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

Table 3

Comparative results between 4 versions of the algorithms ORBIT and NMSMAX.

Name		Total number of function evaluations						Absolute difference to known minimum
		V1	V2	V3	V4	ORBIT	NMS	V1	V2	V3	V4	ORBIT	NMS
BEALE	2	28	25	32	42	419	63	5,75e-07	6,25e-09	3,10e-07	1,34e-07	5,16e-10	2,93e-07
BRANIN	2	24	25	32	36	53	56	1,10e-07	5,35e-07	7,60e-08	6,14e-07	1,10e-05	7,81e-07
ROSENBROCK	2	37	37	33	39	838	100	2,51e-07	9,56e-08	9,40e-07	1,69e-07	1,80e-03	3,71e-07
SCHWEFEL36	2	26	25	26	32	69	69	9,35e-07	4,29e-07	1,44e-07	7,43e-08	9,17e-07	4,39e-07
GULF	3	494	159	165	226	1000	389	3,29e-07	7,71e-07	1,84e-09	8,95e-07	2,66e+00	5,60e-07
HART3	3	52	46	49	69	348	129	9,98e-09	8,33e-07	7,14e-07	2,64e-08	3,91e-06	6,08e-07
HELIX	3	53	42	48	48	443	115	8,29e-07	5,97e-07	3,08e-07	4,50e-07	4,61e-04	4,31e-07
ROSENBROCK	3	77	68	80	88	1000	176	3,81e-07	4,41e-07	6,66e-07	1,18e-07	5,20e-03	5,12e-07
SCHWEFEL4	3	55	46	41	67	77	93	1,72e-07	7,98e-08	7,20e-07	1,81e-08	8,05e-07	7,07e-07
BROWNDEN	4	118	84	112	121	398	236	6,77e-07	9,34e-06	5,16e-06	3,44e-06	9,60e-06	9,77e-06
HART4	4	50	42	48	38	62	122	3,86e-07	2,78e-07	3,95e-07	2,94e-07	5,56e-07	8,85e-07
POWELL	4	201	92	104	148	615	366	6,77e-07	7,43e-07	8,85e-07	4,51e-07	6,01e-05	9,45e-07
ROSENBROCK	4	136	111	143	144	1000	332	8,67e-07	9,90e-07	3,10e-07	7,74e-07	2,75e-02	8,78e-07
SCHWEFEL4	4	63	61	62	74	112	156	2,46e-07	9,04e-07	5,55e-07	3,18e-07	9,25e-07	9,75e-07
WOOD	4	166	79	85	109	255	217	6,35e-07	5,16e-07	3,78e-07	2,13e-08	4,04e-04	7,57e-07
BIGGS	6	660	294	243	529	156	1000	7,54e-04	1,52e-07	9,65e-07	9,48e-07	6,60e-03	5,68e-05
HART6	6	104	116	95	107	139	179	5,63e-07	5,43e-07	5,23e-07	4,08e-07	8,21e-07	9,39e-07
ROSENBROCK	6	302	257	264	435	1000	818	3,02e-07	6,78e-07	8,09e-07	7,34e-07	7,22e-02	9,90e-07
SCHWEFEL4	6	124	116	111	169	173	221	8,37e-07	7,10e-07	2,38e-07	7,37e-07	9,47e-07	8,81e-07
TRID	6	405	206	205	194	399	541	6,30e-03	6,67e-07	2,77e-07	1,79e-07	6,90e-03	7,94e-07
WATSON	6	117	83	97	119	222	305	2,11e-07	8,63e-07	1,56e-07	4,16e-07	9,83e-07	7,21e-07
POWELL	8	168	135	139	151	225	410	7,61e-07	2,88e-07	5,77e-07	3,95e-07	1,00e-06	9,70e-07
ROSENBROCK	8	912	648	624	769	1000	1000	7,41e-07	7,25e-07	9,35e-07	8,96e-07	4,81e-01	2,75e-01
TRID	8	1000	648	585	778	1000	1000	1,10e-04	9,81e-07	8,49e-07	3,68e-07	3,53e-04	2,40e-03