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In optimization, particularly evolutionary computation, we often try to optimize (through either minimization or maximization) non-smooth, non-differentiable, discrete functions that aren't readily visualized (for example through function plotting).

Given this, it's often challenging to picture the shape of the resulting fitness landscape imposed by a selected fitness function, and selection/variation operators (crossover and mutation).

How then can we predict the behaviour of initial guesses within basins of attraction? That is, how to we know the (or attempt to find) trajectories toward local optima?

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    $\begingroup$ Often we can't/don't. $\endgroup$
    – D.W.
    Commented Oct 29, 2021 at 5:15
  • $\begingroup$ When we can, is there a general approach? $\endgroup$ Commented Oct 29, 2021 at 5:28
  • $\begingroup$ No general approach. Run your optimization method and see how it goes. (If you know something about your function, eg smoothness, you can at least show that your method converges to a local minimum) $\endgroup$
    – Dmitry
    Commented Oct 29, 2021 at 8:28

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