The optimizer is deterministic, so given the same starting conditions, it will always produce the same result.
It looks like in this case, locking the gem/enchant causes it to find a different solution that scores almost exactly the same. (The score isn’t shown right now, but I’m able to see it on my dev server. With nothing locked it finds a set that scores 783775, with the gem/enchant locked it finds a different set that scores 783698.)
Firstly, you will notice how close these are to your simulations
Set 1: 784k predicted, 781k actual
Set 2: 784k predicted, 787k actual
Secondly, you will notice that as far as the optimizer is concerned, it has found the better of the two solutions when you don’t constrain it.
Thirdly, you will see that the predicted value is only 0.38% different than the actual value for each set.
Getting an optimizer that has any better margin of error than that would be… kind of crazy. At that point you would just have to start simulating many more combinations directly, rather than trying to predict it based on a smaller sampling of simulations. This post might be of interest to you as well: BiB Suggestion Sims Lower Than Original Gear - #6 by yellowfive
In this case, you were able to do some direct simulations that show a theoretical gain for one set over the other, so go ahead and use it (and as mentioned earlier, we want to make these “user refinements” more easily integrated with BiB in the future). The optimizer is getting you really close though, to the point where most players won’t feel it, without having to do any manual tweaking or simulation.