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 number Global optimum Methods Best Mean Median Worst MAPE% 5 1227.1978 AIA-2 [10 ] 1227.3191 1228.6097 1227.8216 1239.5205
1
.
1
5
𝐸
−
0
1
GA-3 [9 ] 1228.5118 1279.3825 1263.2589 1481.3710
4.266
The proposed RGA-PSO 1227.2321 1228.8471 1228.3935 1231.6003
1
.
3
4
𝐸
−
0
1
The proposed AIA-PSO 1227.1598 1228.1800 1227.9762 1229.6590
8
.
0
2
𝐸
−
0
2
6 3.9511 AIA-2 [10 ] 3.9518 4.1005 4.0460 4.2997
3.781
GA-3 [9 ] 3.9697 4.1440 4.1358 4.3743
4.881
The proposed RGA-PSO 3.9521 3.9577 3.9566 3.9722
1
.
6
7
𝐸
−
0
1
The proposed AIA-PSO 3.9516 3.9581 3.9569 3.9735
1
.
7
7
𝐸
−
0
1
7 −5.7398 AIA-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 −83.254 AIA-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 −6.0482 AIA-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
10 6300 AIA-2 [10 ] 6299.8232 6299.8388 6299.8403 6299.8494
2
.
5
6
𝐸
−
0
3
GA-3 [9 ] 6299.8399 6299.8546 6299.8453 6299.9407
2
.
3
1
𝐸
−
0
3
The proposed RGA-PSO 6299.8374 6299.8412 6299.8419 6299.8428
2
.
5
2
𝐸
−
0
3
The proposed AIA-PSO 6299.8395 6299.8420 6299.8423 6299.8425
2
.
5
1
𝐸
−
0
3
11 10122.6964 AIA-2 [10 ] 10122.4343 10122.5014 10122.5023 10122.6271
1
.
9
3
𝐸
−
0
3
GA-3 [9 ] 10122.4809 10125.2441 10123.9791 10155.1349
2
.
5
8
𝐸
−
0
4
The proposed RGA-PSO 10122.4732 10122.4925 10122.4925 10122.6444
2
.
0
1
𝐸
−
0
3
The proposed AIA-PSO 10122.4852 10122.4920 10122.4927 10122.4931
2
.
0
2
𝐸
−
0
3
12 — AIA-2 [10 ] 0.012665 0.012703 0.012719 0.012725 — GA-3 [9 ] 0.012665 0.012739 0.012717 0.013471 — The proposed RGA-PSO 0.012692 0.012724 0.012721 0.012784 — The proposed AIA-PSO 0.012667 0.012715 0.012719 0.012778 — 13 — AIA-2 [10 ] 5885.5312 5900.4860 5894.7929 6014.2198 — GA-3 [9 ] 5885.3076 5943.4714 5897.2904 6289.7314 — The proposed RGA-PSO 5885.3018 5895.0381 5885.3326 6005.4351 — The proposed AIA-PSO 5885.3310 5886.5426 5885.3323 5906.7404 —
(The “—” denotes unavailable information.)