Optimizing Himmelblau’s function

Another frequently used function for benchmarking optimization algorithms is Himmelblau’s function, depicted in the following diagram:

Figure 6.5: Himmelblau’s function

Source: https://commons.wikimedia.org/wiki/File:Himmelblau_function.svg

Image by Morn the Gorn

The function can be mathematically expressed as follows:

f(x, y) = (x 2 + y − 11) 2 + (x + y 2 − 7) 2

It is usually evaluated on the search space bounded by [-5, 5] in each dimension.

Although this function seems simpler in comparison to the Eggholder function, it draws interest as it is multi-modal; in other words, it has more than one global minimum. To be exact, the function has four global minima evaluating to 0, which can be found in the following locations:

• x=3.0, y=2.0
• x=−2.805118, y=3.131312
• x=−3.779310, y=−3.283186
• x=3.584458, y=−1.848126...