Table 2 Test functions 1.
From: Balanced dung beetle optimization algorithm based on parameter substitution and escape strategy
Function expression | Search area | Solution |
|---|---|---|
\({f}_{1}(x)={x}_{1}^{2}+{10}^{6}\sum_{i=2}^{D}{x}_{i}^{2}\) | \([-\text{100,100}]\) | 100 |
\({f}_{2}(x)=\sum_{i=1}^{D-1}(100({x}_{i}^{2}-{x}_{i+1}{)}^{2}+({x}_{i}-1{)}^{2})\) | \([-\text{100,100}]\) | 400 |
\({f}_{3}(x)=\sum_{i=1}^{D}({x}_{i}^{2}-10\text{cos}(2\pi {x}_{i})+10)\) | \([-\text{100,100}]\) | 500 |
\({f}_{4}(\mathbf{x})=g({x}_{1},{x}_{2})+g({x}_{2},{x}_{3})+\dots +g({x}_{D-1},{x}_{D})+g({x}_{D},{x}_{1})\) | \([-\text{100,100}]\) | 600 |
\({f}_{5}(\mathbf{x})=dD+s\sum_{i=1}^{D}{({\hat{x}}_{i}-{\mu }_{1})}^{2}+10(D-\sum_{i=1}^{D}\text{cos}(2\pi {z}_{i}),min(\sum_{i=1}^{D}{({\hat{x}}_{i}-{\mu }_{0})}^{2}))\) | \([-\text{100,100}]\) | 700 |
\({f}_{6}(\mathbf{x})=\sum_{i=1}^{D}({z}_{i}^{2}-10\text{cos}(2\pi {z}_{i})+10)+{f}_{13}\) | \([-\text{100,100}]\) | 800 |
\({f}_{7}\left(\mathbf{x}\right)={\left({w}_{D}-1\right)}^{2}\left[1+{\text{sin}}^{2}\left(2\pi {w}_{D}\right)\right]+\sum_{i=1}^{D-1}{({w}_{i}-1)}^{2}[1+10{\text{sin}}^{2}(\pi {w}_{i+1})]+{\text{sin}}^{2}(\pi {w}_{1})\) | \([-\text{100,100}]\) | 900 |
\({f}_{8}(\mathbf{x})=418.9829\times D-\sum_{i=1}^{D}g({z}_{i})\) | \([-\text{100,100}]\) | 1000 |
\({f}_{9}(\mathbf{x})={10}^{6}{x}_{1}^{2}+\sum_{i=2}^{D}{x}_{i}^{2}\) | \([-\text{100,100}]\) | 1200 |
\({f}_{10}\left(\mathbf{x}\right)=-\text{exp}\left(\frac{1}{D}\sum_{i=1}^{D}\text{cos}\left(2\pi {x}_{i}\right)\right)\) \(+20+e-20\text{exp}(-0.2\sqrt{\frac{1}{D}\sum_{i=1}^{D}{x}_{i}^{2}})\) | \([-\text{100,100}]\) | 1300 |
