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Table 1.

The main steps of QPSO.

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Table 1 Expand

Table 2.

The main steps of FQPSO.

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Table 2 Expand

Table 3.

Benchmark test functions.

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Table 3 Expand

Fig 1.

Comparison between FQPSO with different fractional-order on Group 1.

(a) f1, (b) f2, (c) f3, (d) f4, (e) f5.

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Fig 1 Expand

Fig 2.

Comparison between FQPSO with different fractional-order on Group 2.

(a) f6, (b) f7, (c) f8.

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Fig 2 Expand

Table 4.

Comparison between FQPSOs with different fractional-order on function 1–2.

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Table 4 Expand

Table 5.

Comparison between FQPSOs with different fractional-order on function 3–4.

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Table 5 Expand

Table 6.

Comparison between FQPSOs with different fractional-order on function 5–6.

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Table 6 Expand

Table 7.

Comparison between FQPSOs with different fractional-order on function 7–8.

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Table 7 Expand

Table 8.

Time consumption.

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Table 8 Expand

Fig 3.

Comparison between different PSO algorithms on Group 1.

(a) f1, (b) f2, (c) f3, (d) f4, (e) f5.

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Fig 3 Expand

Fig 4.

Comparison between different PSO algorithms on Group 2.

(a) f6, (b) f7, (c) f8.

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Fig 4 Expand

Table 9.

Comparison between different PSO algorithms on function 1–3.

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Table 9 Expand

Table 10.

Comparison between different PSO algorithms on function 4–6.

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Table 10 Expand

Table 11.

Comparison between different PSO algorithms on function 7–8.

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Table 11 Expand