zakharov
The Zakharov function has no local minima except the global one [1].
of = zakharov(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
| \[ f(\mathbf{x}) = \sum_{i=1}^{d} x^2_{i} + \left ( \sum_{i=1}^{d} 0.5ix_{i} \right )^2 + \left ( \sum_{i=1}^{d} 0.5ix_{i} \right )^4 \] | (1) |
| \[x_{i} \in [-5, 10], i=1, ... , d; \;...\; f(\mathbf{x}^*) = 0, \; \mathbf{x}^* = (0,...,0) \] | (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 = zakharov(x)
# Output details
print("of_best zakharov: of = {:.4f}".format(of))
of_best zakharov: of = 0.0000