Table 3: The best solutions obtained using the RGA-PSO algorithm from TPs 1–13.

TP number 𝑓 ( x βˆ— R G A - P S O ) x βˆ— R G A - P S O

1 24.323 𝐱 βˆ— R G A - P S O = ( 2 . 1 6 7 2 7 7 6 0 , 2.37789634, 8.78162804, 5.12372885, 0.97991270, 1.39940993, 1.31127142, 9.81945011, 8.30004549, 8.45891329)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( βˆ’ 0 . 0 0 0 1 7 1 ≀ 0 , βˆ’ 0 . 0 0 3 1 0 9 ≀ 0 , βˆ’ 0 . 0 0 0 0 2 7 ≀ 0 , βˆ’ 0 . 0 0 0 1 2 3 ≀ 0 , βˆ’ 0 . 0 0 1 3 7 1 ≀ 0 , βˆ’ 0 . 0 0 2 1 0 1 ≀ 0 , βˆ’ 6 . 2 4 5 9 5 7 ≀ 0 , βˆ’ 4 7 . 8 4 6 3 0 2 ≀ 0 )

2 −30665.539 𝐱 βˆ— R G A - P S O = (78, 33, 29.99525450, 45, 36.77581373)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( βˆ’ 9 2 . 0 0 0 0 0 0 ≀ 0 , 2 . 2 4 𝐸 βˆ’ 0 7 ≀ 0 , βˆ’ 8 . 8 4 0 5 0 0 ≀ 0 , βˆ’ 1 1 . 1 5 9 5 0 0 ≀ 0 , 4 . 2 8 𝐸 βˆ’ 0 7 ≀ 0 , βˆ’ 5 . 0 0 0 0 0 0 ≀ 0 )

3 680.632 𝐱 βˆ— R G A - P S O = ( 2.33860239, 1.95126191, −0.45483579, 4.36300325, −0.62317747, 1.02938443, 1.59588410)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( βˆ’ 7 . 7 6 𝐸 βˆ’ 0 7 ≀ 0 , βˆ’ 2 5 2 . 7 2 1 1 ≀ 0 , βˆ’ 1 4 4 . 8 1 4 0 ≀ 0 , βˆ’ 6 . 1 5 𝐸 βˆ’ 0 5 ≀ 0 )

4 −15 𝐱 βˆ— R G A - P S O = ( 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 0 ≀ 0 , 0 ≀ 0 , 0 ≀ 0 , βˆ’ 5 ≀ 0 , βˆ’ 5 ≀ 0 , βˆ’ 5 ≀ 0 , 0 ≀ 0 , 0 ≀ 0 , 0 ≀ 0 )

5 1227.1139 𝐱 βˆ— R G A - P S O = ( 1697.13793410, 54.17332240, 3030.44600072, 90.18199040, 94.99999913, 10.42097385, 153.53771370)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 0 . 9 9 9 9 7 8 ≀ 1 , 0 . 9 8 0 1 1 4 ≀ 1 , 1 . 0 0 0 0 0 5 ≀ 1 , 0 . 9 8 0 0 9 7 ≀ 1 , 0 . 9 9 0 5 6 5 ≀ 1 , 1 . 0 0 0 0 0 5 ≀ 1 , 1 . 0 0 0 0 0 ≀ 1 , 0 . 9 7 6 7 0 1 ≀ 1 , 1 . 0 0 0 0 0 3 ≀ 1 , 0 . 4 5 9 3 1 1 ≀ 1 , 0 . 3 8 7 4 3 2 ≀ 1 , 0 . 9 8 1 9 9 7 ≀ 1 , 0 . 9 8 0 3 6 4 ≀ 1 , βˆ’ 8 . 2 4 1 9 2 6 ≀ 1 )

6 3.9521 𝐱 βˆ— R G A - P S O = ( 6.444100620, 2.243029250, 0.642672939, 0.582321363, 5.940008650, 5.531235784, 1.018087316, 0.403665649)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 1 . 0 0 0 0 0 0 ≀ 1 , 1 . 0 0 0 0 0 0 ≀ 1 , 0 . 9 9 9 9 9 6 ≀ 1 , 0 . 9 9 9 8 6 ≀ 1 )

7 −5.7398 𝐱 βˆ— R G A - P S O = ( 8.12997229, 0.61463971, 0.56407162, 5.63623069)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 1 . 0 0 0 0 0 0 ≀ 1 , 1 . 0 0 0 0 0 0 ≀ 1 )

8 −83.2497 𝐱 βˆ— R G A - P S O = ( 88.35595404, 7.67259607, 1.31787691)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 1 . 0 0 0 0 0 0 ≀ 1 )

9 −6.0441 𝐱 βˆ— R G A - P S O = ( 6.40497368, 0.64284563, 1.02766984, 5.94729224, 2.21044814, 0.59816471, 0.42450835, 5.54339987)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 0 . 9 9 9 9 9 7 ≀ 1 , 0 . 9 9 9 9 5 9 ≀ 1 , 0 . 9 9 9 9 3 0 ≀ 1 , 0 . 9 9 9 9 7 5 ≀ 1 )

10 6299.8374 𝐱 βˆ— R G A - P S O = ( 108.66882633, 85.10837983, 204.35894362)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 1 . 0 0 0 0 0 2 ≀ 1 )

11 10122.4732 𝐱 βˆ— R G A - P S O = ( 78, 33, 29.99564864, 45, 36.77547104)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( βˆ’ 0 . 3 0 9 9 9 1 ≀ 1 , 1 . 0 0 0 0 0 4 ≀ 1 , βˆ’ 0 . 0 2 1 3 7 9 ≀ 1 , 0 . 6 2 1 4 0 3 ≀ 1 , 1 . 0 0 0 0 0 2 ≀ 1 , 0 . 6 8 1 5 1 6 ≀ 1 )

12 0.012692 𝐱 βˆ— R G A - P S O = ( 0.050849843, 0.336663305, 12.579603478)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( βˆ’ 0 . 0 0 0 1 4 3 ≀ 0 , βˆ’ 0 . 0 0 0 4 6 9 ≀ 0 , βˆ’ 4 . 0 0 9 0 2 1 ≀ 0 , βˆ’ 0 . 7 4 1 6 5 8 ≀ 0 )

13 5885.3018 𝐱 βˆ— R G A - P S O = ( 0.77816852, 0.38464913, 40.31961883, 199.99999988)
𝑔 π‘š ( 𝐱 βˆ— R G A - P S O ) = ( 1 . 2 3 𝐸 βˆ’ 0 7 ≀ 0 , 3 . 3 6 𝐸 βˆ’ 0 8 ≀ 0 , βˆ’ 0 . 0 0 6 9 1 6 ≀ 0 , βˆ’ 4 0 . 0 0 0 0 0 0 1 2 ≀ 0 )