Table 1: The parameter settings for the RGA-PSO and AIA-PSO algorithms.

MethodsParameter settingsSearch space

The external RGA 𝑝 𝑐 = 1
𝑝 𝑚 , R G A = 0 . 1 5 [ 𝜒 𝑙 , 𝜒 𝑢 ] = [ 0 . 1 , 1 ]
p s R G A = 1 0 [ 𝑐 𝑙 1 , 𝑐 𝑢 1 ] = [ 0 . 1 , 2 ]
𝑔 m a x , R G A = 3 [ 𝑐 𝑙 2 , 𝑐 𝑢 2 ] = [ 0 . 1 , 2 ]
The external AIA 𝑝 𝑟 𝑡 = 0 . 9 [ 𝜌 𝑙 , 𝜌 𝑢 ] = [ 1 × 109 , 1 × 1 0 1 1 ]
r s = 1 0 [ 𝑝 𝑙 𝑚 , P S O , 𝑝 𝑢 𝑚 , P S O ] = [ 0 . 1 , 0 . 5 ]
𝑔 m a x , A I A = 3
The internal PSO algorithm p s P S O = 1 0 0 [ 𝑥 𝑙 𝑛 , 𝑥 𝑢 𝑛 ] for a CGO problem
𝑔 m a x , P S O = 3 5 0 0 for TPs 1–4
𝑔 m a x , P S O = 3 0 0 0 for TPs 5–13

[ 𝜒 𝑙 , 𝜒 𝑢 ]: the lower and upper boundaries of parameter 𝜒 .
[ 𝑐 𝑙 1 , 𝑐 𝑢 1 ]: the lower and upper boundaries of parameter 𝑐 1 .
[ 𝑐 𝑙 2 , 𝑐 𝑢 2 ]: the lower and upper boundaries of parameter 𝑐 2 .
[ 𝜌 𝑙 , 𝜌 𝑢 ]: the lower and upper boundaries of parameter 𝜌 .
[ 𝑝 𝑙 𝑚 , P S O , 𝑝 𝑢 𝑚 , P S O ]: the lower and upper boundaries of 𝑝 𝑚 , P S O for the internal PSO algorithm 𝑝 𝑚 , P S O .