sphere
The sphere function has \(d\) local minima except for the global one. It is continuous, convex and unimodal [1].
of = sphere(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
| \[f(\mathbf{x}) = \sum_{i=1}^{n} x_{i}^{2}\] | (1) |
| \[ x_{i} \in [-5.12, 5.12], i = 1,..., d; \;...\; f(\mathbf{x}^*) = (0,..,0), \; \mathbf{x}^* = [0,...,0] \] | (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 = sphere(x)
# Output details
print("of_best sphere: of = {:.4e}".format(of))
of_best sphere: of = 0.0000e+00