Research Article
Efficient Conical Area Differential Evolution with Biased Decomposition and Dual Populations for Constrained Optimization
Table 8
Comparison of function error values achieved by five DE-based approaches when FES =
for test instances g02-g05, g07-g10, g13-g19, g21, and g23.
| | Prob. | Item | SaDE | MPDE | GDE | CMODE | CADE |
| | | Best | 8.0719e-10(0) | 2.3414e-06(0) | 5.0812e-08(0) | 4.1726e-09(0) | 8.2885e-12(0) | | Worst | 1.8353e-02(0) | 1.1014e-02(0) | 2.2776e-02(0) | 1.1836e-07(0) | 2.1762e-08(0) | | Mean | 2.0560e-03 | 8.0224e-04 | 4.3170e-03 | 2.0387e-08 | 4.8107e-09 |
| | Best | 1.3749e-10(0) | -1.0003e-11(0) | -9.8170e-12(0) | 2.3964e-10(0) | -1.0003e-11(0) | | Worst | 1.3389e-04(0) | 4.0082e-01(0) | 9.9739e-01 | 2.5794e-09(0) | -1.0002e-11(0) | | Mean | 1.3532e-05 | 2.5237e-02 | - | 1.1665e-09 | -1.0002e-11 |
| | Best | 2.1667e-07(0) | 3.6380e-12(0) | 8.0036e-11(0) | 7.6398e-11(0) | -2.9104e-11(0) | | Worst | 2.1667e-07(0) | 3.6380e-12(0) | 8.0036e-11(0) | 7.6398e-11(0) | -2.5466e-11(0) | | Mean | 2.1667e-07 | 3.6380e-12 | 8.0036e-11 | 7.6398e-11 | -2.7649e-11 |
| | Best | 0.0000e+00(0) | 0.0000e+00(0) | 0.0000e+00(0) | -1.8190e-12(0) | -1.8190e-12(0) | | Worst | 0.0000e+00(0) | 1.8190e-12(0) | 8.2996e+02 | -1.8190e-12(0) | -1.8190e-12(0) | | Mean | 0.0000e+00 | 7.2760e-14 | - | -1.8190e-12 | -1.8190e-12 |
| | | Best | 6.8180e-08(0) | -2.0190e-11(0) | 7.9822e-11(0) | 7.9783e-11(0) | -2.0229e-11(0) | | Worst | 6.3431e-05(0) | -2.0179e-11(0) | 1.6532e-06(0) | 7.9783e-11(0) | -2.0229e-11(0) | | Mean | 4.7432e-06 | -2.0186e-11 | 1.2966e-07 | 7.9783e-11 | -2.0229e-11 |
| | Best | 8.1964e-11(0) | 4.1633e-17(0) | 8.1964e-11(0) | 8.1964e-11(0) | -1.8036e-11(0) | | Worst | 8.1964e-11(0) | 4.1633e-17(0) | 8.1964e-11(0) | 8.1964e-11(0) | -1.8036e-11(0) | | Mean | 8.1964e-11 | 4.1633e-17 | 8.1964e-11 | 8.1964e-11 | -1.8036e-11 |
| | | Best | 3.7440e-07(0) | 1.1369e-13(0) | -9.7884e-11(0) | -9.8225e-11(0) | 1.7053e-12(0) | | Worst | 3.7440e-07(0) | 1.1369e-13(0) | -9.7771e-11 (0) | -9.8111e-11(0) | 1.7053e-12(0) | | Mean | 3.7440e-07 | 1.1369e-13 | -9.7884e-11 | -9.8198e-11 | 1.7053e-12 |
| | | Best | 6.6393e-11(0) | -1.8190e-12(0) | 6.9122e-11(0) | 6.2755e-11(0) | -3.8199e-11(0) | | Worst | 7.8300e-06(0) | -9.0949e-13(0) | 6.9122e-11(0) | 6.3664e-11(0) | -3.7289e-11(0) | | Mean | 1.6907e-06 | -1.0186e-12 | 6.9122e-11 | 6.2827e-11 | -3.7471e-11 |
| | | Best | 4.1898e-11(0) | -9.7145e-17(0) | 4.1898e-11(0) | 4.1897e-11(0) | 4.1897e-11(0) | | Worst | 1.0696e-06(0) | 9.2964e-01(0) | 1.4403e+00 | 4.1897e-11(0) | 4.1897e-11(0) | | Mean | 8.0263e-08 | 2.5364e-01 | - | 4.1897e-11 | 4.1897e-11 |
| | | Best | 2.9050e-06(0) | 8.5123e-12(0) | 9.1518e-12(0) | 8.5123e-12(0) | 8.5123e-12(0) | | Worst | 2.5233e-04(0) | 8.5123e-12(0) | 1.9281e-02(0) | 8.5194e-12(0) | 8.5123e-12(0) | | Mean | 4.6979e-05 | 8.5123e-12 | 7.7373e-04 | 8.5194e-12 | 8.5123e-12 |
| | | Best | 6.0822e-11(0) | 0.0000e+00(0) | 6.0936e-11(0) | 6.0822e-11(0) | -3.9108e-11(0) | | Worst | 6.0822e-11(0) | 2.1514e-05(0) | 4.8047e+00(0) | 6.0822e-11(0) | -3.9108e-11(0) | | Mean | 6.0822e-11 | 8.6055e-07 | 1.9219e-01 | 6.0822e-11 | -3.9108e-11 |
| | | Best | 6.5214e-11(0) | 5.3291e-15(0) | 6.5216e-11(0) | 6.5213e-11(0) | -3.4786e-11(0) | | Worst | 6.5214e-11(0) | 5.3291e-15(0) | 6.5217e-11(0) | 6.5213e-11(0) | -3.4786e-11(0) | | Mean | 6.5214e-11 | 5.3291e-15 | 6.5216e-11 | 6.5213e-11 | -3.4786e-11 |
| | | Best | 8.1858e-11(0) | 3.6380e-12(0) | 1.8189e-12(0) | 1.8189e-12(0) | -1.8190e-11(0) | | Worst | 7.4058e+01(0) | 7.4058e+01(0) | 2.8637e+02 | 1.8189e-12(0) | -1.8190e-11(0) | | Mean | 6.9670e+01 | 5.1353e+01 | - | 1.8189e-12 | -1.8190e-11 |
| | | Best | 2.7581e-011(0) | 3.3307e-16(0) | 1.5561e-11(0) | 1.5561e-11(0) | 1.5561e-11(0) | | Worst | 1.9163e-001(0) | 4.4409e-16(0) | -3.1844e+00 | 1.5561e-11(0) | 1.5561e-11(0) | | Mean | 1.5312e-002 | 4.2633e-16 | - | 1.5561e-11 | 1.5561e-11 |
| | | Best | 5.4456e-11(0) | 4.6327e-11(0) | 4.6448e-11(0) | 1.1027e-10(0) | 4.6327e-11(0) | | Worst | 3.1141e-09(0) | 4.6526e-11(0) | 1.8287e-04(0) | 5.4446e-10(0) | 4.6327e-11(0) | | Mean | 4.2052e-10 | 4.6348e-11 | 1.7894e-05 | 2.4644e-10 | 4.6327e-11 |
| | | Best | 0.0000e+00(0) | 3.3498e-11(0) | 3.4987e-11(0) | -3.1237e-10(0) | -7.7904e-11(0) | | Worst | 6.0712e-03(0) | 1.3098e+02(0) | 2.3612e+02 | 1.3097e+02(0) | 1.3098e+02(0) | | Mean | 7.6753e-04 | 4.1913e+01 | - | 2.6195e+01 | 1.0478e+01 |
| | | Best | 3.9790e-13(0) | 3.9790e-13(0) | 1.3112e-08(0) | 1.8758e-12(0) | -2.8422e-13(0) | | Worst | 1.3788e-03(0) | 6.2527e-13(0) | 6.4487e+02 | 2.8063e-10(0) | 4.5844e-10(0) | | Mean | 1.2061e-04 | 3.9790e-13 | - | 4.4772E-11 | 4.5668e-11 |
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