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most cases, larger than the means. We have also calculated the analogous statis-
tics for problems #3 and #4 (see tables 3 and 4), but because of the large spread
of these distributions they are probably not the most meaningful statistics to
quote. To provide more detailed information, in figures 4,5 and 6 we have plotted
bar charts displaying the number of times (runs) out of 100 that the BCA or a
variant converged in a given number of steps (function evaluations).
60
BCA
Mega Mutation 1
Mega Mutation 2
Anti Elitism
50
40
30
20
10
0
0
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
4
x 10
5
Number of Evaluations
Fig. 4.
Barchartforproblem#2
Table 3.
Number of fitness evaluations (mean and standard deviation) for problem #3
Algorithm:
BCA #1 #2 #3
Mean Fitness Evaluations
×
10
6
2.4 2.1 2.1 0.57
Standard Deviation
×
10
6
3.1 2.5 2.6 0.67
Table 4.
Number of fitness evaluations (mean and standard deviation) for problem #4
Algorithm:
BCA #1 #2 #3
10
7
Mean Fitness Evaluations
×
4.0 6.3 5.3 3.9
Standard Deviation
×
10
7
4.9 2.6 3.0 3.2
Since the megamutations provide a method of dealing with local optima, which
the original BCA does not have, the algorithms with megamutation are less likely
to remain stuck for long periods of time and thus can reduce the number of eval-
uations needed. The higher number of evaluations needed by the megamutation
algorithms for equation 4 can be explained as follows: when the original BCA
