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 |
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“FES” denotes the number of function evaluations. “—” indicates that the algorithm cannot find the optimum within Max_FES.
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