makeModifiedRastriginFunction function

Rastrigin Function

A modified version of the Rastrigin function following the formula: [REMOVE_ME]$f(\mathbf{x}) = \sum_{i=1}^{n} 10\left(1 + \cos(2\pi k_i \mathbf{x}_i)\right) + 2 k_i \mathbf{x}_i^2. [REMOVE_ME_2]$

The box-constraints are given by $\mathbf{x}_i \in [0, 1]$ for $i = 1, \ldots, n$ and $k$ is a numerical vector. Deb et al. (see references) use, e.g., $k = (2, 2, 3, 4)$ for $n = 4$. See the reference for details.

makeModifiedRastriginFunction(dimensions, k = rep(1, dimensions))

Arguments

• dimensions: [integer(1)]

  Size of corresponding parameter space.

• k: [numeric]

  Vector of numerical values of length dimensions. Default is rep(1, dimensions)

Returns

[smoof_single_objective_function]

Description

A modified version of the Rastrigin function following the formula:

The box-constraints are given by $\mathbf{x}_i \in [0, 1]$ for $i = 1, \ldots, n$ and $k$ is a numerical vector. Deb et al. (see references) use, e.g., $k = (2, 2, 3, 4)$ for $n = 4$. See the reference for details.

References

Kalyanmoy Deb and Amit Saha. Multimodal optimization using a bi- objective evolutionary algorithm. Evolutionary Computation, 20(1):27-62, 2012.