y

஺

஻^,

,

൬^߬஺

߬஻

ߠ஺

ߠ஻

ߩ஺

ߩ஻^൰

(8.1)

ual-chromosome crossover is to swap ߠ஺ and

from two elite

ߠ஻

omosomes. A recombination is thus implemented for this dual-

ome crossover. Two new RPN chromosomes generated by this

omosome crossover are shown below, where ࣷଵ and ࣷଶ stand for

new RPN chromosomes,

ࣷଵൌ߬஺ߠ஻ߩ஺

ࣷଶൌ߬஻ߠ஺ߩ஻

(8.2)

equations used for the demonstration are shown below,

൫ሺݔ൅ݕሻݖ൅4ݔݖ൯ݕ

ሺݖሺݔ൅ݕሻ൅3ݕሻݖݔ

RPN chromosomes used for the demonstration of the dual-

ome crossover operation are shown in Figure 8.13. Figure 8.14

eir tree expressions. In a dual-chromosome crossover operation,

nits of RPN expressions (or two subtrees) were selected randomly

swapped. Thus, two new chromosomes were generated.

Fig. 8.13. Two RPN chromosomes for the crossover operation.

are two ways for a dual-chromosome crossover operation after

nits of RPN chromosomes have been selected. The first is to

the branch nodes (two operator tokens from two chromosomes)

es unchanged, but the variables are swapped. The second is to

wap of two whole subtrees, i.e., swapping both variables and