Can it happen that the grid size or resolution (to use such language) of the local solutions of a non-linear optimization problem are, or become, too fine for the evolutionary algorithm to pick up?
Is this just a matter of proper sampling? Will the algorithm conduct the appropriate sampling in all cases?
if i understand you correctly, too fine implies there are too many sample points. If this is true, this increases your combinatorics especially in a high dimensional problem hence your evolutionary algo could struggle. One way to circumvent this would be to generate many more initial solution as in the case of generic algorithm and of course to give it more time.
with excel solver evolutionary algorithm, if i don't cut up and bound the solution space into blocks or areas through constraints, and separately search these blocks or areas, the algorithm misses certain fair solutions... so i am currently implementing something like that "manually" it also helps me to note the different possible local solutions.
I am not sure if I understand your question clearly but if you are having a problem that your evolutionary algorithm (EA) gets stuck on local optimum, this is called as "premature convergence" and yes this can happen if the problem is too complex, local optima is too good, or your algorithm is designed badly.
You may try to redesign/change your genetic operators (selection, crossover, mutation). For example, the selection operator of Excel EA may be allowing only good individuals to survive which decreases diversity and after a number of generations causes to be stucked in the same region.
Using a selection operator which also allows a small number of bad individuals to survive during generations may increase the diversity of the population. You may also increase the mutation rate but since mutation is a random process, it may take too long to leave the solution region you got stuck in. Moreover, increasing randomness will decrease your convergence time.
I recommend you to use Python or R programming languages, which have well designed EA packages, or any programming language you are famililar with. This will give you chance to modify the operators when neccessary.
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