makeMichalewiczFunction function

Michalewicz Function

Highly multimodal single-objective test function with $n!$ local minima with the formula: [REMOVE_ME]$f(\mathbf{x}) = -\sum_{i=1}^{n} \sin(\mathbf{x}_i) \cdot \left(\sin\left(\frac{i \cdot \mathbf{x}_i}{\pi}\right)\right)^{2m}. [REMOVE_ME_2]$

The recommended value $m = 10$, which is used as a default in the implementation.

makeMichalewiczFunction(dimensions, m = 10)

Arguments

• dimensions: [integer(1)]

  Size of corresponding parameter space.

• m: [integer(1)]

  Steepness parameter.

Returns

[smoof_single_objective_function]

Description

Highly multimodal single-objective test function with $n!$ local minima with the formula:

The recommended value $m = 10$, which is used as a default in the implementation.

Note

The location of the global optimum s varying based on both the dimension and $m$ parameter and is thus not provided in the implementation.

References

Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Berlin, Heidelberg, New York: Springer-Verlag, 1992.