Appendix A. NEAT System Parameters

Each population had 256 NEAT networks, for a total of 512. The coefficients for measuring compatibility were $c_1=1.0$, $c_2=1.0$, and $c_3=2.0$. The initial compatibility distance was $\delta_t=3.0$. However, because population dynamics can be unpredictable over hundreds of generations, we assigned a target of 10 species. If the number of species grew above 10, $\delta_t$ was increased by $0.3$ to reduce the number of species. Conversely, if the number of species fell below 10, $\delta_t$ was decreased by $0.3$ to increase the number of species. The normalization factor $N$ used to compute compatibility was fixed at one. In order to prevent stagnation, the lowest performing species over 30 generations old was not allowed to reproduce. The champion of each species with more than five networks was copied into the next generation unchanged. There was an 80% chance of a genome having its connection weights mutated, in which case each weight had a 90% chance of being uniformly perturbed and a 10% chance of being assigned a new random value. (The system is tolerant to frequent mutations because of the protection speciation provides.) There was a 75% chance that an inherited gene was disabled if it was disabled in either parent. In 40% of crossovers, the offspring inherited the average of the connection weights of matching genes from both parents, instead of the connection weight of only one parent randomly. In each generation, 25% of offspring resulted from mutation without crossover. The interspecies mating rate was 0.05. The probability of adding a new node was 0.01 and the probability of a new link mutation was 0.1. We used a modified sigmoidal transfer function, $\varphi(x)=\frac{1}{1+e^{-4.9x}}$, at all nodes. These parameter values were found experimentally, and they follow a logical pattern: Links need to be added significantly more often than nodes, and an average weight difference of 0.5 is about as significant as one disjoint or excess gene. Performance is robust to moderate variations in these values. NEAT software is available in the software section at http://nn.cs.utexas.edu.