TABLE 4. Comparison Between IP Algorithm and Other Meta-Heuristics for 30 Dimensional Problems.
| Fn. | IPA | PSO [11], [50] | DE [7], [50] | RCBBO [9], [50] | CS [12], [50] | FA [13], [50] | GSA [34], [50] | ABC [16], [50] | AMO [50] | |
|---|---|---|---|---|---|---|---|---|---|---|
 |
Mean | 2.0347e−156 | 3.3340e−10 | 5.6016e−14 | 3.7370e−01 | 5.6565e−06 | 1.7000e−03 | 3.3748e−18 | 2.9860e−20 | 8.6464e−40 |
| Std. | 7.7432e−156 | 7.0387e−10 | 4.4053e−14 | 1.1810e−01 | 2.8611e−06 | 4.0608e−04 | 8.0862e−19 | 2.1455e−20 | 1.0435e−39 | |
| Rank | 1 | 6 | 5 | 9 | 7 | 8 | 4 | 3 | 2 | |
 |
Mean | 9.6800e−139 | 6.6598e−11 | 4.7348e−10 | 1.6560e−01 | 2.0000e−03 | 4.5300e−02 | 8.9211e−09 | 1.4213e−15 | 8.2334e−32 |
| Std. | 5.2951e−138 | 9.2553e−11 | 1.7759e−10 | 3.4200e−02 | 8.0959e−04 | 3.3800e−02 | 1.3340e−09 | 5.5340e−16 | 3.4120e−32 | |
| Rank | 1 | 4 | 5 | 9 | 7 | 8 | 6 | 3 | 2 | |
 |
Mean | 4.5184e−275 | 2.9847e+00 | 2.8038e−11 | 1.5972e+03 | 1.4000e−03 | 1.8200e−02 | 1.1260e−01 | 2.4027e+03 | 8.8904e−04 |
| Std. | 0.0000e+00 | 2.2778 e+00 | 3.6788e−11 | 8.3360e+02 | 6.0987e−04 | 6.4000e−03 | 1.2660e−01 | 6.5696e+02 | 8.7256e−04 | |
| Rank | 1 | 7 | 2 | 8 | 4 | 5 | 6 | 9 | 3 | |
 |
Mean | 2.3725e−75 | 7.9997e+00 | 2.2160e−01 | 7.9738e+00 | 3.2388e+00 | 5.5400e−02 | 9.9302e−10 | 1.8522e+01 | 2.8622e−05 |
| Std. | 1.2994e−74 | 2.5351e+00 | 2.4300e−01 | 2.6633e+00 | 6.6440e−01 | 1.0100e−02 | 1.1899e−10 | 4.2477e+00 | 2.3468e−05 | |
| Rank | 1 | 8 | 5 | 7 | 6 | 4 | 2 | 9 | 3 | |
 |
Mean | 2.4992e−02 | 4.69202e+01 | 2.6570e−01 | 6.4690e+01 | 8.0092e+00 | 3.81248e+01 | 2.0081e+01 | 4.4100e−02 | 4.1817e+00 |
| Std. | 5.0594e−02 | 3.80312 e+01 | 1.0293e+00 | 3.6278e+01 | 1.9188e+00 | 3.03962e+01 | 1.7220e−01 | 7.0700e−02 | 2.1618e+00 | |
| Rank | 1 | 5 | 3 | 9 | 6 | 8 | 7 | 2 | 4 | |
 |
Mean | 0.0000e+00 | 3.6925e−10 | 4.5028e−14 | 3.6950e−01 | 5.4332e−06 | 1.7000e−03 | 3.3385e−18 | 3.0884e−20 | 0.0000e+00 |
| Std. | 0.0000e+00 | 6.3668e−10 | 2.3309e−14 | 1.1150e−01 | 2.2446e−06 | 4.1593e−04 | 5.6830e−19 | 4.0131e−20 | 0.0000e+00 | |
| Rank | 1 | 6 | 5 | 9 | 7 | 8 | 4 | 3 | 1 | |
 |
Mean | 7.4919e−05 | 1.3500e−02 | 4.2000e−03 | 3.0000e−03 | 9.6000e−03 | 8.2000e−03 | 3.9000e−03 | 3.2400e−02 | 1.7000e−03 |
| Std. | 9.5360e−05 | 4.1000e−03 | 1.4000e−03 | 1.2000e−03 | 2.8000e−03 | 9.3000e−03 | 1.3000e−03 | 5.9000e−03 | 4.7058e−04 | |
| Rank | 1 | 8 | 5 | 3 | 7 | 6 | 4 | 9 | 2 | |
 |
Mean | -1.2569e+04 | -8.8278e+03 | -1.1276e+04 | -1.2568e+04 | -9.1492e+03 | -6.2238e+03 | -3.0499e+03 | -1.2507e+04 | -1.2569e+04 |
| Std. | 5.5502e−12 | 6.1115e+02 | 1.8135e+03 | 5.7580e−01 | 2.5314e+02 | 7.7230e+02 | 3.3886e+02 | 6.1118e+01 | 1.2384e−07 | |
| Rank | 1 | 7 | 5 | 3 | 6 | 8 | 9 | 4 | 1 | |
 |
Mean | 0.0000e+00 | 1.8267e+01 | 1.3467e+02 | 3.8500e−02 | 5.1220e+01 | 2.35213e+01 | 7.2831e+00 | 0.0000e+00 | 0.0000e+00 |
| Std. | 0.0000e+00 | 4.796e+00 | 2.8859e+01 | 1.5400e−02 | 8.1069e+00 | 8.3683e+00 | 1.8991e+00 | 0.0000e+00 | 0.0000e+00 | |
| Rank | 1 | 6 | 9 | 4 | 8 | 7 | 5 | 1 | 1 | |
 |
Mean | 4.4408e−16 | 3.8719e−06 | 7.4739e−08 | 1.9470e−01 | 2.3750e+00 | 9.4000e−03 | 1.4717e−09 | 1.1946e−09 | 4.4409e−15 |
| Std. | 1.0029e−31 | 2.8604e−06 | 3.1082e−08 | 4.6100e−02 | 1.1238e+00 | 1.4000e−03 | 1.4449e−10 | 5.0065e−10 | 0.0000e+00 | |
| Rank | 1 | 6 | 5 | 8 | 9 | 7 | 4 | 3 | 2 | |
 |
Mean | 0.0000e+00 | 1.6800e−02 | 0.0000e+00 | 2.7650e−01 | 4.4900e−05 | 2.5000e−03 | 1.2650e−02 | 0.0000e+00 | 0.0000e+00 |
| Std. | 0.0000e+00 | 2.0500e−02 | 0.0000e+00 | 7.9600e−02 | 8.9551e−05 | 4.6910e−04 | 2.1600e−02 | 0.0000e+00 | 0.0000e+00 | |
| Rank | 1 | 8 | 1 | 9 | 5 | 6 | 7 | 1 | 1 | |
 |
Mean | 6.8626e−21 | 8.3000e−03 | 4.7114e−15 | 2.0000e−03 | 5.0710e−01 | 8.8694e−06 | 2.0358e−20 | 1.1928e−21 | 1.5705e−32 |
| Std. | 7.0664e−21 | 2.8700e−02 | 3.2597e−15 | 2.3000e−03 | 2.6620e−01 | 2.7999e−06 | 4.5322e−21 | 1.0783e−21 | 2.8080e−48 | |
| Rank | 3 | 8 | 5 | 7 | 9 | 6 | 4 | 2 | 1 | |
 |
Mean | 4.9344e−21 | 4.6694e−07 | 3.1598e−14 | 2.1800e−02 | 4.6965e−04 | 1.2812e−04 | 5.6991e−33 | 2.2990e−20 | 1.3498e−32 |
| Std. | 6.8120e−21 | 1.3713e−06 | 2.2825e−14 | 9.6000e−03 | 2.9932e−04 | 4.1539e−05 | 6.2589e−33 | 2.2886e−20 | 2.8080e−48 | |
| Rank | 3 | 6 | 5 | 9 | 8 | 7 | 1 | 4 | 2 | |
| Average Rank | 1.3077 | 6.5385 | 4.6154 | 7.2308 | 6.8462 | 6.7692 | 4.8462 | 4.0769 | 1.9231 | |
| Overall Rank | 1 | 6 | 4 | 9 | 8 | 7 | 5 | 3 | 2 | |