powell
The Powell function has several local minima [1].
of = powell(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
| \[ f(\mathbf{x}) = \sum^{d/4}_{i=1} \left [ \left ( x_{4i-3} + 10x_{4i-2} \right )^2 + 5\left ( x_{4i-2} - 2x_{4i-1} \right )^4 + 10\left ( x_{4i-3} -x_{4i} \right )^4 \right ] \] | (1) |
| \[x_{i} \in [-4, 5], i=1, ... ,d; \;...\; f(\mathbf{x}^*) = 0, \; \mathbf{x}^* = \left ( 0, ... , 0 \right ) \] | (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 = powell(x)
# Output details
print("of_best powell: of = {:.4f}".format(of))
of_best powell: of = 0.0000