效地校正三维/二维情况下近地表三维电性不均匀体所造成的畸变影响.最后,在已有算法基础上,研究了基于遗传算法的多频率GB分解算法和MT数据静校正算法,并通过实际MT数据的处理证明了这些算法的有效性.     

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

An inexact stochastic mixed integer linear semi-infinite programming (ISMISIP) model is developed for municipal solid waste (MSW) management under uncertainty. By incorporating stochastic programming (SP), integer programming and interval semi-infinite programming (ISIP) within a general waste management problem, the model can simultaneously handle programming problems with coefficients expressed as probability distribution functions, intervals and functional intervals. Compared with those inexact programming models without introducing functional interval coefficients, the ISMISIP model has the following advantages that: (1) since parameters are represented as functional intervals, the parameter’s dynamic feature (i.e., the constraint should be satisfied under all possible levels within its range) can be reflected, and (2) it is applicable to practical problems as the solution method does not generate more complicated intermediate models (He and Huang, Technical Report, 2004; He et al. J Air Waste Manage Assoc, 2007). Moreover, the ISMISIP model is proposed upon the previous inexact mixed integer linear semi-infinite programming (IMISIP) model by assuming capacities of the landfill, WTE and composting facilities to be stochastic. Thus it has the improved capabilities in (1) identifying schemes regarding to the waste allocation and facility expansions with a minimized system cost and (2) addressing tradeoffs among environmental, economic and system reliability level.     

A non-breaking-wave-generated turbulence mixing scheme for a global ocean general circulation model

Ocean Dynamics - A novel vertical mixing scheme to describe the influence of the non-breaking surface waves in ocean general circulation models is proposed based on the second-order turbulence...     

基于混合差分进化算法的地球物理线性反演

地球物理反问题线性化处理之后, 各种反演算法归结为对病态线性方程组的求解. 为了快速准确地计算出地球物理参数, 本文提出了一种全新的基于LSQR算法的混合差分进化算法(Hybrid Differential Evolution Algorithm, HDE). 该算法利用LSQR算法给出DE算法的初始种群, 提高DE算法的计算速度和稳定性. 在不同噪声水平下, 对四种正则化方法Tikhonov、TSVD、LSQR和HDE的反演结果进行详细比较. 理论模型和实际数据反演的结果都表明: 改进的HDE算法应用于地球物理反问题的求解是成功的: 反演结果与原设定模型具有较高的相关性, 在稳定性和准确性上较常规的反演算法都具有一定的优势; 而且不需要给定正则化参数, 具有更强的实用性.     

一种线性走时插值射线追踪改进算法

针对线性走时插值算法(LTI)不能正确追踪逆向传播射线的问题, 目前已提出多种改进算法, 如扩张收缩LTI算法、 循环计算LTI算法、 动态网络最短路径射线追踪算法等, 但这些算法的计算效率普遍偏低. 在分析各种改进LTI算法的优劣后, 本文提出了改进动态网络最短路径射线追踪算法. 该改进算法依据波的传播规律以及LTI算法的基本方程, 排除动态网络最短路径射线追踪算法中大量冗余节点计算, 并采用传统的二叉树堆排序算法对波前阵列节点进行管理. 数值算例表明, 本文提出的改进算法具有较高的计算效率, 其计算效率是动态网络最短路径射线追踪算法的4.5—30倍, 是原始LTI算法的2—6.5倍; 当动态网络最短路径射线追踪算法采用堆排序算法时, 改进算法的计算效率是其3.5—15倍.      

A recursive decomposition algorithm for network seismic reliability evaluation

A new probabilistic analytical approach to evaluate seismic system reliability of large lifeline systems is presented in this paper. The algorithm takes the shortest path from the source to the terminal of a node weight or edge weight network as decomposition policy, using the Boolean laws of set operation and probabilistic operation principal, a recursive decomposition process then could be constructed. For a general weight network, the modified Torrieri method (NTR/T method) is introduced to combine with the suggested algorithm. Therefore, the recursive decomposition algorithm may be applied to evaluate the seismic reliability of general lifeline systems. A series of case studies, including a practical district electric power network system and a large urban water supply system, show that the suggested algorithm supplies a useful probabilistic analysis means for the seismic reliability evaluation of large lifeline systems. Copyright © 2002 John Wiley & Sons, Ltd.     

基于混合优化算法的MT阻抗张量畸变分解方法

在前人研究基础上,对Groom-Bailey(GB)张量分解畸变因子和区域阻抗的求解方法进行了改进.首先,通过Swift旋转与GB分解的扭变和剪切矩阵的求逆变换,利用变换后区域阻抗主对角元素为0的条件获得关于扭变因子和剪切因子的超定方程组,采用模拟退火全局优化算法进行求解.其次,由得到的扭变因子和剪切因子,结合Swift旋转确定的走向角和区域阻抗元素的估计,作为非线性最小二乘局部优化算法的初始值,对GB分解定义式的超定方程组进行求解,得到各畸变参数和区域阻抗的解.通过模型试验验证了方法的正确,对方法的稳定性进行了比较与评价,并通过与已有结果的对比和实际资料的应用,表明了方法实际应用的效果.