Table 6 Different GWO algorithms’ benchmark functions simulation results.
From: Hierarchical multi step Gray Wolf optimization algorithm for energy systems optimization
Function | Dim | Range | \(f_{min}\) | |
|---|---|---|---|---|
\(f_{1} \left( x \right) = \sum\nolimits_{{i = 1}}^{n} {x_{i}^{2} }\) | 30 | [-100,100] | 0 | |
\(f_{2} \left( x \right) = \sum _{{i = 1}}^{n} \left| {x_{i} } \right| + \prod\nolimits_{{i = 1}}^{n} {\left| {x_{i} } \right|}\) | 30 | [-10,10] | 0 | |
\(f_{3} \left( x \right) = \sum _{{i = 1}}^{n} \left( {\sum\nolimits_{{j - 1}}^{i} {x_{j} } } \right)^{2}\) | 30 | [-100,100] | 0 | |
\(f_{4} \left( x \right) = {\text{max}}_{i} \left\{ {\left| {x_{i} } \right|,1 \le i \le n} \right\}\) | 30 | [-100,100] | 0 | |
\(f_{5} \left( x \right) = \sum\nolimits_{{i = 1}}^{n} {\left[ {100\left( {x_{{i + 1}} - x_{i}^{2} } \right)^{2} + \left( {x_{i} - 1} \right)^{2} } \right]}\) | 30 | [-30,30] | 0 | |
\(f_{6} \left( x \right) = \sum\nolimits_{{i = 1}}^{n} {\left( {\left| {x_{i} + 0.5} \right|} \right)^{2} }\) | 30 | [-100,100] | 0 | |
\(f_{7} \left( x \right) = \sum\nolimits_{{i = 1}}^{n} {ix_{i}^{4} } + {\text{random}}\left[ {0,1} \right)\) | 30 | [-1.28,1.28] | 0 | |
