Table 1 Ten benchmark functions in the experiment.
From: Coverage optimization of wireless sensor network utilizing an improved CS with multi-strategies
No. | Function | Formula | Dim | Interval | f (x*) |
|---|---|---|---|---|---|
F1 | Sphere | \(F_{1} = \sum\limits_{i = 1}^{D} {x_{i}^{2} }\) | 30, 50 | [− 5.12, 5.12] | 0 |
F2 | Step | \(F_{2} = \sum\limits_{i = 1}^{D} {\left[ {x_{i} + 0.5} \right]^{2} }\) | 30, 50 | [− 100, 100] | 0 |
F3 | Schwefel 2.22 | \(F_{3} { = }\sum\limits_{i = 1}^{D} {\left| {x_{i} } \right|} + \prod_{i = 1}^{D} \left| {x_{i} } \right|\) | 30, 50 | [− 100, 100] | 0 |
F4 | Rosenbrock | \(F_{4} = \sum\limits_{i = 1}^{D} {\left[ {100\left( {x_{i + 1} - x_{i}^{2} } \right)^{2} + \left( {x_{i} - 1} \right)^{2} } \right]}\) | 30, 50 | [− 30, 30] | 0 |
F5 | Ackley | \(\begin{gathered} F_{5} = - 20\exp \left( { - 0.2\sqrt {\frac{1}{D}\sum\limits_{i = 1}^{D} {x_{i}^{2} } } } \right) \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} - \exp \left( {\frac{1}{D}\sum\limits_{i = 1}^{D} {\cos \left( {2\pi x_{i} } \right)} } \right) + 20 + e \hfill \\ \end{gathered}\) | 30, 50 | [− 32, 32] | 0 |
F6 | Griewank | \(F_{6} = \sum\limits_{i = 1}^{D} {\frac{{x_{i}^{2} }}{4000}} - \prod\limits_{i = 1}^{D} {\cos \left( {\frac{{x_{i} }}{\sqrt i }} \right)} + 1\) | 30, 50 | [− 600, 600] | 0 |
F7 | Rastrigin | \(F_{7} = \sum\limits_{i = 1}^{D} {\left( {x_{i}^{2} - 10\cos \left( {2\pi x_{i} } \right) + 10} \right)}\) | 30, 50 | [− 600, 600] | 0 |
F8 | Bohachevsky | \(F_{8} = \sum\limits_{i = 1}^{D - 1} {\left[ \begin{gathered} x_{i}^{2} + 2x_{i + 1}^{2} - 0.3\cos \left( {3\pi x_{i} } \right) \hfill \\ - 0.4\cos \left( {4\pi x_{i + 1} } \right) + 0.7 \hfill \\ \end{gathered} \right]}\) | 30, 50 | [− 100, 100] | 0 |
F9 | Beale | \(\begin{gathered} F_{9} = (1.5 - x_{1} + x_{1} x_{2} )^{2} + (2.25 - x_{1} + x_{1} x_{2}^{2} )^{2} \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} + (2.625 - x_{1} + x_{1} x_{2}^{3} )^{2} \hfill \\ \end{gathered}\) | 2 | [− 4.5, 4.5] | 0 |
F10 | SchafferN.2 | \(F_{10} = 0.5 + \frac{{\sin^{2} (x_{1}^{2} - x_{2}^{2} ) - 0.5}}{{\left[ {1 + 0.001(x_{1}^{2} + x_{2}^{2} )} \right]^{2} }}\) | 2 | [− 100, 100] | 0 |
