rastrigin
The Rastrigin function has several local minima. It is highly multimodal, but locations of the minima are regularly distributed [1].
of = rastrigin(x)
Input variables
| Name | Description | Type |
|---|---|---|
x | Current design variables of the i agent. | List |
Output variables
| Name | Description | Type |
|---|---|---|
of | Objective function value of the i agent. | Float |
Problem
| \[f(\mathbf{x}) = 10d + \sum_{i=1}^{d} \left [ x_{i}^{2} -10 \cos{(2\pi x_{i})} \right ] \] | (1) |
| \[ x_{i} \in [-5.12, 5.12], i=1, ... , d; \;...\; f(\mathbf{x}^*) = 0, \; \mathbf{x}^* = (0,...,0) \] | (2) |
Example 1
Considering the design variable \(\mathbf{x} = [0,0]\), what value does the objective function expect?
# Data
x = [0, 0]
# Call function
of = rastrigin(x)
# Output details
print("of_best rastrigin: of = {:.4f}".format(of))
of_best rastrigin: of = 0.0000