Table 5: Performance comparison between PSOSA, Sid.GA, Hybrid and HPSO-SA for benchmark functions [9].

𝐹 𝑢 𝑛 𝑐 𝑡 𝑖 𝑜 𝑛 𝐷 𝑖 𝑚 𝑒 𝑛 𝑠 𝑖 𝑜 𝑛 𝑃 𝑆 𝑂 𝑆 𝐴 𝑆 𝑡 𝑑 . 𝐺 𝐴 𝐻 𝑦 𝑏 𝑟 𝑖 𝑑 HPSO-SA

Sphere 1 0 0 ± 0 2 . 4 3 𝑒 0 4 ± 1 . 1 4 𝑒 0 5 2 . 4 2 𝑒 0 4 ± 2 . 1 7 𝑒 0 5 0 ± 0
2 0 0 ± 0 0 . 0 0 1 4 5 ± 6 . 2 2 𝑒 0 5 0 . 0 0 2 1 2 ± 2 . 7 5 𝑒 0 4 0 ± 0
3 0 0 ± 0 0 . 0 0 4 4 2 ± 1 . 7 8 𝑒 0 4 0 . 0 1 2 0 3 ± 6 . 3 3 𝑒 0 4 0 ± 0

Rastrigin 1 0 0 ± 0 3 . 1 6 6 7 ± 0 . 2 2 3 7 3 . 0 5 9 9 ± 0 . 1 5 3 5 0 ± 0
2 0 0 ± 0 1 6 . 8 7 3 2 ± 0 . 6 0 0 7 1 1 . 6 5 9 0 ± 0 . 3 6 0 2 0 ± 0
2 0 0 ± 0 4 9 . 3 2 1 2 ± 1 . 1 2 0 4 2 7 . 8 1 1 9 ± 0 . 8 0 5 9 0 ± 0

Griewank 1 0 0 ± 0 2 8 3 . 2 5 1 ± 1 . 8 1 2 0 . 0 9 0 7 8 ± 0 . 0 3 3 0 6 0 ± 0
2 0 0 ± 0 6 1 1 . 2 6 6 ± 3 . 5 7 2 0 . 0 0 4 5 9 ± 0 . 0 1 2 0 9 0 ± 0
3 0 0 ± 0 8 8 9 . 5 3 7 ± 3 . 9 3 9 0 . 0 9 9 1 1 ± 0 . 0 0 1 0 6 0 ± 0

Rosenbrock 1 0 0 . 1 7 8 5 6 ± 1 . 2 5 9 8 8 1 0 9 . 8 1 0 ± 6 . 2 1 2 4 3 . 5 2 1 ± 1 6 . 0 4 7 0 . 1 4 6 ± 0 . 2 2 4 1 9 3
2 0 0 . 0 0 0 4 3 ± 0 . 0 0 1 1 1 1 4 6 . 9 1 2 ± 1 0 . 9 5 1 1 6 9 . 1 1 2 ± 2 1 . 5 3 5 0 . 2 4 6 8 9 7 ± 0 . 2 3 1 9 8 2
3 0 0 . 5 7 4 3 1 ± 4 . 0 5 9 7 6 1 9 9 . 7 3 0 ± 1 6 . 2 8 5 1 8 7 . 0 3 3 ± 2 2 . 9 6 0 0 . 4 3 9 1 4 9 ± 0 . 3 0 4 3 4 7