What are some good quantitative metrics to describe an objective function that may help choose which optimization method will work best?

E.g. if there are a lot of local minima we know that we should use something like a particle swarm optimization rather than a gradient descent method. But how to quantity this so that the metic is normalized and applicable to various problems with varying dimensionality?

I'm particularly interested in non-derivative numerical methods, but if there are any general metrics, I'd love to hear them too.


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