Page 28 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

16 Chapter 1

¾ Order based form
Suppose the requirement is to find the order in which sales man is
traveling among the ‘n’ places such that total distance traveled by that
person is minimum. In this case, the data is the order in which the characters
are arranged. Example data = [a b e f g c]. This type of representation is
called Order based form of representation.
The tree diagram given above summarizes the different type of Genetic
operators. The Examples for every operators are listed below

2.3.1 Simple crossover

Suppose the requirement is to maximize the function f (x, y, z) subject to the
constraints x varies from 0.2 to 0.4, y varies from 0.3 to 0.6 and z varies
from 0.1 to 0.4.
Let the two chromosomes of the current population be C1 and C2
respectively.
Before crossover

C1 = [0.31 0.45 0.11] and C2 = [0.25 0.32 0.3] (say).
After crossover

C1 = [0.3100 0.3200 0.3000]
C2 = [0.2500 0.4500 0.1100]

Simple cross over can also be applied for Binary representation as
mentioned below

Before Crossover

C1 = [‘10101’, ‘01010’,’01011’]
C2 = [‘11111’, ‘01011’, ‘10100’]
After Crossover

C1 = [‘10101’,’01010’,’01100’]
C2 = [‘11111’,’01011’,’10011’]

Note that the crossover point is selected by combining all the binary string
into the single string.
2.3.2 Heuristic crossover

Suppose the requirement is to maximize the function f (x, y, z) subject to the
constraints x varies from 0.2 to 0.4, y varies from 0.3 to 0.6 and z varies
from 0.1 to 0.4.