Table 2: Numerical results of the proposed RGA-PSO and AIA-PSO algorithms for TPs 1–13.

TP numberGlobal optimumMethodsBestMeanMedianWorstMAPE %S.D.MCCT (sec)P value

124.306The proposed
RGA-PSO
24.32324.56824.52124.8311.0780.13432.390.643
The proposed
AIA-PSO
24.35824.57924.56424.8091.1250.11417.63
2−30665.539The proposed
RGA-PSO
−30665.539−30665.539−30665.539−30665.534 1 . 3 4 𝐸 0 6 7 . 3 6 𝐸 0 4 349.550.478
The proposed
AIA-PSO
−30665.539−30665.539−30665.539−30665.539 9 . 9 5 𝐸 0 7 3 . 8 1 𝐸 0 5 349.76
3680.630The proposed
RGA-PSO
680.632680.640680.639680.658 1 . 4 6 𝐸 0 3 5 . 5 5 𝐸 0 3 398.720.839
The proposed
AIA-PSO
680.633680.640680.640680.657 1 . 5 0 𝐸 0 3 0.01398.84
4−15The proposed
RGA-PSO
−15−15−15−15 1 . 2 7 𝐸 0 6 1 . 2 7 𝐸 0 6 466.000.294
The proposed
AIA-PSO
−15−15−15−15 1 . 2 0 𝐸 1 0 2 . 6 4 𝐸 1 1 450.28
51227.1978The proposed
RGA-PSO
1227.23211228.84711228.39351231.6003 1 . 3 4 𝐸 0 1 1.27481.860.002*
The proposed
AIA-PSO
1227.15981228.18001227.97621229.6590 8 . 0 2 𝐸 0 2 0.71461.30
63.9511The proposed
RGA-PSO
3.95213.95773.95663.9722 1 . 6 7 𝐸 0 1 5 𝐸 0 3 439.160.682
The proposed
AIA-PSO
3.95163.95813.95693.9735 1 . 7 7 𝐸 0 1 4 . 7 9 𝐸 0 3 438.55
7−5.7398The proposed
RGA-PSO
−5.7398−5.7398−5.7398−5.7398 2 . 5 4 𝐸 0 4 1 . 1 3 𝐸 0 5 325.730.358
The proposed
AIA-PSO
−5.7398−5.7398−5.7398−5.7398 2 . 4 2 𝐸 0 4 7 . 7 4 𝐸 0 6 329.12
8−83.254The proposed
RGA-PSO
−83.2497−83.2497−83.2497−83.2497 5 . 1 3 𝐸 0 3 1 . 2 6 𝐸 0 6 211.910.291
The proposed
AIA-PSO
−83.2497−83.2497−83.2497−83.2497 5 . 1 3 𝐸 0 3 6 . 8 5 𝐸 0 7 213.01
9−6.0482The proposed
RGA-PSO
−6.0441−5.9883−5.9968−5.80510.9910.05440.720.577
The proposed
AIA-PSO
−6.0467−5.9828−5.9979−5.82741.0820.05441.42
106300The proposed
RGA-PSO
6299.83746299.84126299.84196299.8428 2 . 5 2 𝐸 0 3 1 . 4 2 𝐸 0 3 224.130.001*
The proposed
AIA-PSO
6299.83956299.84206299.84236299.8425 2 . 5 1 𝐸 0 3 6 . 8 3 𝐸 0 4 223.91
1110122.6964The proposed
RGA-PSO
10122.473210122.492510122.492510122.6444 2 . 0 1 𝐸 0 3 2 . 2 6 𝐸 0 2 340.890.884
The proposed
AIA-PSO
10122.485210122.492010122.492710122.4931 2 . 0 2 𝐸 0 3 1 . 8 5 𝐸 0 3 338.37
12The proposed
RGA-PSO
0.0126920.0127240.0127210.012784 1 . 4 6 𝐸 0 5 293.670.014*
The proposed
AIA-PSO
0.0126670.0127150.0127190.012778 2 . 0 0 𝐸 0 5 296.15
13The proposed
RGA-PSO
5885.30185895.03815885.33266005.435124.33291.170.019*
The proposed
AIA-PSO
5885.32495886.54265885.33235906.74044.54292.16

(The “—” denotes unavailable information, and *represents that the mean values obtained using the RGA-PSO and AIA-PSO algorithms are statistically different.)