GEATbx: Tutorial 3 Variable Representation

3 Variable Representation

The first step in deciding which evolutionary algorithm is to use is a close look to the format/representation of your variables. The second step is the direct decision on which format the evolutionary algorithm should work. The representation determines the overall algorithm, that means, the used evolutionary operators.

In the GEATbx 3 different representations are supported:

1. real value representation
2. binary value representation
3. integer value representation

When working with different representations, the toolbox provides functions for conversion between these representations:

• binary to integer (bin2int)
• binary to real (bin2real)

Let's give an example: The variables of the objective function are in real value representation. Now it could be chosen between binary and real value representation for the evolutionary algorithm. Recommended is the real value representation (tbxmpga). It works much quicker than the binary one. However, if the decision comes to use the binary values inside the evolutionary algorithm, the population is initialized as if the variables would be binary (initbp), the evolutionary operators (mutbin and, for instance, xovsp) are applied, and before the evaluation of the objective function the binary values are converted to real values (bin2real).

One more example. In this case the variables are in integer representation. The evolutionary algorithm can work on integer values (mutint and recdis), however, there are no really specialized operators for integer variable representation. Thus, the best decision would be to work with binary values and convert them to integer (bin2int) before evaluation of the objective function.

The use of a representation and necessary conversion is controlled by parameter GOPTIONS(19) of the options structure.

Tab. 3-1: Combinations of variable representation and conversion

EA works on	variable representation	conversion
real	real	-
integer	integer	-
binary	real	bin2real
binary	integer	bin2int
binary	binary	-

In the end it can be stated:

• If the variables of the objective function are real use the real value presentation for the evolutionary algorithm as well.
• If the variables of the objective function are binary use the binary value presentation for the evolutionary algorithm as well.
• If the variables of the objective function are integer use the integer value presentation for the evolutionary algorithm.

Matlab Examples:

Real --- Real:

tbxmpga('objfun1',[],[-5,-5,-5],[5,5,5])

• objfun1 is an objective function using real representation.

Binary --- Binary:

tbxdbin('objone1',[],repmat[0,[1 100]],repmat[1,[1 100]])

• objone1 is an objective function using binary representation

Real --- Binary:

GOPTIONS(19)=1; tbxdbin('objfun1', opt, [-5,-5,-5], [5,5,5])

• objfun1a is another objective function using real representation.
• GOPTIONS(19)=1 determines working on binary representation and convert binary to real before evaluation.

Integer --- Binary:

GOPTIONS(19)=3; tbxdbin('objint2, opt, [0,0,0], [511,1023,255])

• objint2 is an objective function using integer representation.
• GOPTIONS(19)=3 determines working on binary representation and convert binary to integer before evaluation.