Table 9: Comparison of the numerical results of the proposed RGA-PSO and AIA-PSO algorithms and those of the published individual AIA and RGA for TPs 5–13.

TP numberGlobal optimumMethodsBestMeanMedianWorstMAPE%

51227.1978AIA-2 [10]1227.31911228.60971227.82161239.5205 1 . 1 5 𝐸 0 1
GA-3 [9]1228.51181279.38251263.25891481.3710 4.266
The proposed RGA-PSO1227.23211228.84711228.39351231.6003 1 . 3 4 𝐸 0 1
The proposed AIA-PSO1227.15981228.18001227.97621229.6590 8 . 0 2 𝐸 0 2
63.9511AIA-2 [10]3.95184.10054.04604.2997 3.781
GA-3 [9]3.96974.14404.13584.3743 4.881
The proposed RGA-PSO3.95213.95773.95663.9722 1 . 6 7 𝐸 0 1
The proposed AIA-PSO3.95163.95813.95693.9735 1 . 7 7 𝐸 0 1
7−5.7398AIA-2 [10]−5.7398−5.7398−5.7398−5.7396 6 . 0 3 𝐸 0 4
GA-3 [9]−5.7398−5.7375−5.7383−5.7316 3 . 9 8 𝐸 0 2
The proposed RGA-PSO−5.7398−5.7398−5.7398−5.7398 2 . 5 4 𝐸 0 4
The proposed AIA-PSO−5.7398−5.7398−5.7398−5.7398 2 . 4 2 𝐸 0 4
8−83.254AIA-2 [10]−83.2504−83.2499−83.2499−83.2496 4 . 9 3 𝐸 0 3
GA-3 [9]−83.2497−83.2490−83.2494−83.2461 6 . 0 6 𝐸 0 3
The proposed RGA-PSO−83.2497−83.2497−83.2497−83.2497 5 . 1 3 𝐸 0 3
The proposed AIA-PSO−83.2497−83.2497−83.2497−83.2497 5 . 1 3 𝐸 0 3
9−6.0482AIA-2 [10]−6.0471−5.9795−6.0138−5.7159 1.136
GA-3 [9]−6.0417−5.8602−5.8772−5.6815 3.108
The proposed RGA-PSO−6.0441−5.9883−5.9968−5.8051 0.991
The proposed AIA-PSO−6.0466−5.9808−5.9969−5.8274 1.082
106300AIA-2 [10]6299.82326299.83886299.84036299.8494 2 . 5 6 𝐸 0 3
GA-3 [9]6299.83996299.85466299.84536299.9407 2 . 3 1 𝐸 0 3
The proposed RGA-PSO6299.83746299.84126299.84196299.8428 2 . 5 2 𝐸 0 3
The proposed AIA-PSO6299.83956299.84206299.84236299.8425 2 . 5 1 𝐸 0 3
1110122.6964AIA-2 [10]10122.434310122.501410122.502310122.6271 1 . 9 3 𝐸 0 3
GA-3 [9]10122.480910125.244110123.979110155.1349 2 . 5 8 𝐸 0 4
The proposed RGA-PSO10122.473210122.492510122.492510122.6444 2 . 0 1 𝐸 0 3
The proposed AIA-PSO10122.485210122.492010122.492710122.4931 2 . 0 2 𝐸 0 3
12AIA-2 [10]0.0126650.0127030.0127190.012725
GA-3 [9]0.0126650.0127390.0127170.013471
The proposed RGA-PSO0.0126920.0127240.0127210.012784
The proposed AIA-PSO0.0126670.0127150.0127190.012778
13AIA-2 [10]5885.53125900.48605894.79296014.2198
GA-3 [9]5885.30765943.47145897.29046289.7314
The proposed RGA-PSO5885.30185895.03815885.33266005.4351
The proposed AIA-PSO5885.33105886.54265885.33235906.7404

(The “—” denotes unavailable information.)