Optimizing the Eggholder function

The Eggholder function, depicted in the following diagram, is often used as a benchmark for function optimization algorithms. Finding the single global minimum of this function is considered a difficult task due to the large number of local minima, which give it the eggholder shape:

Figure 6.1: The Eggholder function

Source: https://en.wikipedia.org/wiki/File:Eggholder_function.pdf

The function can be mathematically expressed as follows:

f(x, y) = − (y + 47) ⋅ sin √ ___________ | x _ 2  + (y + 47)|  − x ⋅ sin √ ___________ |x − (y + 47)| 

It is usually evaluated on the search space bounded by [-512, 512] in each dimension. The global minimum of the function is known to be at x=512, y = 404.2319, where the function’s value is -959.6407.

In the next subsection, we will attempt to find the global minimum...