Algorithm to separate circles to reduce collision the maximum between them
If you want to brute force it, this is a constrained optimization problem where the quantity you're minimizing is the overlap area, the variables are the x and y coordinates of each circle's center, and the constraints are that each center lies within a red circle.

Depending on how you want to count areas inside three or more circles, the formula for the overlap arra can be reasonably simple or a huge mess that gets worse with the number of circles.