An Improved Approach for Estimating the Hyperparameters of the Kriging Model for High-Dimensional Problems through the Partial Least Squares Method

Table 3

Results of the Griewank function in 60D over the interval . Ten trials are done for each test (50, 100, 200, and 300 training points). Best results of the relative error are highlighted in bold type for each case.

Surrogate	Statistic	50 points		100 points
		Error (%)	CPU time	Error (%)	CPU time
Kriging	Mean	1.39	560.19 s	1.04	920.41 s
	std	0.15	200.27 s	0.05	231.34 s
KPLS	Mean	0.92	0.07 s	0.87	0.10 s
	std	0.02	0.02 s	0.02	0.007 s
KPLS	Mean	0.91	0.43 s	0.87	0.66 s
	std	0.03	0.54 s	0.02	1.06 s
KPLS	Mean	0.92	1.57 s	0.86	3.87 s
	std	0.04	1.98 s	0.02	5.34 s
KPLS+K	Mean	0.99	2.14 s	0.90	2.90 s
	std	0.03	0.72 s	0.03	0.03 s
KPLS+K	Mean	0.98	2.44 s	0.88	3.44 s
	std	0.04	0.63 s	0.02	1.06 s
KPLS+K	Mean	0.99	3.82 s	0.88	6.68 s
	std	0.05	2.33 s	0.03	5.34 s
Surrogate	Statistic	200 points		300 points
		Error (%)	CPU time	Error (%)	CPU time
Kriging	Mean	0.83	2015.39 s	0.65	2894.56 s
	std	0.04	239.11 s	0.03	728.48 s
KPLS	Mean	0.82	0.37 s	0.79	0.86 s
	std	0.02	0.02 s	0.03	0.04 s
KPLS	Mean	0.78	2.92 s	0.74	1.85 s
	std	0.02	2.57 s	0.03	0.51 s
KPLS	Mean	0.78	6.73 s	0.70	20.01 s
	std	0.02	10.94 s	0.03	26.59 s
KPLS+K	Mean	0.76	9.88 s	0.66	22.00 s
	std	0.03	0.06 s	0.02	0.15 s
KPLS+K	Mean	0.75	12.38 s	0.60	23.03 s
	std	0.03	2.56 s	0.03	0.50 s
KPLS+K	Mean	0.74	16.18 s	0.61	41.13 s
	std	0.03	10.95 s	0.03	26.59 s