An Improved Nonlinear Grey Bernoulli Model Based on the Whale Optimization Algorithm and Its Application

Table 8

Simulated and predicted performance by five grey models using raw data of the number of R&D institutions of China’s higher education.

Actual data	GM (1, 1)	DGM (1, 1)	NGBM (1, 1)	ONGBM (1, 1)	INGBM (1, 1)
8630
9225	9041.86	9049.01	9224.89	9225.38	9225.08
9842	9882.75	9890.73	9820.48	9810.66	9798.18
10632	10801.83	10810.73	10692.04	10677.82	10672.23
11732	11806.39	11816.31	11760.42	11744.56	11757.27
13062	12904.37	12915.43	13011.49	12995.95	13037.11
RMSE	0.14	0.14	0.04	0.04	0.03
MAPE	1.17	1.18	0.28	0.27	0.25
14971	14104.46	14116.78	14450.13	14436.68	14516.89
16280	15416.16	15429.88	16090.00	16080.46	16211.58
RMSE	0.87	0.85	0.39	0.40	0.32
MAPE	5.54	5.46	2.32	2.39	1.72