Nonlinear grey Bernoulli multivariate model NGBMC (1, n) is known as a novel forecasting model for nonlinear time series with small samples. However, ill-posed problem would make it less efficient and even cause large errors. In order to improve its generality, a hybrid method combining Elastic Net and multi-objective optimization is introduced in this work. This method effectively solves the essential defect of the ill-posed problem of the NGBMC (1, n) model, making the NGBMC (1, n) model more stable, more reliable, and more interpretable. The parameter identification of the new model uses the alternating direction method of multipliers, and the nonlinear parameter of the model and the regularization parameter of Elastic Net regression are optimized by the multi-objective grey wolf optimizer (MOGWO). Eight numerical cases all show that the use of the Elastic Net regularization method and multi-objective optimization technology can significantly improve the prediction accuracy of the NGBMC (1, n) model for future data. In addition, the hybrid method combing the regularization and optimization strategies proposed in this paper is a general framework for the grey prediction models, which has a high potential in improving the other grey models.

非线性灰色伯努利多元模型NGBMC（1，n）被称为具有小样本的非线性时间序列的新型预测模型。但是，不适定的问题会使效率降低，甚至会导致较大的错误。为了提高其通用性，本文引入了一种将弹性网和多目标优化相结合的混合方法。该方法有效地解决了NGBMC（1，n）模型不适定问题的本质缺陷，使NGBMC（1，n）模型更稳定，更可靠并且更易于解释。新模型的参数辨识采用乘子的交替方向法，并通过多目标灰狼优化器（MOGWO）对模型的非线性参数和Elastic Net回归的正则化参数进行了优化。八个数值案例均表明，使用弹性网正则化方法和多目标优化技术可以显着提高NGBMC（1，n）模型对未来数据的预测准确性。此外，本文提出的将正则化和优化策略相结合的混合方法是灰色预测模型的通用框架，在改进其他灰色模型方面具有很大的潜力。