Enhanced Differential Evolution Algorithm with Local Search Based on Hadamard Matrix

Table 3

Experimental results of HLS with three sizes of Hadamard matrix.

Fun	DE/rand/1/bin + HLS_4	DE/rand/1/bin + HLS_8	DE/rand/1/bin + HLS_16
f1	1.12E − 112 ± 6.03E − 112†	7.60E − 84 ± 4.16E − 83	3.12E − 59 ± 1.63E − 58
f2	2.30E − 58 ± 1.22E − 57†	2.81E − 45 ± 1.07E − 44	1.15E − 30 ± 6.27E − 30
f3	1.65E + 00 ± 2.73E + 00†	1.61E + 01 ± 1.58E + 01	1.95E + 02 ± 2.89E + 02
f4	1.73E − 165 ± 0.00E + 00†	6.10E − 129 ± 3.31E − 128	1.58E − 88 ± 7.30E − 88
f5	1.19E + 01 ± 1.38E + 01	1.11E + 01 ± 1.39E + 01†	1.29E + 01 ± 1.41E + 01
f6	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†
f7	3.54E − 03 ± 4.00E − 03	3.50E − 03 ± 3.33E − 03†	4.63E − 03 ± 4.28E − 03
f8	1.26E + 04 ± 0.00E + 00+	1.26E + 04 ± 0.00E + 00†	1.26E + 04 ± 0.00E + 00†
f9	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†
f10	4.74E − 16 ± 1.23E − 15†	4.74E − 16 ± 1.23E − 15†	1.07E − 15 ± 1.66E − 15
f11	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†
f12	1.57E − 32 ± 1.91E − 34	1.57E − 32 ± 5.57E − 48†	1.57E − 32 ± 5.57E − 48†
f13	1.35E − 32 ± 5.57E − 48	1.35E − 32 ± 5.57E − 48†	1.35E − 32 ± 5.57E − 48†
f14	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†
f15	1.16E + 00 ± 1.75E + 00†	1.13E + 01 ± 1.05E + 01	1.61E + 02 ± 1.52E + 02
f16	2.76E − 01 ± 5.10E − 01†	2.88E + 00 ± 3.635E + 00	4.42E + 01 ± 4.02E + 01
f17	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†	0.00E + 00 ± 0.00E + 00†
f18	3.55E − 16 ± 1.08E − 15†	3.55E − 16 ± 1.08E − 15†	9.47E − 16 ± 1.60E − 15
f19	1.57E − 32 ± 1.77E − 34†	1.58E − 32 ± 7.07E − 34†	1.57E − 32 ± 5.57E − 48†
f20	1.35E − 32 ± 5.57E − 48†	1.35E − 32 ± 5.57E − 48†	1.35E − 32 ± 5.57E − 48†
Best Num	16	14	10