Self-Adaptive Binary-Addition-Tree Algorithm-Based Novel Monte Carlo Simulation for Binary-State Network Reliability Approximation

TL;DR

This paper introduces a self-adaptive binary-adaption-tree Monte Carlo simulation method that significantly reduces computational time and variance in network reliability approximation, demonstrating improved efficiency over traditional methods.

Contribution

The paper presents a novel self-adaptive BAT-MCS algorithm that enhances Monte Carlo simulation efficiency for binary-state network reliability problems.

Findings

Reduces simulation runtime compared to traditional MCS.

Achieves lower variance in reliability estimates.

Effective on large-scale network problems.

Abstract

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.