Word Count : 681

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To solve the problem of maximizing \( f(x) = \sqrt{x} \) subject to \( 1 \leq x \leq 25 \) using a genetic algorithm (GA), we can break it down into the following steps: 1. Encoding: Represent the value of \( x \) using a binary string of length 4. The possible range for \( x \) is from 1 to 25, so the binary representation of \( x \) should cover this range. With 4 bits, the maximum number we can represent is 15, which is insufficient for the range of 1 to 25. Hence, we will map the 4-bit binary string to the range \( 1 \leq x \leq 25 \). 2. Initial Population: Generate a population of random binary strings of length 4, representing possible values for \( x \). 3. Fitness Function: __________ ______ ______ ________ _____ _____ __________ _________ ______.
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