This document describes how genetic algorithms work through an example. It shows three iterations of a genetic algorithm optimizing a function y=x1-x2, where x1 and x2 are integers between 0-7 and 0-3 respectively. In each iteration, the algorithm calculates the y value for different combinations of x1 and x2. The best solutions are used to generate the values for the next iteration, getting closer to the highest y value each time.

1. Genetik Algoritma
Nasıl Çalışır?
Emre Akadal

2. y = x1 – x2
20.2.2015 2
ymax = ?
x1 x2≤ 70 ≤ ≤ 30 ≤

3. 20.2.2015 3
x1 ≤ 70 ≤
x1 = 0, 1, 2, 3, 4, 5, 6, 7
(x1)min = (0)10 = (0)2
(x1)max = (7)10 = (111)2
x2 ≤ 30 ≤
x2 = 0, 1, 2, 3
(x2)min = (0)10 = (0)2
(x2)max = (3)10 = (11)2
10101

4. 20.2.2015 4
0 1 0 1 1
1 0 1 1 0
1 1 0 1 1
0 1 1 1 0
0 0 0 0 1
1 0 1 1 1
0 1 1 0 1
0 0 0 1 0
0 1 0 0 0
0 0 0 0 1
X1 = 2 x2 = 3 y = -1
X1 = 5 x2 = 2 y = 3
X1 = 6 x2 = 3 y = 3
X1 = 3 x2 = 2 y = 1
X1 = 0 x2 = 1 y = -1
X1 = 5 x2 = 3 y = 2
X1 = 3 x2 = 1 y = 2
X1 = 0 x2 = 2 y = -2
X1 = 2 x2 = 0 y = 2
X1 = 0 x2 = 1 y = -1

5. 20.2.2015 5
0 1 0 1 1
1 0 1 1 0
1 1 0 1 1
0 1 1 1 0
0 0 0 0 1
1 0 1 1 1
0 1 1 0 1
0 0 0 1 0
0 1 0 0 0
0 0 0 0 1




1 0 1 1 0 = 3
0 1 1 1 0 = 1
0 0 0 1 0 = - 2
0 1 0 0 0 = 2
1 0 1 1 0
0 1 0 0 0
1 0 0 0 0
1 0 1 1 0
0 1 0 0 0
1 0 1 1 0
0 1 0 0 0
1 1 0 0 0

6. 20.2.2015 6
1 0 1 1 0
1 1 0 1 1
1 0 0 0 0
1 1 0 0 0
1 1 0 0 0
1 1 0 1 0
1 0 1 1 1
1 1 0 1 1
1 1 1 1 0
1 0 1 1 0
X1 = 5 x2 = 2 y = 3
X1 = 6 x2 = 3 y = 3
X1 = 4 x2 = 0 y = 4
X1 = 6 x2 = 0 y = 6
X1 = 6 x2 = 0 y = 6
X1 = 6 x2 = 2 y = 4
X1 = 5 x2 = 3 y = 2
X1 = 6 x2 = 3 y = 3
X1 = 6 x2 = 2 y = 4
X1 = 5 x2 = 2 y = 3

7. 20.2.2015 7
1 1 0 0 0
1 1 0 0 0
1 0 1 1 0
1 0 0 0 0
1 0 0 0 0
1 1 0 0 0
1 1 0 1 1
1 1 0 1 1
1 1 0 0 0
1 1 1 0 0
X1 = 6 x2 = 0 y = 6
X1 = 6 x2 = 0 y = 6
X1 = 5 x2 = 2 y = 3
X1 = 4 x2 = 0 y = 4
X1 = 4 x2 = 0 y = 4
X1 = 6 x2 = 0 y = 6
X1 = 6 x2 = 3 y = 3
X1 = 6 x2 = 3 y = 3
X1 = 6 x2 = 0 y = 6
X1 = 7 x2 = 0 y = 7

8. 20.2.2015 8
iterasyon #1
y = -1
y = 3
y = 3
y = 1
y = -1
y = 2
y = 2
y = -2
y = 2
y = -1
iterasyon #2
y = 3
y = 3
y = 4
y = 6
y = 6
y = 4
y = 2
y = 3
y = 4
y = 3
iterasyon #3
y = 6
y = 6
y = 3
y = 4
y = 4
y = 6
y = 3
y = 3
y = 6
y = 7

9. 11100
y = 7
20.2.2015 9
x1 = (111)2 = 7
x2 = (00)2 = 0