Example:
Suppose there is equality a + 2b + 3c + 4d = 30, genetic algorithm will be used to find the value
of a, b, c, and d that satisfy the above equation. First, we should formulate the objective function,
for this problem the objective is minimizing the value of function f(x) where f(x) = ((a + 2b + 3c
+ 4d) - 30). Since there are four variables in the equation, namely a, b, c, and d, we can compose
the chromosome as follow: To speed up the computation, we can restrict that the values of
variables a, b, c, and d are integers between 0 and 30.
Step 1. Initialization
For example, we define the number of chromosomes in population are 6, then we generate
random value of gene a, b, c, d for 6 chromosomes.
Chromosome[1] = [a ;b ;c ;d] = [12 ;05 ;23; 08]
Chromosome[2] = [a ;b ;c ;d] = [02 ;21 ;18 ;03]
Chromosome[3] = [a ;b ;c ;d] = [10 ;04 ;13 ;14]
Chromosome[4] = [a ;b ;c ;d] = [20 ;01 ;10 ;06]
Chromosome[5] = [a ;b ;c ;d] = [01 ;04 ;13 ;19]
Chromosome[6] = [a ;b ;c ;d] = [20 ;05 ;17 ;01]
Step 2. Evaluation
We compute the objective function value for each chromosome produced in initialization step:
F_obj[1] = Abs(( 12 + 2*05 + 3*23 + 4*08 ) - 30) = Abs((12 + 10 + 69 + 32 ) - 30)
= Abs(123 - 30) = 93
F_obj[2] = Abs((02 + 2*21 + 3*18 + 4*03) - 30) = Abs((02 + 42 + 54 + 12) - 30)
= Abs(110 - 30) = 80
F_obj[3] = Abs((10 + 2*04 + 3*13 + 4*14) - 30) = Abs((10 + 08 + 39 + 56) - 30)
= Abs(113 - 30) = 83
F_obj[4] = Abs((20 + 2*01 + 3*10 + 4*06) - 30) = Abs((20 + 02 + 30 + 24) - 30)
= Abs(76 - 30) = 46
