#3 ### Using Genetic Algorithms to Optimize Functions#### Problem StatementUse a Genetic Algorithm to find the value of \( x \) that maximizes the function:\[ f(x) = \sin\left(\frac{x \pi}{256}\right) \]given that \( x \) is an integer in the interval \( 0 \leq x \leq 255 \).#### DetailsAssume that a binary representation for the chromosome is used. Determine which one of the following binary representations is a valid chromosome at random:1. \( 01001 \)2. \( 0100101 \)3. \( 11001101 \)4. \( 1010101010 \)#### AnalysisWhen using genetic algorithms, chromosomes are typically represented in binary to encode the possible values of \( x \). The binary length of the chromosome must be sufficient to represent all values within the given interval \( 0 \leq x \leq 255 \). Since 255 is represented as \( 11111111 \) in binary, exactly 8 bits are required.Considering this requirement:- \( 01001 \) (5 bits, insufficient)- \( 0100101 \) (7 bits, insufficient)- \( 11001101 \) (8 bits, valid length)- \( 1010101010 \) (10 bits, more than sufficient but not necessary)Thus, the correct chromosome in random among the given options is:**Option 3: \( 11001101 \)**

We have to discuss Use a Genetic Algorithm to find the value of x that maximizes.

Use a Genetic Algorithm to find the value of x that maximizes XTC f(x) = sin( in the interval 0 ≤ x ≤ 255 256. where x is restricted to being an integer. Assume that a binary representation for the chromosome is used. Which one is the correct chromosome in random? 01001 0100101 11001101 1010101010

Use a Genetic Algorithm to find the value of x that maximizes XTC f(x) = sin( in the interval 0 ≤ x ≤ 255 256. where x is restricted to being an integer. Assume that a binary representation for the chromosome is used. Which one is the correct chromosome in random? 01001 0100101 11001101 1010101010