[PvK]

Usually I haven't see happiness crises in my test games (especially in the home system), except when there is a cause like plague, large casualties, enemy ships, or battle losses. If you turned down your happiness though, it could be an issue. Your racial techs have some useful facilities for happiness improvement.

What's your happiness type and modifiers? Culture type? Are there enemy ships in your home system? Millions been dying lately? Firing on your own ships to scrap them?

Troops have no effect on happiness in Proportions, because the effect of infantry would be too great. Ships and bases help both for the whole system, and for the specific planet they are on. Cultural centers give happiness bonuses, but you may be able to increase the effect with specialized and localized facilities. Urban Pacification, Temporal Vacation Service, Religious Shrines, will I think stack their effects with multiple types.

Another idea would be to build a "pleasure craft" class - scout hull, cheap bridge, cheap life support, crew quarters, and may one efficient ion engine iii, and park them over a planet that is having happiness issues.

For increasing population, unless you have the organic tech to mass-clone them, and apart from trying to improve planet conditions and happiness, the main thing is to keep exporting colonists from your homeworld, which means building a fleet of starliners. They aren't particularly expensive to build or maintain, especially if you use cheap components, and you can set them on course and tell them to repeat it so you don't have to keep giving them orders. I usually end up with around twenty starliners buzzing around even in the early game. Of course, first build several shipyard bases at your homeworld so you can multiply your construction capacity.

Construction is necessary for Metropolis (lvl 1), Megalopolis (lvl 2), Arcology (lvl 4), Fighters, Mechanized Troops, and Mines.

Industry is necessary for Megalopolis (lvl 2), Arcology (lvl 3), and Computers.

PvK