Novel self-adaptive Monte Carlo simulation based on binary-addition-tree algorithm for binary-state network reliability approximation

•Propose the first BAT-based Monte Carlo simulation (BAT-MCS).•The simulation number in BAT-MCS is self-adaptive intelligently.•BAT-MCS uses the super vectors to reduce the runtime and space.•BAT-MCS is more efficient than the traditional MCS.•BAT-MCS is suitable for large-scale network reliability problems. The Monte Carlo simulation method (MCS) is a computational algorithm and statistical methodology for the problems that are too complex to solve analytically. The computational cost and total runtime of the MCS can be quite high as it requires many samples to obtain an accurate approximation with low variance. In this paper, a novel self-adaptive MCS, called BAT-MCS, is proposed to reduce the runtime and variance based on the binary-adaption-tree algorithm (BAT) and the self-adaptive simulation number. The time complexity and simulation number of the BAT-MCS are discussed with the expectation and variance of obtained estimators. The performance of the proposed BAT-MCS is compared to that of the traditional MCS extensively on a large-scale network reliability problem.