Fig 7. Discovering suppressors for uniform initialization.
When seeking to minimize the ratio ρ′/ρ∘, the genetic algorithm produced structures consisting of a well-connected part and a tail. We compared these to Lollipop graphs (known for their random walk properties [51–53]), and two new families, which we call Balloons and Balloon-Stars. The minimal ρ′ from these families improved on the genetic algorithm results for N = 12, 13, 14 (albeit by less than 10−4 for N = 14), and matched the genetic algorithm results for N = 11 and N = 15.