The two graphs in figure 3.4 show the percentage of
real improvement for the SMART and RANDOM recombination
operators across 3 domains. Real improvement can generally be thought
of as an instance where a main population program is measured to be
more fit after recombination than before. In all three of the domains
over which these graphs were averaged, the fitness values (for main
population programs) ranged from - 
to + 
where a
fitness of 0 could be achieved by random guessing on the part of the
programs. In such a case, real improvement caused by a SMART operator
can more accurately be thought of as instances in which a program is
measured to be more fit after recombination than before and in which
its new fitness is greater than 0. Figure 3.4 shows
the percentage of the time that this happened.
Figure 3.4: Tracking recombination-operator real improvement percentage across generations (in MAIN and ADF graphs).
Figure 3.4 shows percentage real improvements, not operator fitness as defined in section 3.4.5. The reason for this is two-fold. Because these graphs are averaged across 3 domains, both the absolute and relative changes in main population fitness (two of the factors in operator fitness) vary widely between domains. These varied absolute and relative fitnesses tend to make the graphs less readable and less meaningful without detailed information about the absolute and relative fitness dynamics in each of the domains.
These graphs are averaged over five runs in each of the three domains, all of which used SMART operators as the recombination strategy. In each run the average SMART operator real improvement was taken from the actual recombination phase. The random recombination operator was applied to the same population on each generation and its average improvement measured on this temporary new population. Then, this random operator-generated main population was discarded and the next population began.
The question is ``Can SMART recombination operators learn (co-evolve) to produce a higher percentage of real improvements per recombination than the random recombination strategy over a range of domains?'' If they can, and we can show it, we will have taken an important step towards showing the general usefulness of the SMART operator paradigm.
As can be seen from the MAIN graph in figure 3.4, the power of the SMART operators seems to come from their increased ability to produce improvements when performing recombination in the MAIN program. This may be because there are strategies for good recombination which are simply easier to learn for the MAIN program graphs than for the ADF program graphs. Interestingly, both SMART and RANDOM recombination are considerably more likely to improve a program by performing recombination on its ADF than on its MAIN program. While it is tempting to guess that this higher real improvement percentage happens because most ADFs are simply unused and a program's fitness may simply be measured higher next generation, this turns out not to be the case. In these runs, about 80% of the main population programs actually used their ADF. Figure 3.4, then, suggests that the rate (or even maximum height) of evolution might be raised by doing recombination more often on the ADFs than on the MAIN program graphs. Since this was not the focus of research here, the experiments mentioned all performed recombination on the MAIN and ADF programs equally often.