. 2022 Mar 24;2022:1535957. doi: 10.1155/2022/1535957

Table 3.

Fixed-dimension multimodal benchmark functions.

Function	Dim	Range	f _min
F ₁₄(x)=(1/500+∑_j=1²⁵1/j+∑_i=1²(x_i − a_ij)⁶)⁻¹	2	[−65, 65]	0.998
F ₁₅(x)=∑_i=1¹¹[a_i − x₁(b_i²+b_ix₂)/b_i²+b_ix₃+x₄]²	4	[−5, 5]	0.00030
F ₁₆(x)=4x₁² − 2.1x₁⁴+1/3x₁⁶+x₁x₂ − 4x₂²+x₂⁴	2	[−5, 5]	−1.0316
F ₁₇(x)=(x₂ − 5.1/4π²x₁²+5/πx₁ − 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
F ₁₉(x)=−∑_i=1⁴c_iexp(−∑_j=1³a_ij(x_j − p_ij)²)	3	[−1, 2]	−3.86
F ₂₀(x)=−∑_i=1⁴c_iexp(−∑_j=1⁶a_ij(x_j − p_ij)²)	6	[0, 1]	−3.32
F ₂₁(x)=−∑_i=1⁵[(X − a_i)(X − a_i)^T+c_i]⁻¹	4	[0, 10]	−10.1532
F ₂₂(x)=−∑_i=1⁷[(X − a_i)(X − a_i)^T+c_i]⁻¹	4	[0, 10]	−10.4028
F ₂₃(x)=−∑_i=1¹⁰[(X − a_i)(X − a_i)^T+c_i]⁻¹	4	[0, 10]	−10.5363