Optimal Source Selection in Shooting Random Walk Monte Carlo Radiosity

In this paper we study how to optimally select between different sources in shooting random walk Monte Carlo Radiosity. Until now the probability of selecting a source has been made proportional to the importance of that source for the region of interest. We will show here that, whenever the transition probabilities are the Form Factors, this is not optimal, and will consequently give the optimal case. This will correspond to probabilities proportional to the square root of importances, rather than to importances themselves.     

Monte Carlo methods in fuzzy queuing theory

In this paper, we consider an optimization problem in fuzzy queuing theory that was first used in web planning. This fuzzy optimization problem has no solution algorithm and approximate solutions were first produced by computing the fuzzy value of the objective function for only sixteen values of the fuzzy variables. We introduce our fuzzy Monte Carlo method, using a quasi-random number generator, to produce 100,000 random sequences of fuzzy vectors for the fuzzy variables, which will present a much better approximate solution.     

Monte Carlo methods in fuzzy linear regression II

We apply our new fuzzy Monte Carlo method to a certain fuzzy linear regression problem to estimate the best solution. The best solution is a vector of crisp numbers, for the coefficients in the model, which minimizes one of two error measures. We use a quasi-random number generator to produce random sequences of these crisp vectors which uniformly fill the search space. We consider an example problem and show this Monte Carlo method obtains the best solution for both error measures.     

蒙特卡罗与准蒙特卡罗相互融合的整体光照计算

蒙特卡罗方法具备普适性、鲁棒性以及与问题复杂度无关性等优点,非常适于十分难解的整体光照计算问题,但缺点是生成图像随机噪声大．准蒙特卡罗方法计算连续被积函数低维积分的收敛速度快于蒙特卡罗方法,但不适于直接求解复杂的整体光照计算问题．文中研究蒙特卡罗整体光照计算最根本环节,即随机游动的抽样模式,提出融合蒙特卡罗与准蒙特卡罗的两种通用的新型整体光照计算策略．两种新型策略可以应用于所有基于蒙特卡罗的整体光照算法,不仅能够降低生成图像的随机噪声,而且实现简单、不增加计算和存储开销．     

New hybrid Monte Carlo methods and computing the dominant generalized eigenvalue

In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed.     

Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors.     

Exploring pseudo- and chaotic random Monte Carlo simulations

Computer simulations are an increasingly important area of geoscience research and development. At the core of stochastic or Monte Carlo simulations are the random number sequences that are assumed to be distributed with specific characteristics. Computer-generated random numbers, uniformly distributed on (0, 1), can be very different depending on the selection of pseudo-random number (PRN) or chaotic random number (CRN) generators. In the evaluation of some definite integrals, the resulting error variances can even be of different orders of magnitude. Furthermore, practical techniques for variance reduction such as importance sampling and stratified sampling can be applied in most Monte Carlo simulations and significantly improve the results. A comparative analysis of these strategies has been carried out for computational applications in planar and spatial contexts. Based on these experiments, and on some practical examples of geodetic direct and inverse problems, conclusions and recommendations concerning their performance and general applicability are included.     

基于Monte Carlo method的均衡度确定模型

蒙特卡罗方法(Monte Carlo method),也称统计模拟方法,是一种以概率统计理论为指导的一类非常重要的数值计算方法,是指使用随机数(或更常见的伪随机数)来解决很多计算问题的方法,本文尝试建立警察服务平台的均衡度模型并用蒙特卡罗方法求解,实验结果可以满足一般的应用需求。     

Parallel computing for lattice Monte Carlo simulation of large-scale thin film growth

This paper proposes two viable computing strategies for distributed parallel systems: domain division with sub-domain overlapping and asynchronous communication. We have implemented a parallel computing procedure for simulation of Ti thin film growing process of a system with 1000 x 1000 atoms by means of the Monte Carlo (MC) method. This approach greatly reduces the computation time for simulation of large-scale thin film growth under realistic deposition rates. The multi-lattice MC model of deposition comprises two basic events: deposition, and surface diffusion. Since diffusion constitutes more than 90% of the total simulation time of the whole deposition process at high temperature, we concentrated on implementing a new parallel diffusion simulation that reduces communication time during simulation. Asynchronous communication and domain overlapping techniques are used to reduce the waiting time and communication time among parallel processors. The parallel algorithms we propose can simulate the thin     

A heuristic algorithm based on Monte Carlo methods for the Rural Postman Problem

In Routing Problems the aim is to determine a minimum cost traversal over a graph satisfying some specified constraints. Most of them are NP-hard problems and many different heuristic solution algorithms have been proposed. The name Monte Carlo, MC, applies to a set of heuristic procedures with the common feature of using random numbers to simulate a given process. MC approach has not been applied to the framework of Routing Problems in the literature. The purpose of this paper is to demonstrate that MC methods could be useful in implementing heuristic algorithms for Routing Problems. In particular, we design an efficient MC heuristic algorithm for the well known Rural Postman Problem (RPP), for which we have a set of instances with known optimal solution taken from the literature.The Rural Postman Problem (RPP) consists of finding a minimum cost traversal of a specified arc subset of a graph. Given that the RPP is a NP-hard problem, heuristic algorithms are interesting both to handle large size instances and to provide upper bounds that could be used in branch and cut procedures. In this paper we propose a heuristic algorithm for the RPP based on Monte Carlo methods. We simulate a vehicle travelling randomly over the graph, jumping from one node to another on the basis of certain probabilities. Monte Carlo methods provide a simple approach to many different Routing Problems and they are easily implemented in a computer code. The application of this algorithm to a set of RPP instances taken from the literature demonstrates that, using the appropriate probabilities, they are also efficient.     

Uncertainty quantification through the Monte Carlo method in a cloud computing setting

The Monte Carlo (MC) method is the most common technique used for uncertainty quantification, due to its simplicity and good statistical results. However, its computational cost is extremely high, and, in many cases, prohibitive. Fortunately, the MC algorithm is easily parallelizable, which allows its use in simulations where the computation of a single realization is very costly. This work presents a methodology for the parallelization of the MC method, in the context of cloud computing. This strategy is based on the MapReduce paradigm, and allows an efficient distribution of tasks in the cloud. This methodology is illustrated on a problem of structural dynamics that is subject to uncertainties. The results show that the technique is capable of producing good results concerning statistical moments of low order. It is shown that even a simple problem may require many realizations for convergence of histograms, which makes the cloud computing strategy very attractive (due to its high scalability capacity and low-cost). Additionally, the results regarding the time of processing and storage space usage allow one to qualify this new methodology as a solution for simulations that require a number of MC realizations beyond the standard.     

应用G语言平台LabVIEW进行Monte Carlo模拟实验

本文讨论了应用G语言平台labview进行Monte Carlo模拟实验,并以敌我双方的射击实验为实例进行详细说明。     

Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced.     

Heuristics for the probabilistic traveling salesman problem with deadlines based on quasi-parallel Monte Carlo sampling

The Probabilistic Traveling Salesman Problem with Deadlines (PTSPD) is a Stochastic Vehicle Routing Problem with a computationally demanding objective function. In this work we propose an approximation for that objective function based on Monte Carlo Sampling and using the novel approach of quasi-parallel evaluation of samples. We perform comprehensive computational studies that reveal the efficiency of this approximation. Additionally, we examine different Local Search Algorithms and present a Random Restart Local Search Algorithm for solving the PTSPD together with an extensive computational study on a large set of benchmark instances.     

基于三维Savitzky-Golay滤波的蒙特卡罗剂量分布去噪

提出了一种基于三维Savitzky-Golay滤波的蒙特卡罗（MC）剂量分布的去噪方法。该方法首先利用MC方法模拟粒子轨迹数目较少时得到剂量的三维分布,然后对该剂量分布用三维Savitzky-Golay平滑滤波方法进行去噪处理。结果表明：采用三维Savitzky-Golay平滑滤波方法去噪,不仅提高了剂量分布的可视性,降低了MC计算剂量分布的不确定性。而且也相应地提高了MC剂量计算方法的计算效率。     

基于量子遗传的蒙特卡洛节点定位算法

针对无线传感器网络(WSNs)节点定位的问题,提出了一种量子遗传算法与蒙特-卡洛相结合的定位算法(QGA-MCL).将QGA应用于MCL中的采样过滤阶段,通过合理的编码方案、译码方案以及量子旋转门对采样区域中随机产生的量子染色体进行操作,提高了样本寻优效率和定位精度,并加快了算法的收敛速度.仿真结果表明:与蒙特-卡洛定位算法相比,提出的QGA-MCL算法能够减少约10.2％的定位误差,同时,算法的收敛速度也得到了显著提升.     

Interacting sequential Monte Carlo samplers for trans-dimensional simulation

The methodology of interacting sequential Monte Carlo (SMC) samplers is introduced. SMC samplers are methods for sampling from a sequence of densities on a common measurable space using a combination of Markov chain Monte Carlo (MCMC) and sequential importance sampling/resampling (SIR) methodology. One of the main problems with SMC samplers when simulating from trans-dimensional, multimodal static targets is that transition kernels do not mix which leads to low particle diversity. In such situations poor Monte Carlo estimates may be derived. To deal with this problem an interacting SMC approach for static inference is introduced. The method proceeds by running SMC samplers in parallel on, initially, different regions of the state space and then moving the corresponding samples onto the entire state space. Once the samplers reach a common space the samplers are combined and allowed to interact. The method is intended to increase the diversity of the population of samples. It is established that interacting SMC admit a Feynman-Kac representation; this provides a framework for the convergence results that are developed. In addition, the methodology is demonstrated on a trans-dimensional inference problem in Bayesian mixture modelling and also, using adaptive methods, a mixture modelling problem in population genetics.     

Probability of graphs with large spectral gap by multicanonical Monte Carlo

Graphs with large spectral gap are important in various fields such as biology, sociology and computer science. In designing such graphs, an important question is how the probability of graphs with large spectral gap behaves. A method based on multicanonical Monte Carlo is introduced to quantify the behavior of this probability, which enables us to calculate extreme tails of the distribution. The proposed method is successfully applied to random 3-regular graphs and large deviation probability is estimated.     

一种基于Monte Carlo滤波的对POMDPRS系统性能的改进

规划是人工智能研究的一个重要方向,具有极其广泛的应用背景.POMDPRS是一种结合了PRS的持续规划机制、POMDP的概率分布信念模型和极大效用原理的持续规划系统.它具有较强的对动态不确定性环境的适应能力.但是在大状态空间下的信念更新是其作为实时系统的瓶颈.该文试图将Monte Carlo滤波引入POMDPRS,从而达到降低信念更新的复杂度的目的,满足系统实时性的要求.     

Domain Decomposition Models for Parallel Monte Carlo Transport

We present a strategy for parallelizing computations that use the transport method. It combines spatial domain decomposition with domain replication to realize the scaling benefits of replication while allowing for problems whose computational mesh will not fit in a single processor's memory. The mesh is decomposed into a small number of spatial domains—typically fewer domains than there are processors—and heuristics are used to estimate the computational effort required to generate the solution in each subdomain using Monte Carlo. That work estimate determines the number of times a subdomain is replicated relative to the others. Timing of runs for two problems show that the new method scales better than traditional domain decomposition.