Table 4 Optimal solution for coil spring problem
Branch-Bound | GA | Meta-GA | DE/rand | This article: \(\cdot\) / \(\cdot\) / 1 | ||||
|---|---|---|---|---|---|---|---|---|
Sandgren (1990) | Chen and Tsao (1993) | Wu and Chow (1995) | Lampinen and Zelinka (1999) | DE/best | mDEOB/best | DE/cur_to_best | mDEOB/cur_to_best | |
\(x_1\) | 10 | 9 | 9 | 9 | 9 | 9 | 9 | 10 |
\(x_2\) | 1.180701 | 1.2287 | 1.227411 | 1.223041 | 1.22304 | 1.22304 | 1.22304 | 1.18104 |
\(x_3\) | 0.283 | 0.283 | 0.283 | 0.283 | 0.283 | 0.283 | 0.283 | 0.283 |
\(g_1\) | 54309 | 415.969 | 550.993 | 1008.8114 | 1006.92 | 1006.93 | 1006.93 | 5389.66 |
\(g_2\) | 8.8187 | 8.9207 | 8.9624 | 8.94564 | 8.94562 | 8.94562 | 8.94562 | 8.64751 |
\(g_3\) | 0.08298 | 0.08300 | 0.08300 | 0.083000 | 0.08300 | 0.08300 | 0.08300 | 0.08300 |
\(g_4\) | 1.8193 | 1.7713 | 1.7726 | 1.77696 | 1.77696 | 1.77696 | 1.77696 | 1.81896 |
\(g_5\) | 1.1723 | 1.3417 | 1.3371 | 1.32170 | 1.32170 | 1.32170 | 1.32170 | 1.17330 |
\(g_6\) | 5.4643 | 5.4568 | 5.4585 | 5.46429 | 5.46427 | 5.46427 | 5.46427 | 5.46398 |
\(g_7\) | 0.0 | 0.0 | 0.0 | 2.68 × 10−16 | 0.0 | 0.0 | 0.0 | 0.0 |
\(g_8\) | 0.0 | 00174 | 0.0134 | 5.08 × 10−16 | 2.34 × 10−7 | 2.76 × 10−9 | 9.61 × 10−8 | 6.71 × 10−4 |
f(x) | 2.7995 | 2.6709 | 2.6681 | 2.65856 | 2.65856 | 2.65856 | 2.65856 | 2.65856 |
S.A. | – | – | – | 95.0% | 69.0% | 88.0% | 90.0% | 95.0% |