An Efficient Hybrid Optimization Approach Using Adaptive Elitist Differential Evolution and Spherical Quadratic Steepest Descent and Its Application for Clustering

Table 2

The descriptive statistics.

No	Min	FBEST mean (rank)
		HaeDE	aeDE	PSO	SHO	SSA	DA
1	0.398	0.3979 (4)	0.3979 (5)	0.3979 (1)	0.3979 (2)	0.3979 (3)	0.3979 (6)
2	0	0 (1)	0 (3)	0.0413 (6)	0.0138 (5)	0 (2)	0.0014 (4)
3	0	0 (4)	0 (5)	0 (1)	0 (3)	0 (2)	0 (6)
4	0	20.1717 (1)	20.6465 (2)	183.3748 (6)	55.2204 (3)	72.7645 (4)	149.0701 (5)
5	−12569.5	−12027.9391 (1)	−11886.7727 (2)	−6470.1728 (5)	−10658.3841 (3)	−7816.4553 (4)	−5825.5215 (6)
6	−1.8013	−1.8013 (2)	−1.8013 (4)	−1.8013 (1)	−1.7817 (6)	−1.8013 (3)	−1.8013 (5)
7	−4.6877	−4.6527 (1)	−4.6486 (2)	−4.5941 (3)	−4.1299 (5)	−4.3921 (4)	−3.854 (6)
8	−9.6602	−9.4678 (2)	−9.4813 (1)	−7.6207 (5)	−7.8455 (3)	−7.7399 (4)	−6.1953 (6)
9	0	0.0058 (3)	0.0068 (4)	0.0103 (6)	0.01 (5)	0 (1)	0.0016 (2)
10	−1.03163	−1.0316 (4)	−1.0316 (5)	−1.0316 (1)	−1.0316 (2)	−1.0316 (3)	−1.0316 (6)
11	0	0 (1)	0 (3)	0.0218 (6)	0.0146 (5)	0 (2)	0.002 (4)
12	0	0 (3)	0 (4)	0 (1)	0.0151 (6)	0 (2)	0.0018 (5)
13	−186.73	−186.7309 (2)	−186.7309 (4)	−186.7309 (1)	−184.6258 (6)	−186.7309 (3)	−186.7289 (5)
14	3	3 (3)	3 (4)	3 (1)	5.7 (6)	3 (2)	3 (5)
15	0.00031	0.0013 (4)	0.0006 (2)	0.0005 (1)	0.0042 (5)	0.0008 (3)	0.0042 (6)
16	−10.15	−8.3881 (4)	−8.8613 (3)	−7.4454 (5)	−6.6581 (6)	−9.4795 (1)	−9.296 (2)
17	−10.4	−9.5579 (2)	−9.4621 (3)	−7.8864 (4)	−5.8977 (6)	−10.0486 (1)	−7.7742 (5)
18	−10.53	−9.7993 (2)	−9.9541 (1)	−8.5676 (4)	−5.3894 (6)	−9.2793 (3)	−6.8984 (5)
19	0	0.1427 (4)	0.0989 (3)	0.8412 (6)	0.0497 (2)	0.0251 (1)	0.4327 (5)
20	0	0.0056 (3)	0.0066 (4)	0.0168 (6)	0.0004 (2)	0.0002 (1)	0.0107 (5)
21	−3.86	−3.8628 (5)	−3.8628 (4)	−3.8628 (1)	−3.8628 (3)	−3.8628 (2)	−3.8623 (6)
22	−3.32	−3.2747 (2)	−3.2866 (1)	−3.238 (6)	−3.2745 (3)	−3.2429 (5)	−3.2719 (4)
23	0	0.079 (3)	0.1389 (4)	33.4143 (6)	0.0135 (1)	0.0146 (2)	3.5681 (5)
24	0	1.1253 (1)	1.2893 (2)	12.1837 (6)	2.888 (4)	2.1901 (3)	5.6063 (5)
25	0	0.2291 (2)	0.0915 (1)	57.75 (6)	3.1098 (3)	21.3042 (4)	41.9515 (5)
26	0	0.0492 (3)	0.0591 (4)	163.2041 (6)	0.0003 (1)	0.0034 (2)	20.0337 (5)
27	−1.08	−1.0764 (3)	−1.0764 (4)	−1.0809 (1)	−1.0629 (5)	−1.0809 (2)	−1.0272 (6)
28	−1.5	−1.4175 (2)	−1.4212 (1)	−0.9667 (4)	−0.7674 (5)	−1.3188 (3)	−0.5915 (6)
29		−0.2872 (3)	−0.3065 (2)	−0.1523 (5)	−0.26 (4)	−0.3763 (1)	−0.0818 (6)
30	0	0 (2)	0 (4)	0 (1)	94.0393 (6)	0 (3)	0.0004 (5)
31	0	14.7267 (2)	83.2492 (3)	1.3738 (1)	395.239 (5)	189.9685 (4)	637.8159 (6)
32	0	356.7752 (1)	1168.6692 (2)	7531.9408 (5)	1495.7068 (3)	3859.5778 (4)	9598.2252 (6)
Sum of ranks		80	96	118	130	84	164