ly be mutated to another available variable which is available

an an operator. If it is mistakenly mutated by an operator +, the

system is ill-conditioned as shown in Figure 8.9(a), where the

ly mutated token is shown in the box with the dark box. It can be

this tree does not represent a proper equation. Parsing the RPN

r this tree will encounter an error. Figure 8.9(b) shows another

ere an operator (+) as the eighth token of the RPN shown in the

nel of Figure 8.7 is wrongly mutated to a variable x. The

ly mutated token is shown in the box with the dark box. Certainly,

ee on the right side in Figure 8.9(b) is also an ill-conditioned tree

conditioned RPN string.

(a) (b)

) The tree of wrongly mutated type (from the variable x to the operator +) for

hown in a tree shown in Figure 8.8(a). (b) The tree of wrongly mutated type

perator + to the variable x) for the RPN shown in a tree shown in Figure 8.8(a).

fore, both the mutation operator and the crossover operator must

ully designed for handling RPN strings when they are used for

new chromosomes in a GP model. In an RPN chromosome, it is

t to know in advance how many token styles have been employed.

y, there are three types of tokens. They are the constants, the

and the operators. In a complex system, where one operator may

d to a varying number of variables, the brackets will be used. For

the RPN string xyz**uv*+w/ can be used for the following

However, an efficient way for this equation is to use the brackets,

akes the evaluation of such an RPN string much easier and