Wednesday, May 16, 2018

Overdoing a plot

Lots of things are going on here. This is a visualization of a packing problem: place 50 circles in a square that is as small as possible, Things are solved by 50 solves by SNOPT with a random starting point (i,e, a multi-start approach).

  1. On the left we have the best packing so far. The small light-blue area indicates how much we improved on the first solve.
  2. The second plot shows the objective function value of each solve. The red line is the best objective so far.
  3. The density plot shows the probability of a better solution out there. Just using a normal distribution. The blue area is the probability. The blue area is the tail area corresponding to the red line in the second picture.
  4. The last plot shows these probabilities in a different format. The trend is downhill, but not uniformly so.
I went a bit overboard with my ggplot scripts....