soobench (version 1.9.18)

generate_batman_function: Generator for the Batman function.

Description

The definition used is

Usage

generate_batman_function(dimensions, alpha = 0.25)

Arguments

dimensions

[integer(1)] Size of parameter space.

alpha

[numeric(1)] Parameter for control of groove shape

Value

A soo_function.

Details

$$f(x) = \left[\left((x^Tx)^2 - (\sum_{i=1}^n)^2\right)^2\right]^\alpha + \frac{1}{N}\left(\frac{1}{2}x^Tx + \sum_{i=1}^n x_i\right) + \frac{1}{2}$$

References

H.-G. Beyer and S. Finck. HappyCat - A Simple Function Class Where Well-Known Direct Search Algorithms Do Fail. In: PPSN XII (Parallel Problem Solving from Nature), 367-376, Springer, Heidelberg, 2012.

Examples

# NOT RUN {
f <- generate_batman_function(2, 1/4)
plot(f)

# }