. 2021 Sep 7;2021:6379469. doi: 10.1155/2021/6379469

Table 3.

Fixed-dimension multimodal benchmark functions.

Function	Dim	Range	F _min
F₁₄(x)=((1/500)+∑_j=1²⁵1/(j+∑_i=1²(x_i − a_ij)⁶))⁻¹	2	[−65, 65]	0.998
F₁₅(x)=∑_i=1¹¹[a_i − (x₁(b_i²+b_ix₂)/(b_i²+b_ix₃+x₄))]²	4	[−5, 5]	0.00030
F₁₆(x)=4x₁² − 2.1x₁⁴+(1/3)x₁⁶+x₁x₂ − 4x₂²+x₂⁴	2	[−5, 5]	−1.0316
F₁₇(x)=(x₂ − (5.1/4π²)x₁²+(5/π)x₁ − 6)²+10(1 − (1/8π))cos x₁+10	2	[−5, 5]	0.398
$\begin{matrix} F_{18} (x) = [[) 1 + {(x_{1} + x_{2} + 1)}^{2} (19 - 14 x_{1} + 3 x_{1}^{2} - 14 x_{2} + 6 x_{1} x_{2} + 3 x_{2}^{2})] \\ \times [30 + {(2 x_{1} - 3 x_{2})}^{2} \times (18 - 32 x_{2} + 12 x_{1}^{2} + 48 x_{2} - 36 x_{1} x_{2} + 27 x_{2}^{2})] \end{matrix}$	2	[−2, 2]	3
F₁₉(x)=−∑_i=1⁴c_iexp(−∑_j=1³a_ij(x_j − p_ij)²)	3	[−1, 2]	−3.86
F₂₀(x)=−∑_i=1⁴c_iexp(−∑_j=1⁶a_ij(x_j − p_ij)²)	6	[0, 1]	−3.32
F₂₁(x)=−∑_i=1⁵[(X − a_i)(X − a_i)^T+c_i]⁻¹	4	[0, 10]	−10.1532
F₂₂(x)=−∑_i=1⁷[(X − a_i)(X − a_i)^T+c_i]⁻¹	4	[0, 10]	−10.4028
F₂₃(x)=−∑_i=1¹⁰[(X − a_i)(X − a_i)^T+c_i]⁻¹	4	[0, 10]	−10.5363