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).
- On the left we have the best packing so far. The small light-blue area indicates how much we improved on the first solve.
- The second plot shows the objective function value of each solve. The red line is the best objective so far.
- 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.
- The last plot shows these probabilities in a different format. The trend is downhill, but not uniformly so.