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. 2025 May 2;15:15460. doi: 10.1038/s41598-025-98816-0

Table 3.

The benchmark functions in this paper.

Functions Source Dim Range Inline graphic Function type
F1 CEC 2005 F1 10/30/50/100 [−100, 100Inline graphic 0 unimodal
F2 CEC 2005 F3 10/30/50/100 [−100, 100Inline graphic 0 unimodal
F3 CEC 2005 F6 10/30/50/100 [−100, 100Inline graphic 0 unimodal
F4 CEC 2017 F1 10/30/50/100 [−100, 100Inline graphic 100 unimodal
F5 CEC 2005 F8 10/30/50/100 [−500, 500Inline graphic −418.98Inline graphic multimodal
F6 CEC 2005 F10 10/30/50/100 [−32, 32Inline graphic 0 multimodal
F7 CEC 2005 F12 10/30/50/100 [−50, 50Inline graphic 0 multimodal
F8 CEC 2005 F14 2 [−65.536, 65.536] ≈ 0.998 multimodal
F9 CEC 2005 F16 2 [−5, 5Inline graphic ≈ −1.0316 multimodal
F10 CEC 2005 F19 3 [0, 1Inline graphic ≈ −3.86 multimodal
F11 CEC 2005 F21 4 [0, 10Inline graphic ≈ −10.1532 multimodal
F12 CEC 2005 F23 4 [0, 10Inline graphic ≈ −10.5364 multimodal
F13 CEC 2017 F4 10/30/50/100 [−100, 100Inline graphic 400 multimodal
F14 CEC 2017 F6 10/30/50/100 [−100, 100Inline graphic 600 multimodal
F15 CEC 2017 F8 10/30/50/100 [−100, 100Inline graphic 800 multimodal
F16 CEC 2017 F11 10/30/50/100 [−100, 100Inline graphic 1100 multimodal
F17 CEC 2017 F13 10/30/50/100 [−100, 100Inline graphic 1300 hybrid
F18 CEC 2017 F15 10/30/50/100 [−100, 100Inline graphic 1500 hybrid
F19 CEC 2017 F17 10/30/50/100 [−100, 100Inline graphic 1700 hybrid
F20 CEC 2017 F19 10/30/50/100 [−100, 100Inline graphic 1900 hybrid
F21 CEC 2017 F21 10/30/50/100 [−100, 100Inline graphic 2200 compositional
F22 CEC 2017 F25 10/30/50/100 [−100, 100Inline graphic 2500 compositional
F23 CEC 2017 F27 10/30/50/100 [−100, 100Inline graphic 2700 compositional
F24 CEC 2017 F29 10/30/50/100 [−100, 100Inline graphic 2900 compositional