As expected the improved training technique made the task of evolving suitable programs easier. This can be seen in Figure 1 which plots the estimated minimum number of individuals that the GP with a population size of 500 needs to create in order to have a probability of at least 99% of finding at least one solution. (This is known as ``Effort'' required, cf. [Koza1992, page 194,]).
Figure 1:
Effort v. no. food pellets ahead the ant can see and eat.
Error bars indicate estimates given by one standard deviation above
and below minimum measured figure.
Original Santa Fe trail always allows all 89 food pellets to be seen.
Figure 2 plots effort calculated from 50 runs (or 100 for x=89, size limit=200) for the original Santa Fe trail and the same trail but with x set to five. No run found any of the very smallest solutions (of length 11). Considering first the original problem, the minimium estimate for the Effort is 189,000 and occurs with a size limit of 100 however values for 25--100 seem similar at about two thirds of the Effort required when no size limit is imposed. Also Effort values for size limits of 200--500 appear to be much the same as when there is no size limit. Now considering the case where food is only placed on the grid as the ant approaches it in along the trail (i.e. x=5), the minimium estimate for the Effort is 104,000 and occurs with a size limit of 50 however values for 25--100 seem similar at about 80% of the Effort required when no size limit is imposed. Again Effort values for size limits of 200--500 appear to be much the same as with no size limit.
Figure:
Effort v. maximium program size (11, 18, 25, 50, 64, 100, 200, 300,
400 and 500) for original Santa Fe trail and ant restructed to load
ahead of 5.
(For comparison, cf. Figure 1,
values for runs without a size restriction are plotted at 600).
Error bars indicate estimates given by one standard deviation above
and below minimum measured figure.
Changing amount of food on the trail has no obvious effect on the size of solutions.