makeMichalewiczFunction: Michalewicz Function

In smoof: Single and Multi-Objective Optimization Test Functions

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.

smoof documentation built on March 31, 2023, 11:48 p.m.