ackley
The Ackley function is widely used for testing optimization algorithms. In its two-dimensional form, as shown in the plot above, it is characterized by a nearly flat outer region, and a large hole at the centre [1].
of = ackley(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
| \[ f(\mathbf{x}) = -\alpha \exp \left( -b \sqrt{\frac{1}{d}\sum_{i=1}^{d} x_{i}^{2}} \right ) -\exp \left ( \frac{1}{d} \sum_{i=1}^{d} \cos (cx_{i}) \right ) + \alpha + exp(1) \] | (1) |
| \[ x_{i} \in [-32.768, 32.768], i=1, ... , d; \;...\; f(\mathbf{x}^*) = 0, \; \mathbf{x}^* = (0,...,0) \] | (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 = ackley(x)
# Output details
print("of_best rastrigin: of = {:.4f}".format(of))
of_best ackley: of = 0.0000