Journal of Applied Mathematics

Research Article

Sufficient Conditions for Global Convergence of Differential Evolution Algorithm

Table 2

FES to achieve the Ter_Err for Rastrigin function.
Alg.
best/1 rand/1 cur-to-best/1 best/2 rand/2
DE CDE-um DE CDE-um DE CDE-um DE CDE-um DE CDE-um
FES
— 103376 — 1680 1184 824 1088 1232 2000 2400
— 1392 1472 1408 3328 976 1392 2112 2432
560 1664 1424 1264 2160 1264 1392 1584 2512
— 942224 — 1200 1392 1384 1168 1280 1936 2176
— 672 1440 1584 1280 560 1136 1280 1792 2480
— 452064 1696 1600 1184 1360 1120 1312 1856 2304
560 624 1536 1456 1600 464 1088 1184 2000 1792
720 688 1424 1648 1280 2944 — 1472 — 2352
— 576 1296 1552 1312 664 — 1296 1920 2128
672 576 1184 1248 1184 22736 1056 1296 1776 1936
— 198368 1424 1424 2720 520 1072 1280 2176 2368
— 60336 — 1856 1104 240 1200 1280 2000 2480
656 1424 1584 1136 4272 896 5840 1840 2304
— 267360 1552 28192 1376 824 1056 1056 1728 2288
— 1568 1344 1376 976 1136 1408 1792 2720
672 1296 1440 — 832 1136 1552 2416 2144
608 800 1408 1856 1200 4200 800016 1216 1936 2240
672 1600 1600 1456 1192 1088 1568 2112 2496
704 1536 3712 1184 1232 1168 1232 2096 2512
560 236592 1328 1648 1344 1328 1072 1408 1904 2240
— 1536 1808 1952 1240 — 1328 2336 2368
— 241776 1200 1872 1280 376 1216 1312 1744 2880
— 1072 1408 218208 1344 2888 1152 1248 2000 2512
— 1520 1408 1232 632 1264 1152 1904 2464
— 1344 689360 1136 752 1200 5568 1856 2352
— 640 1424 1488 1376 408 1184 1424 1808 2448
— 788880 1344 1376 9792 1216 1424 2416 2512
576 656 1408 1168 1056 1128 1168 1296 1856 2240
640 560 1408 1536 1184 672 960 1344 1856 2432
— 1376 228048 5136 512 1312 1312 1888 2512
— 672 1312 1520 1456 520 1232 1184 2112 2160
736 17952 — 1584 1536 2456 1200 3504 1920 2560
592 1264 1536 1408 680 1296 1136 2000 2432
— 15456 1328 24288 1280 936 1296 1264 1856 2272
624 1232 1680 1264 2456 1136 1152 2144 2448
— 1264 1504 1040 1008 1264 1504 1776 2352
544 656 1440 1616 1184 352 944 1200 1824 2432
640 1296 1520 1184 1680 960 1360 2064 2048
720 656 1600 1520 20664 976 1296 1744 2080
672 1536 1392 1120 592 1056 1232 1904 2464
— 784 1472 1456 1344 800 1072 1168 1776 2176
528 1472 1472 2168 1280 12944 1824 2672
640 576 1344 1648 1376 672 1056 10960 1984 2528
624 1680 1360 1328 1368 1120 1248 1952 2768
720 87056 1568 1392 1376 1072 1104 1136 1776 2464
640 640 1280 1696 1344 704 1088 1264 2096 2368
576 1328 1344 1232 560 1232 1312 2000 2240
— 848 — 1504 1344 472 1200 1136 2080 2176
544 688 1600 1440 1344 640 1056 1216 2000 2544
640 1392 1408 1136 592 1056 1344 2096 2336
“FES” denotes the number of function evaluations. “—” indicates that the algorithm cannot find the optimum within Max_FES.