The formula of Ripples is shown as below.

$$ f(\boldsymbol{x})= \sum {i = 1} ^ {dim} \left(e^{-\frac{x_i^2}{2\sigma}} + k cos(\omega x_i) - k \right), \ \text{where} \ x_i = \Vert \boldsymbol{x} + M{i,:} \Vert_2, \ \text{for all} \ i = 1, 2, ..., dim $$

In which,

$$ M = I_{dim} \times bias $$ where $dim$ is the dimension of the function. $I_{dim}$ is an identity matrix with order $dim$. $M_{i,:}$ represents the $i$th row of the matrix $M$. $\sigma$, $k$, $\omega$ and $bias$ are parameters that determine the shape of the function and the locations of the optimal points.