What do you mean by correct generation order? Is there something funny about which GP gets spawned when multiple cities hit the threshold at the same time in Vanilla?
No, nothing funny.
I mean that by assigning or taking out artist specialists you can manipulate the order in which the cities pop their GAs. Doing so intelligently helps your endgame greatly. I'll put an example.
You are playing a cultural game and 2 of your cities have gone Legendary. The third one grows culture too slowly, it will take forever to reach Legendary, but 2 culture bombs will be enough to get it to Legendary. 2 of your cities are about to pop a GA, at a cost of 2000 GPP.
City1 makes 80GPPpt, has already accumulated 1920 GPP.
City2 makes 50GPPpt, has already accumulated 1940 GPP.
If you do nothing, city1 will pop its GA at T1. City2 will pop the following GA at a cost of 2200GPP by T6. You win the game T7.
Now, you change the number of artist specialist in each city. City2 abandons all food tiles and every single citizen is hired as an artist (starvation). City1 gets 1 artist out and works a food tile.
So by T1 City2 has popped the 2000GPP GA. You have changed the order in which the cities pop out their GAs. By T1 City1 has accumulated some 1990GPP.
Now you put all citizens in City2 to do something useful to stop further starvation. In City1 you hire 2 more artists from food tiles for 1 turn (this way you consume the extra food you got the previous turn).
By T2 City1 has accumulated 2080GPP, just as if you had done nothing to the city.
Then you put 1 artist back to food, leaving the citizens in their initial positions. You continue doing 80GPPpt.
City1 will pop its 2200GPP by T4. You win the game T5.
So just by popping the GA in the slow city first, the GA in the fast city later you save 2 turns.
EDIT: I think I already wrote about this kind of ordering tricks in a recent BOTM, I'll try to find the relevant link.
EDIT2: I found it: http://forums.civfanatics.com/showpost.php?p=7419799&postcount=3
This is the relevant text:
On maximizing the number of GAs:
- You first estimate the order in which they are going to appear if you do nothing special and get to know your expected victory date (count on 1 more GA than your estimation will give you).
- Identify the city the won't be able to pop a GA. Look for moments in the GA popping series in which this city could be close to popping.
- Make whatever is necessary to pop a GA in that city. Starve it to death, delay other cities while accumulating food in their granaries...
This way you have made one useless city to contribute to victory.
- Then look for situations in which 2 cities are about to pop a GA more or less at the same time and one of them won' be able to pop another GA after this one, while the other will.
- Force things (accumulate food in one city while approaching starvation in the other) so that the city that won't pop a second GA goes last.
This way, you will get that city to contribute with GPP more time. And you will get the second GA from the city that took over this one much earlier, as the cost of the precious one was inferior.
- When every city left is going to pop a single GA each, try to make the city with less GPP per turn pop first, etc... and the city with the most GPPpt (generally the GPFarm) pop last.
This way the turns difference between the next to last pop and the last pop will be much shorter.
- As doing these kind of things you get 1 or 2 more GAs and you get them earlier, redo your initial estimation. You will realise that your estimated victory date is much earlier now, but of course that will mean that you probably won't have time to pop that last GA.
- In the last stages probably you will win when you bomb your last GA. Make sure you starve the last popping city in order to get that last GA one (or a few) turns sooner. This will probably make necessary to starve also the next to last popping city, or otherwise it will be taken over!
I hope you can find these kind of ideas useful.