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Table 2 Test functions description.

From: A Hybrid Particle Swarm Optimization with Dragonfly for Adaptive ANFIS to Model the Corrosion Rate in Concrete Structures

Function Dim Range \(f_{\min }\)
\(F_{1} (x) = \sum\limits_{i = 1}^{n} {x_{i}^{2} }\) 10 [− 100,100] 0
\(F_{2} (x) = \sum\limits_{i = 1}^{n} {\left| {x_{i} } \right|} + \prod\limits_{i = 1}^{n} {\left| {x_{i} } \right|}\) 10 [− 10,10] 0
\(F_{3} (x) = \sum\limits_{i = 1}^{n} {(\sum\limits_{j - 1}^{i} {x_{j} } )^{2} }\) 10 [− 100,100] 0
\(F_{4} (x) = \mathop {\max }\limits_{i} \{ \left| {x_{i} } \right|,\,\,\,\,1 \le i \le n\}\) 10 [− 100,100] 0
\(F_{5} (x) = \sum\limits_{i = 1}^{n - 1} {[100(x_{i + 1} - x_{i}^{2} ) + (x_{i} - 1)^{2} ]}\) 10 [− 30,30] 0
\(F_{6} (x) = \frac{1}{4000}\sum\limits_{i = 1}^{n} {x_{i}^{2} } - \prod\limits_{i = 1}^{n} {\cos (\frac{{x_{i} }}{\sqrt i })} + 1\) 10 [− 600,600] 0
\(F_{7} (x) = \left( {\frac{1}{500} + \sum\limits_{j = 1}^{25} {\frac{1}{{j + \sum\limits_{i = 1}^{2} {\left( {x_{i} - a_{ij} } \right)^{6} } }}} } \right)^{ - 1}\) 2 [− 65.53,65.53] 1
\(F_{8} (x) = \sum\limits_{i = 1}^{11} {\left[ {a_{i} - \frac{{x_{1} \left( {b_{i}^{2} + b_{i} x_{2} } \right)}}{{b_{i}^{2} + b_{i} x_{3} + x_{4} }}} \right]^{2} }\) 4 [− 5,5] 0.0003
\(F_{9} (x) = 4x_{1}^{2} - 2.1x_{1}^{4} + \frac{1}{3}x_{1}^{6} + x_{1} x_{2} - 4x_{2}^{2} + 4x_{2}^{4}\) 2 [− 5,5] − 1.0316
\(\begin{gathered} F_{10} (x) = \left[ {1 + \left( {x_{1} + x_{2} + 1} \right)^{2} \left( {19 - 14x_{1} + 3x_{1}^{2} - 14x_{2} + 6x_{1} x_{2} + 3x_{2}^{2} } \right)} \right] \hfill \\ \quad \quad \quad \times \left[ {30 + \left( {2x_{1} - 3x_{2} } \right)^{2} \times \left( {18 - 32x_{1} + 12x_{1}^{2} + 48x_{2} - 36x_{1} x_{2} + 27x_{2}^{2} } \right)} \right] \hfill \\ \end{gathered}\) 2 [− 2,2] 3