基于自适应加法树算法的二状态网络可靠性MonteCarlo模拟
Self-Adaptive Binary-Addition-Tree Algorithm-Based Novel Monte Carlo Simulation for Binary-State Network Reliability Approximation
摘要：
蒙特卡罗模拟（MCS）是一种在大量应用中使用的统计方法。它使用重复的随机抽样来解决具有概率解释的问题，以获得高质量的数值结果。MCS是简单的，易于开发，实施和应用。然而，它的计算成本和总运行时间可能相当高，因为它需要许多样本来获得具有低方差的准确近似。本文提出了一种新的MCS，称为自适应BAT-MCS，基于二叉适应树算法（BAT）和我们提出的自适应模拟数算法，简单，有效地减少运行时间和方差的MCS。将所提出的自适应BAT-MCS应用于一个简单的基准测试问题，以展示其在网络可靠性中的应用。讨论了该算法的期望、方差、模拟次数等统计特性和时间复杂度。此外，它的性能进行了比较，传统的MCS广泛的大规模问题。
英文摘要：
The Monte Carlo simulation (MCS) is a statistical methodology used in a large number of applications. It uses repeated random sampling to solve problems with a probability interpretation to obtain high-quality numerical results. The MCS is simple and easy to develop, implement, and apply. However, its computational cost and total runtime can be quite high as it requires many samples to obtain an accurate approximation with low variance. In this paper, a novel MCS, called the self-adaptive BAT-MCS, based on the binary-adaption-tree algorithm (BAT) and our proposed self-adaptive simulation-number algorithm is proposed to simply and effectively reduce the run time and variance of the MCS. The proposed self-adaptive BAT-MCS was applied to a simple benchmark problem to demonstrate its application in network reliability. The statistical characteristics, including the expectation, variance, and simulation number, and the time complexity of the proposed self-adaptive BAT-MCS are discussed. Furthermore, its performance is compared to that of the traditional MCS extensively on a large-scale problem.
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