Lets talk about this for a second though,
Would you necessarily want "stronger" minions?
Part of your ability to effectively control a lane does involve your lane being able to push to you. Ganks are more difficult to accomplish when a lane is always shoved. It actually becomes easier for your enemy to safely farm minions when they are pushed to their tower.
So you would need to be careful as to how you would want to "strengthen" your minions, and it may even be good to incorporate a drawback.
For example,
If you make "Armored Minions", meaning that nothing is different about them aside from their ability to mitigate more damage, then a full minion wave vs another 'non-armored' minion wave would result in a nearly constantly pushed wave.
Logic would suggest that dropping a ton of armor on a minion would weigh it down, and in turn slow it down.
Eh??