michalewicz
The Michalewicz function has d! local minima, and it is multimodal. The parameter m defines the steepness of they valleys and ridges; a larger m leads to a more difficult search [1].
of = michalewicz(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
| \[f(\mathbf{x}) = -\cos{x_{1}} \cos{x_{2}} exp \left ( -\left ( x_{1} - \pi \right )^2 - ( -\left ( x_{2} - \pi \right )^2 \right ) \] | (1) |
| \[ x_{i} \in [0, \pi], i=1, ... , d; \; d = 2: \;...\; f(\mathbf{x}^*) = -1.8013, \; \mathbf{x}^* = (2.20, 1.57) \] | (2) |
| \[x_{i} \in [0, \pi], i=1, ... , d; \; d = 5; \;...\; f(\mathbf{x}^*) = -4.687658 \] | (3) |
| \[x_{i} \in [0, \pi], i=1, ... , d; \; d = 10; \;...\; f(\mathbf{x}^*) = -9.66015 \] | (4) |
Example 1
Considering the design variable \(\mathbf{x} = [2.20, 1.57]\), what value does the objective function expect?
x = [2.20, 1.57]
# Call function
of = michalewicz(x)
# Output details
print("of_best michalewicz: of = {:.4f}".format(of))
of_best michalewicz: of = -0.0010