How to clean outdoor concrete patio?

You could rent a pressure washer from a DIY store like lowes or home depot.

We clean our concrete patio every year with a power washer. You can rent them from the big hardware stores and power wash everything to keep the mold down.

Is there any home remedy without having to rent and haul a power washer?

Dawn dish soap, vinegar, a long handled stiff bristle push broom and your garden hose. That's how I clean mine, quite often. I am in zone 9 with very little humidity, so I don't have to worry about mold.