Table 2 Results of the MWSO and comparison against other competitors on the CEC2017 benchmark.
F(x) | Index | MWSO | WSO | SSA | NOA | KOA | PSO | WOA |
|---|---|---|---|---|---|---|---|---|
F1 | Min | 1.9932e−194 | 3.6522e+00 | 7.6851e−09 | 3.9820e+04 | 3.5508e+04 | 2.6735e−06 | 2.4631e−169 |
Avg | 7.4390e−186 | 1.6060e+01 | 1.2920e−08 | 5.4068e+04 | 4.2092e+04 | 3.9912e−05 | 2.0743e−148 | |
Std | 0.0000e+00 | 1.0322e+01 | 3.3486e−09 | 4.4121e+03 | 3.1944e+03 | 6.8864e−05 | 1.1316e−147 | |
Mean rank | 1.0000e+00 | 5.0000e+00 | 3.0000e+00 | 7.0000e+00 | 6.0000e+00 | 4.0000e+00 | 2.0000e+00 | |
F2 | Min | 9.4274e−98 | 2.9819e−01 | 5.1425e−03 | 2.1049e+05 | 7.8389e+01 | 1.3092e−03 | 1.1534e−116 |
Avg | 4.8694e−94 | 6.2085e−01 | 1.0820e+00 | 1.0628e+09 | 1.2886e+06 | 6.7182e−03 | 1.4894e−104 | |
Std | 1.1095e−93 | 2.2835e−01 | 1.1441e+00 | 3.0026e+09 | 2.0077e+06 | 5.9536e−03 | 5.0498e−104 | |
Mean rank | 2.0000e+00 | 4.5333e+00 | 4.4000e+00 | 6.9333e+00 | 6.0667e+00 | 3.0667e+00 | 1.0000e+00 | |
F3 | Min | 6.5221e−145 | 1.8779e+02 | 5.5282e+01 | 4.1463e+04 | 4.0477e+04 | 5.8665e+00 | 2.4173e+03 |
Avg | 2.8306e−130 | 6.9505e+02 | 2.6853e+02 | 7.4458e+04 | 5.0203e+04 | 2.1389e+01 | 2.1307e+04 | |
Std | 1.3850e−129 | 3.3974e+02 | 1.9808e+02 | 1.1229e+04 | 5.2022e+03 | 9.0540e+00 | 9.3229e+03 | |
Mean rank | 1.0000e+00 | 3.9000e+00 | 3.1000e+00 | 6.9333e+00 | 6.0667e+00 | 2.0000e+00 | 5.0000e+00 | |
F4 | Min | 1.9845e−92 | 7.3432e+00 | 2.8883e+00 | 7.1797e+01 | 6.4039e+01 | 4.1628e−01 | 4.4710e−02 |
Avg | 1.9938e−88 | 1.2150e+01 | 8.3506e+00 | 8.0033e+01 | 7.1198e+01 | 6.8292e−01 | 3.8983e+01 | |
Std | 5.2424e−88 | 2.6366e+00 | 3.5469e+00 | 2.3644e+00 | 2.7995e+00 | 1.7217e−01 | 2.7709e+01 | |
Mean rank | 1.0000e+00 | 4.0333e+00 | 3.4000e+00 | 6.9333e+00 | 5.8333e+00 | 2.1000e+00 | 4.7000e+00 | |
F5 | Min | 2.7223e+01 | 1.6931e+02 | 2.4671e+01 | 7.5841e+07 | 6.7063e+07 | 1.8634e+01 | 2.6279e+01 |
Avg | 2.8228e+01 | 1.2400e+03 | 1.0650e+02 | 1.5660e+08 | 1.0843e+08 | 9.4003e+01 | 2.7082e+01 | |
Std | 2.8797e−01 | 1.6683e+03 | 1.3804e+02 | 2.3965e+07 | 1.6971e+07 | 1.0055e+02 | 4.0881e−01 | |
Mean rank | 2.5667e+00 | 4.9000e+00 | 3.0000e+00 | 6.9667e+00 | 6.0333e+00 | 3.1000e+00 | 1.4333e+00 | |
F6 | Min | 4.2641e−03 | 4.2166e+00 | 6.9384e−09 | 4.1142e+04 | 3.4416e+04 | 2.2344e−06 | 7.6167e−03 |
Avg | 3.1379e−02 | 1.7249e+01 | 1.2490e−08 | 5.1496e+04 | 4.2640e+04 | 1.9953e−05 | 9.5573e−02 | |
Std | 2.7474e−02 | 1.1310e+01 | 2.6446e−09 | 4.2733e+03 | 3.2831e+03 | 2.2893e−05 | 1.1334e−01 | |
Mean rank | 3.2333e+00 | 5.0000e+00 | 1.0000e+00 | 6.9333e+00 | 6.0667e+00 | 2.0000e+00 | 3.7667e+00 | |
F7 | Min | 3.3636e−05 | 2.6410e−02 | 4.2938e−02 | 3.8762e+01 | 2.7258e+01 | 2.6260e−02 | 7.0396e−05 |
Avg | 3.8968e−04 | 1.2871e−01 | 9.0210e−02 | 7.1476e+01 | 4.9218e+01 | 7.8548e−02 | 1.9816e−03 | |
Std | 2.8817e−04 | 6.1893e−02 | 3.3215e−02 | 1.2870e+01 | 6.9079e+00 | 2.9457e−02 | 2.4388e−03 | |
Mean rank | 1.2000e+00 | 4.5333e+00 | 3.8667e+00 | 6.9000e+00 | 6.1000e+00 | 3.6000e+00 | 1.8000e+00 | |
F8 | Min | − 1.1856e+04 | − 8.6242e+03 | − 8.7363e+03 | − 5.4177e+03 | − 5.4177e+03 | − 7.8120e+03 | − 1.2569e+04 |
Avg | − 1.0282e+04 | − 6.6137e+03 | − 7.4827e+03 | − 5.4177e+03 | − 5.4177e+03 | − 6.3816e+03 | − 1.1183e+04 | |
Std | 8.9674e+02 | 1.2738e+03 | 5.8567e+02 | 1.8501e−12 | 1.8501e−12 | 7.8520e+02 | 1.6926e+03 | |
Mean rank | 1.7667e+00 | 4.4333e+00 | 3.3000e+00 | 6.2333e+00 | 6.2333e+00 | 4.7333e+00 | 1.3000e+00 | |
F9 | Min | 0.0000e+00 | 1.1067e+01 | 2.0894e+01 | 3.5064e+02 | 3.0942e+02 | 3.1958e+01 | 0.0000e+00 |
Avg | 0.0000e+00 | 1.9154e+01 | 5.6845e+01 | 3.8445e+02 | 3.4114e+02 | 5.4736e+01 | 1.8948e−15 | |
Std | 0.0000e+00 | 5.5047e+00 | 1.8204e+01 | 1.3984e+01 | 1.4048e+01 | 1.7115e+01 | 1.0378e−14 | |
Mean rank | 1.4833e+00 | 3.0333e+00 | 4.5333e+00 | 7.0000e+00 | 6.0000e+00 | 4.4333e+00 | 1.5167e+00 | |
F10 | Min | 8.8818e−16 | 1.6786e+00 | 3.3794e−05 | 1.9546e+01 | 1.9669e+01 | 1.2149e−03 | 8.8818e−16 |
Avg | 8.8818e−16 | 3.4203e+00 | 2.2748e+00 | 1.9953e+01 | 1.9910e+01 | 2.6531e−02 | 4.2040e−15 | |
Std | 0.0000e+00 | 7.4273e−01 | 7.0387e−01 | 7.6784e−02 | 8.4780e−02 | 1.1697e−01 | 2.2726e−15 | |
Mean rank | 1.1167e+00 | 4.9333e+00 | 4.0333e+00 | 6.7333e+00 | 6.2667e+00 | 3.0333e+00 | 1.8833e+00 | |
F11 | Min | 0.0000e+00 | 1.0385e+00 | 4.6605e−08 | 3.9589e+02 | 3.3058e+02 | 2.3021e−07 | 0.0000e+00 |
Avg | 0.0000e+00 | 1.1709e+00 | 7.6302e−03 | 4.6440e+02 | 3.8146e+02 | 1.2392e−02 | 1.0628e−02 | |
Std | 0.0000e+00 | 9.8272e−02 | 9.2033e−03 | 3.9991e+01 | 3.0929e+01 | 1.2621e−02 | 2.9724e−02 | |
Mean rank | 1.4333e+00 | 5.0000e+00 | 3.0667e+00 | 6.9333e+00 | 6.0667e+00 | 3.6667e+00 | 1.8333e+00 | |
F12 | Min | 7.6123e−04 | 4.1084e−01 | 1.5302e+00 | 2.2733e+08 | 7.3617e+07 | 1.5069e−08 | 4.6340e−04 |
Avg | 4.6373e−03 | 1.5823e+00 | 5.5578e+00 | 3.3847e+08 | 1.8705e+08 | 3.4563e−03 | 5.0799e−03 | |
Std | 2.9583e−03 | 9.5940e−01 | 2.6552e+00 | 6.2117e+07 | 3.9501e+07 | 1.8927e−02 | 5.8770e−03 | |
Mean rank | 2.5333e+00 | 4.0000e+00 | 5.0000e+00 | 7.0000e+00 | 6.0000e+00 | 1.0667e+00 | 2.4000e+00 | |
F13 | Min | 3.7409e−03 | 3.2200e+00 | 1.1488e−09 | 2.4495e+08 | 2.6676e+08 | 4.6491e−07 | 2.4791e−02 |
Avg | 9.3988e−02 | 1.7006e+01 | 8.3911e−01 | 6.6291e+08 | 4.2446e+08 | 2.2059e−03 | 2.5688e−01 | |
Std | 8.7197e−02 | 8.7602e+00 | 3.1879e+00 | 1.4737e+08 | 7.1767e+07 | 4.4681e−03 | 1.6126e−01 | |
Mean rank | 3.0667e+00 | 4.9667e+00 | 1.6667e+00 | 6.9000e+00 | 6.1000e+00 | 1.5333e+00 | 3.7667e+00 | |
F14 | Min | 9.9800e−01 | 9.9800e−01 | 9.9800e−01 | 9.9869e−01 | 9.9803e−01 | 9.9800e−01 | 9.9800e−01 |
Avg | 9.9800e−01 | 9.9800e−01 | 9.9800e−01 | 4.0327e+00 | 1.2030e+00 | 4.5458e+00 | 1.8527e+00 | |
Std | 6.4730e−07 | 0.0000e+00 | 2.3142e−16 | 2.0552e+00 | 4.4364e−01 | 2.5079e+00 | 1.8844e+00 | |
Mean rank | 2.2667e+00 | 1.3000e+00 | 2.6500e+00 | 6.2667e+00 | 4.8333e+00 | 6.1500e+00 | 4.5333e+00 | |
F15 | Min | 3.0749e−04 | 3.0749e−04 | 3.8664e−04 | 3.5648e−03 | 7.9158e−04 | 3.2718e−04 | 3.0760e−04 |
Avg | 1.1765e−03 | 3.5037e−04 | 1.4680e−03 | 1.9990e−02 | 3.0550e−03 | 8.1635e−04 | 7.3231e−04 | |
Std | 3.6341e−03 | 2.3489e−04 | 3.5778e−03 | 1.0115e−02 | 1.6101e−03 | 2.6038e−04 | 4.5385e−04 | |
Mean rank | 2.6333e+00 | 1.3000e+00 | 3.9667e+00 | 6.9333e+00 | 5.8667e+00 | 3.9667e+00 | 3.3333e+00 | |
F16 | Min | − 1.0316e+00 | − 1.0316e+00 | − 1.0316e+00 | − 1.0289e+00 | − 1.0316e+00 | − 1.0316e+00 | − 1.0316e+00 |
Avg | − 1.0316e+00 | − 1.0316e+00 | − 1.0316e+00 | − 9.3965e−01 | − 1.0254e+00 | − 1.0316e+00 | − 1.0316e+00 | |
Std | 6.7752e−16 | 5.5296e−08 | 8.2402e−15 | 7.9640e−02 | 5.1597e−03 | 6.6486e−16 | 1.2296e−10 | |
Mean rank | 1.8833e+00 | 2.3000e+00 | 3.9333e+00 | 6.9667e+00 | 6.0333e+00 | 1.9833e+00 | 4.9000e+00 | |
F17 | Min | 3.9789e−01 | 3.9789e−01 | 3.9789e−01 | 4.0288e−01 | 3.9801e−01 | 3.9789e−01 | 3.9789e−01 |
Avg | 3.9789e−01 | 3.9789e−01 | 3.9789e−01 | 4.7261e−01 | 4.0088e−01 | 3.9789e−01 | 3.9789e−01 | |
Std | 0.0000e+00 | 1.5223e−05 | 1.4947e−14 | 8.0451e−02 | 2.2983e−03 | 0.0000e+00 | 2.2220e−06 | |
Mean rank | 1.9500e+00 | 2.5000e+00 | 3.7333e+00 | 7.0000e+00 | 6.0000e+00 | 1.9500e+00 | 4.8667e+00 | |
F18 | Min | 3.0000e+00 | 3.0000e+00 | 3.0000e+00 | 3.0175e+00 | 3.0025e+00 | 3.0000e+00 | 3.0000e+00 |
Avg | 3.0000e+00 | 3.0000e+00 | 3.0000e+00 | 6.2793e+00 | 3.1109e+00 | 3.0000e+00 | 3.0000e+00 | |
Std | 1.2148e−15 | 1.3065e−15 | 8.4529e−14 | 3.7125e+00 | 1.2168e−01 | 1.7494e−15 | 6.5496e−06 | |
Mean rank | 1.7500e+00 | 1.9833e+00 | 4.0000e+00 | 6.8667e+00 | 6.1333e+00 | 2.2667e+00 | 5.0000e+00 | |
F19 | Min | − 3.8628e+00 | − 3.8628e+00 | − 3.8628e+00 | − 3.8578e+00 | − 3.8610e+00 | − 3.8628e+00 | − 3.8628e+00 |
Avg | − 3.8628e+00 | − 3.8628e+00 | − 3.8628e+00 | − 3.7959e+00 | − 3.8552e+00 | − 3.8628e+00 | − 3.8615e+00 | |
Std | 2.7101e−15 | 2.7101e−15 | 3.6715e−14 | 5.9794e−02 | 6.2723e−03 | 2.7101e−15 | 1.5224e−03 | |
Mean rank | 2.0000e+00 | 2.0000e+00 | 4.0000e+00 | 6.9333e+00 | 5.9333e+00 | 2.0000e+00 | 5.1333e+00 | |
F20 | Min | − 3.3220e+00 | − 3.3220e+00 | − 3.3220e+00 | − 3.1574e+00 | − 3.1910e+00 | − 3.3220e+00 | − 3.3220e+00 |
Avg | − 3.2824e+00 | − 3.3141e+00 | − 3.2115e+00 | − 2.6353e+00 | − 3.0313e+00 | − 3.2744e+00 | − 3.2668e+00 | |
Std | 5.7005e−02 | 3.0164e−02 | 3.7688e−02 | 2.4846e−01 | 7.1081e−02 | 5.9241e−02 | 8.1351e−02 | |
Mean rank | 2.4667e+00 | 1.6833e+00 | 4.5000e+00 | 6.9000e+00 | 6.0667e+00 | 2.5500e+00 | 3.8333e+00 | |
F21 | Min | − 1.0153e+01 | − 1.0153e+01 | − 1.0153e+01 | − 6.6251e+00 | − 7.0479e+00 | − 1.0153e+01 | − 1.0153e+01 |
Avg | − 1.0153e+01 | − 9.6552e+00 | − 8.0541e+00 | − 1.6617e+00 | − 3.7081e+00 | − 7.3121e+00 | − 8.6261e+00 | |
Std | 7.2269e−15 | 1.8953e+00 | 2.8837e+00 | 1.2534e+00 | 1.5068e+00 | 3.3991e+00 | 2.6208e+00 | |
Mean rank | 1.5167e+00 | 1.8667e+00 | 3.9667e+00 | 6.7333e+00 | 5.8000e+00 | 3.7167e+00 | 4.4000e+00 | |
F22 | Min | − 1.0403e+01 | − 1.0403e+01 | − 1.0403e+01 | − 5.6447e+00 | − 7.1042e+00 | − 1.0403e+01 | − 1.0403e+01 |
Avg | − 1.0403e+01 | − 9.8287e+00 | − 8.6141e+00 | − 1.7158e+00 | − 3.8817e+00 | − 9.1114e+00 | − 8.5318e+00 | |
Std | 1.5472e−15 | 1.7650e+00 | 2.8346e+00 | 8.6329e−01 | 1.2337e+00 | 2.6819e+00 | 3.2241e+00 | |
Mean rank | 1.4333e+00 | 2.1500e+00 | 4.1000e+00 | 6.8667e+00 | 5.7667e+00 | 3.0500e+00 | 4.6333e+00 | |
F23 | Min | − 1.0536e+01 | − 1.0536e+01 | − 1.0536e+01 | − 3.3045e+00 | − 5.2821e+00 | − 1.0536e+01 | − 1.0536e+01 |
Avg | − 1.0536e+01 | − 1.0536e+01 | − 9.0693e+00 | − 1.8972e+00 | − 3.3515e+00 | − 9.7433e+00 | − 8.3397e+00 | |
Std | 1.8067e−15 | 1.8949e−15 | 2.7594e+00 | 6.0525e−01 | 7.7805e−01 | 2.0894e+00 | 2.9624e+00 | |
Mean rank | 1.8167e+00 | 1.8667e+00 | 4.2000e+00 | 6.9000e+00 | 5.9000e+00 | 2.5500e+00 | 4.7667e+00 | |
Overall mean rank | 1.8746e+00 | 3.3572e+00 | 3.5833e+00 | 6.8594e+00 | 5.9638e+00 | 2.9790e+00 | 3.3826e+00 | |
Overall rank | 1 | 3 | 5 | 7 | 6 | 2 | 4 | |
