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Previous Year Question (PYQs)

. Let the population of chromosomes in genetic algorithm is represented in terms of binary number. The strength of fitness of a chromosome in decimal form, $x$, is given by

$Sf(x)=\dfrac{f(x)}{\sum f(x)}$ where $f(x)=x^2$

The population is given by $P$ where:

$P={(01101),(11000),(01000),(10011)}$

The strength of fitness of chromosome $(11000)$ is $...............$





Solution

Convert chromosomes into decimal form:

$(01101)_2=13$

$(11000)_2=24$

$(01000)_2=8$

$(10011)_2=19$

Now calculate $f(x)=x^2$

For $13$:

$f(13)=13^2=169$

For $24$:

$f(24)=24^2=576$

For $8$:

$f(8)=8^2=64$

For $19$:

$f(19)=19^2=361$

Now,

$\sum f(x)=169+576+64+361=1170$

Strength of fitness for chromosome $(11000)$:

$Sf(24)=\dfrac{576}{1170}$

$Sf(24)=0.4923$

In percentage:

$0.4923\times 100=49.23%\approx 49.2$


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