Department of Automation, Tsinghua University, Beijing, 10084, China.
College of Information System and Management, National University of Defense Technology, Changsha, 410073, China.
Sci Rep. 2020 Dec 9;10(1):21540. doi: 10.1038/s41598-020-77630-w.
With the advantages of small samples and high accuracy, Grey Model (GM) still has two major problems need to be addressed, high input data requirements and large margin of error. Hence, this paper proposes an algorithm based on Populational Entropy Based Mind Evolutionary Algorithm-Error Back Propagation Training Artificial Neural Algorithm to modify GM residual tail, which will not only keep the advantages of GM, but also expand its scope of use to various non-linear and even multidimensional objects. Meanwhile, it can avoid defects of other algorithms, such as slow convergence and easy to fall into the local minimum. In small samples data experiments, judging from SSE, MAE, MSE, MAPE, MRE and other indicators, this new algorithm has significant advantage over GM, BP algorithm and combined genetic algorithm in terms of simulation accuracy and convergence speed.
灰色模型（GM）具有小样本、高精度的优点，但仍存在两个需要解决的主要问题，即输入数据要求高和误差幅度大。因此，本文提出了一种基于群体熵的思维进化算法-误差反向传播训练人工神经网络算法来修正 GM 残差尾巴的算法，该算法不仅保留了 GM 的优点，而且将其应用范围扩展到各种非线性甚至多维对象。同时，它可以避免其他算法的缺陷，如收敛速度慢，容易陷入局部最小值。在小样本数据实验中，从 SSE、MAE、MSE、MAPE、MRE 等指标来看，新算法在模拟精度和收敛速度方面明显优于 GM、BP 算法和组合遗传算法。
