Differential Evolution

This story will help you understand metaheuristic optimization on the example of the differential evolution algorithm which is based on the biological concept “survival of the fittest” as known by Charles Darwin.

Charles Darwin — Image by Julia Margaret Cameron

Problem formulation

The basic problem with which DE (Differential Evolution) can help is finding global minima of a multivariate, multimodal function. In Addition, the function can be nonlinear and non-differentiable.¹ So the basic idea of finding an extrema through differentiation is inapplicable for these functions.

• Multivariate: This means that the function output depends on more than one variable. The number of variables it depends on is called dimension n of the function.
• Multimodal: This means that the function has more than one extrema in each direction. This is what makes the function so challenging. We have multiple local minima and maxima, so how are we going to find the global extrema? Take a look at this function

Rastrigin Function

As you can see, it has many many local minima, which makes it hard to distinguish the global minimum. This is the kind of function which DE can help to optimize.