Evolutionary algorithms
When to use?
"Typical" optimisation
Multivariate functions, especially non-continous or hard to optimise with gradient-based methods.
Example: Rastrigin function.

Combinatorial optimisation
Problems with huge numerical complexity.
Example: given a list of cities find the shortest route through all of them.

In general

Evolutionary approach
A single iteration of a simple evolutionary algorithm:

Key characteristics
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Algorithm is specific to each problem, no one-size-fits-all.
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Evolutionary algorithms are inherently parallelizable on many levels.