A Radial Basis Function-Based Optimization Algorithm with Regular Simplex Set Geometry in Ellipsoidal Trust-Regions

Table 4

Standard settings of the algorithm.

	1.25	Determines the set of points that is considered in algorithm 3. For , all points must be inside the trust-region. For slightly larger values, the nearby points are also considered. Large values will positively bias the volume so that even for poor set distributions, the volumetric condition will be satisfied.
	0	Standard trust-region parameter. Adopted from [35].
	0.6	See
	0.5	See
	2	See
		Lower-limit for the hyperparameters in the RBF framework. Determines how fast the RBFs decay. For normalized search space and reasonably smooth objective functions, it was determined to be a good limit by trial-and-error.
		Upper-limit for the hyperparameters in the RBF framework. See .
	0	Minimal trust-region size. Determines the smallest focus the trust-region framework can have.
		Maximum trust-region size. Determines the largest focus the trust-region framework can have. Value was adopted from [31].
	100	Maximum number of points to be included in the RBF model. The value was chosen arbitrarily and worked well for relatively low-dimensional problems. When the number is too large, the influence of far-away points may distort the local geometry of the objective. Furthermore, the fitting and evaluating of the interpolation model becomes computationally challenging as a result of hyperparameter optimization.