# Example GIFs

The examples in this subdirectory are concerned with creating GIFs of the algorithm's progress against the following unconstrained maximization problems. 

These GIFs plot the evolution of the population overlayed on its 2D realization.

## Keane's Bump Function

```math
\max f(\mathbf{x}) = \left| 
\frac{
\sum_{i=1}^{n} (\cos(x_i))^4 - 2 \prod_{i=1}^{n} (\cos(x_i))^2
}{
\sqrt{ \sum_{i=1}^{n} i \cdot x_i^2 }
}
\right|
```

```math
\text{subject to} \quad 0 \leq x_i \leq 10 \quad \forall i \in \{1, \ldots, n\}
```

```math
\prod_{i=1}^{n} x_i > 0.75
```

```math
\sum_{i=1}^{n} x_i < \frac{15n}{2}
```

<p align="center">
<img src="KBF_contour.png" height="300" alt="KBF Contour" style="display:inline-block"> <img src="KBF_surf.png" height="300" alt="KBF Surface" style="display:inline-block">
</p>

### Multimodal Gaussian Function
```math
\max f(x,y) = 10 \cdot e^{-\frac{(x-3)^2 + (y-3)^2}{0.5}} + 5 \cdot e^{-\frac{(x-7)^2 + (y-7)^2}{0.3}} + 5 \cdot e^{-\frac{(x-7)^2 + (y-3)^2}{0.2}}
```

```math
\text{subject to} \quad 0 \leq x \leq 10 \quad \text{and} \quad 0 \leq y \leq 10
```


## Sources and more information

- [Keane's Bump Function](https://doi.org/10.1016/S0952-1976(99)00033-0)