what is meaning of "ga stopped because the average change in the penalty function value is less than options.FunctionTolerance and the constraint violation is less than options.ConstraintTolerance."
Consider that ga() is applying a "black box function" -- it effectively cannot "peak inside" the objective function you give it in order to analyze the behavior of the function.
As such, there are a few different outcomes possible:
- the objective function returned a -inf . There is no possible "better" return than -inf so ga might as well stop there
- the objective function returned nan. If there is at least one set of parameters inside the population that returned non-nan then you can just drop the failing members from the population; if the entire population is returning nan then ga() has to give up
And otherwise, the objective function returned some valid value, say -17292.35 . But is that the minimum possible return value? You cannot know that it is -- the objective function might be coded as (-17292.35 - (x == 312.14752)*10000000) which returns a much better result if the input happens to be exactly 312.14752 .
So for any finite outputs, ga() does not have a natural stopping point: there is always the possibility that if you ran another hundred billion iterations that you might shave 1e-15 off of the output value.
ga() therefore has some heuristics about when to stop. One of the heuristics is if over all of the iterations that it did for a generation, none of the outputs improved by more than a preset tolerance, and none of the constraints are violated by more than a (different) preset tolerance. In other words, a number of iterations were done but the results didn't improve.
This is a normal outcome of ga(). ga() is never going to say "This result is definitely the minimum!", because it can never know that; it can, however, know that it gave it a number of tries and nothing improved over the tries.
