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Note that after 150 generations the success rate practically reached the
maximum value for both systems. As expected, the performance, measured
exclusively in terms of success rate, is superior for the system with bigger
populations. However, if we compare the CPU time required for each system
we will see that the 50-chromosome system is more efficient. For instance,
100 runs of 150 generations take 1'30'' for the 50-chromosome system and
3'55'' for populations of 250 individuals. However, if we disable the stop
criterion (i.e., the system does not stop when a perfect solution is found) and
let the system go through all of the 150 generations, we obtain the values of
4'14'' for populations of 50 individuals and 29'42'' for populations of 250
individuals. This is no idle comparison as in real-world problems perfect
solutions (i.e., solutions with 0% or 0.01% of error) do not usually exist and,
consequently, the system does not stop before completing the stipulated
number of generations.
In summary, in gene expression programming, as long as mutation is used,
it is advantageous to use small populations of 30-100 individuals for they
allow an efficient evolution in record time.
These facts are further supported by the second experiment where only
recombination was used as source of genetic diversity (Figure 12.14). The
types of recombination used in this experiment and their rates are shown in
the second column of Table 12.6.
100
90
80
70
HP50
HP250
60
50
40
30
20
10
0
0
25
50
75
100
125
150
175
200
225
250
275
300
Number of generations
Figure 12.14.
Variation of success rate with evolutionary time for homogenizing
populations of 50 (HP50) and 250 individuals (HP250). The success rate was
evaluated over 100 identical runs.
