Adaptive Randomness: A New Population Initialization Method
Table 1
Comparison of convergence speed (NFC) and success rate (SR) for DE with random population initialization (DEr), with opposition-based population initialization (DEo), with generalized opposition-based population initialization (DEgo), and with AR-based population initialization (DEar).
DEr
DEo
DEgo
DEar
ARE
NFC
SR
NFC
SR
NFC
SR
NFC
SR
30
49725
1
49670
1
49510
1
49505
1
1.0044
1.0033
1.0001
30
55650
1
55735
1
55620
1
55530
1
1.0022
1.0037
1.0016
20
121666
1
120482
1
121136
1
120314
1
1.0112
1.0014
1.0068
30
327670
1
327185
1
324500
1
326530
1
1.0035
1.0020
0.9938
10
230525
0.95
254545
0.95
237175
0.95
227935
0.95
1.0114
1.1167
1.0405
30
63895
0.98
62490
0.96
62148
0.96
64725
1
0.9872
0.9655
0.9602
30
11751
1
11645
1
11698
1
11621
1
1.0112
1.0021
1.0066
30
97624
1
97816
1
97437
1
97411
1
1.0022
1.0042
1.0003
2
3180
1
3150
1
3193
1
3137
1
1.0137
1.0041
1.0179
4
13272
1
13470
1
13544
1
13255
1
1.0013
1.0162
1.0218
2
15250
1
15488
1
15380
1
15220
1
1.0020
1.0176
1.0105
2
4325
1
4475
1
4410
1
4215
1
1.0261
1.0574
1.0463
30
8164
1
8157
1
8153
1
8129
1
1.0043
1.0034
1.0030
2
2681
1
2705
1
2716
1
2678
1
1.0011
1.0101
1.0142
4
—
0
—
0
—
0
1541
0.01
—
—
—
10
33032
0.24
53652
0.36
50060
0.32
49760
0.36
0.6638
1.0782
1.0060
30
250184
1
250848
1
251408
1
249712
1
1.0019
1.0045
1.0068
30
102236
1
101268
1
102068
1
101344
1
1.0088
0.9993
1.0071
30
—
0
—
0
—
0
—
0
—
—
—
30
22485
1
22370
1
22402
1
22331
1
1.0069
1.0017
1.0032
30
—
0
—
0
—
0
—
0
—
—
—
4
—
0
—
0
—
0
—
0
—
—
—
4
—
0
—
0
—
0
—
0
—
—
—
4
—
0
—
0
—
0
—
0
—
—
—
4
—
0
—
0
—
0
—
0
—
—
—
2
7980
0.97
7923
0.96
8136
0.98
8061
0.98
0.9900
0.9829
1.0093
2
856
1
859
1
839
1
801
1
1.0687
1.0724
1.0474
30
172487
1
172489
1
177257
1
171543
1
1.0055
1.0055
1.0333
2
4952
1
4781
1
4924
1
4845
1
1.0221
0.9868
1.0163
5
—
0
21
0.02
—
0
—
0
—
—
—
5
28396
0.99
29204
1
28974
1
28903
1
0.9825
1.0104
1.0025
2
1567
1
1558
1
1564
1
1549
1
1.0116
1.0058
1.0097
2
6386
1
6305
1
6309
1
6230
1
1.0250
1.0120
1.0127
2
4110
1
4083
1
4086
1
4069
1
1.0101
1.0034
1.0042
Average values
—
68488
0.997727
69504
0.997727
68879
0.997727
68087
0.997727
1.0116
1.0152
1.0138
Note. The reported average values (the last row) are calculated only on the functions where all the algorithms have the same success rate (i.e., all SRs = 1 and one SR = 0.95).