I agree with thorwik but with one addition.

When faced with a high pop planet with high morale, one can do a two step invasion.

First, invade with one transport and use mass drivers or some other high bonus approach that damages the planet.  The damage is only inflicted on a planet if the invasion is successful, but the combat advantage is still applied in reducing the defenders.

Second, invade with mini-soldiers to take the planet, needing only to fight the greatly reduced number of defenders.

Result, lower losses of troops and no damage to planet.

On planets where the pop is high because of farms, I guess I use a two step process.

First, put spies on the farms and wait a turn.  This drops the pop to 6 if the spies live.

Second, put spies on morale structures to see if it makes the planet morale low enough for Info Warfare.  If not, then mini-soldiers.

I use a three process when the planet has a high pop but not due entirely to farms.  This is generally a Homeworld, perhaps one previously taken by the AI from a minor race and then filled back up.

1) Spies on farms to reduce pop as can (e.g., drop 24 to 16), then test spies on morale structures, generally not useful on Homeworlds, but possible.  If yes, Info Warfare.

2) Mass driver attack with one transport, intending to lose (but reduce 16 to 4)

3) Mini-soldiers to conquer. 

I just finished experimenting with invasion tactics! let me set up the situation.

I'm approaching the end of a very successful sandbox game playing Drath at crippling with version 2.02 TA. A mega event allows the Jagged Edge to take 47 planets including 34 of my planets. I can easily win a tech victory or with some patience, an ascension victory. Since the JE is a minor race I suppose I could go ahead and finish off the Yor and Korath Clan. Since those options don't go away, I decided to try to recover my lost planets.

First let me say that the advice offered by LTjim is great. I couldn't use info warfare since the JE planets were all 100% happy. I didn't have mini soldiers despite being very near the end of all branches in my tech tree.

Early in my recovery effort, I arrived with 10 transports loaded with 1.5B troops each, next to a pop 8B JE planet . Since this was soon after the JE coupe, the advantage and tech in battle were virtually identical. Lot's of reloads coming up. First I tried attacking with 15.0B, 10.5B and 6.0B 4 times each with Traditional Warfare. I won every time and the number of casualties I took was exclusively dependent on the invasion roll. With identical invasion rolls I took identical casualties with different size invasion forces.

Next I tried attacking with one transport at a time until I won. The resulting casualties were very close to the average of attacking with larger forces.

Next I tried attacking with a single transport of 1.5B using each of the invasion tactics I had available . Mass Driver was the most variable, sometimes taking out all 8B defenders and sometimes only a bit over half. The effectiveness and variability of Core Detonation, Tidal Disruption and Gas Warfare were most to least in that order.

Considering the very limited sample won't give very accurate projections and the fact that you will probably never have such closely matched advantages and tech in battle, here are some approximations. (JE Loss:My Loss)

Traditional Warfare 2:1, Mass Drivers 5:1, Core Detonation 4;1, Tidal Disruption 7;2 and Gas Warfare 3:1.

In conclusion, there is no advantage to attacking with overwhelming numbers. Attack with single transports using the most powerful tactic that won't conquer the planet until you can take it out with a single transport using traditional warfare. Smaller numbers of troops per transport give more flexibility.

   The Jagged Knife certainly is a valid testing ground.  I will try the tiny transport trick if I ever decide to grind through them again.

My tactic is to split one transport off at the start of the invasion and send them on a suicide mission using something like mass drivers to give them a massive advantage. this decimates the enemy ground forces while you only lose one transport. the other, fleeted transports can then mop up the survivors with traditional warfare.

this tactic is also useful because the failure of the first transport to capture the planet causes no damage, even though you were using a damaging tactic like mass drivers. you get all the benefits and none of the cost!