makeMichalewiczFunction {smoof}

Michalewicz Function

Description

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

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}.

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

Usage

makeMichalewiczFunction(dimensions, m = 10)

Arguments

dimensions

[integer(1)]
Size of corresponding parameter space.

m

[integer(1)]
“Steepness” parameter.

Value

[smoof_single_objective_function]

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.