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Table 3.3 Performance of enzyme GP with different operators.
Operator
Average
Success
CE
Two-bit multiplier, bounds 12-16, pop. 324
Uniform
118
77%
136,080
TR
76
75%
169,128
Mutation
94
56%
334,368
Two-bit adder, bounds 10-20, pop. 324
Uniform
113
74%
244,620
TR
107
57%
340,200
Mutation
114
53%
392,364
Even-three-parity, bounds 5-10, pop. 100
Uniform
54
43%
79,000
TR
47
32%
96,000
Mutation
40
7%
250,800
Even-four-parity, bounds 10-25, pop. 625
Uniform
150
25%
2,588,750
TR
165
24%
2,703,125
Mutation
154
36%
1,830,000
viable length. Second, uniform crossover is more disruptive than TR crossover
because it targets multiple sections of the genome and always causes genes to be
replaced rather than appended. Consequently, it is able to explore a larger region
of the search space during a run. Conversely, TR crossover prefers exploitation
of existing genetic material to exploration of new material and, accordingly, is
perhaps able to carry out a more structured search and reach the optimum in
less generations.
The adder, multiplier, and even-four-parity problems have been solved by
Miller [29] using Cartesian GP [28], a graph-based genetic programming sys-
tem. Results from Koza [15, 16], using tree-based GP, are available for both
parity problems. Koza [16] has also attempted the 2-bit adder problem, but
quantitative results are not available. Miller records minimum computational
effort of between 210,015 and 585,045 for the 2-bit multiplier problem. Enzyme
GP, requiring a minimum computational effort of 136,080 for a population of
324, compares favorably with these results. For the 2-bit adder problem, Miller
cites a minimum computational effort of 385,110. For enzyme GP, using the
same functions as Miller, mimimum effort is 244,620.
Koza has evolved even-
n
-parity circuits using populations of size 4000
[16] and 16,000 [15]. For the even-three-parity problem (and without using
Automatically Defined Functions [ADFs]), this gives minimum computational
efforts of 80,000 and 96,000 respectively. For the even-four-parity problem,
