Let the population of chromosomes in genetic algorithm is represented in terms…
2019
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
\(S f(x) = \dfrac{f(x)}{\Sigma f(x)}\) 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 ________
- A.
24
- B.
576
- C.
14.4
- D.
49.2
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Correct answer: D
Answer: 49.2 (rounded to one decimal place)
Convert binary chromosomes to decimal: 01101 → 13, 11000 → 24, 01000 → 8, 10011 → 19.
Compute fitness f(x)=x^2 for each: 13^2 = 169, 24^2 = 576, 8^2 = 64, 19^2 = 361.
Sum the fitness values: 169 + 576 + 64 + 361 = 1170.
Compute the strength for chromosome (11000): 576 / 1170 = 0.49230769 ≈ 49.23% → rounded to 49.2.
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