1 Hypothesis

The increase in instance difficulty makes it more difficult to find good programs, and, when the population converges, to find one or more similarly good (optimal or sub-optimal) programs as well. In the case of easier instances, entropy decreases when the population converges toward individuals with the same optimal (or sub-optimal) fitness. In harder instances, the lack of this behaviour causes higher entropy, which does not decrease as quickly, maintaining higher selection pressure. This non-decreased selection pressure is hypothesised as a cause of more code growth and less diversity, which also causes more code growth. This hypothesis of the causal relationship between difficulty, entropy, diversity and growth is shown in Figure 6.9. The experiments show evidence of higher entropy, less genetic diversity and a higher rate of code growth for harder instances. Supporting evidence for the conjectures that higher selection pressure and lower diversity cause an increased rate of code growth is now given.