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X value(Initial Population) 13 24 8 16 Initial population Representation as binary String 01101 fx=x² 169 f(x)/ sum of all f(x) =169/1065-0.16 Roulette Wheel (Portion that covers Each X) 16%

X value(Initial Population) 13 24 8 16 Initial population Representation as binary String 01101 fx=x² 169 f(x)/ sum of all f(x) =169/1065-0.16 Roulette Wheel (Portion that covers Each X) 16%

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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### Genetic Algorithm - Initial Population and Roulette Wheel Selection This table illustrates an example of the selection process in a genetic algorithm, specifically focusing on the representation of an initial population, their fitness values, and how selection might be visualized through a roulette wheel. | X value (Initial Population) | Initial Population Representation as Binary String | \( f_x = x^2 \) | \( \frac{f(x)}{\text{sum of all } f(x)} \) | Roulette Wheel (Portion that covers Each X) | |------------------------------|----------------------------------------------------|-----------------|------------------------------------------|---------------------------------------------| | 13 | 01101 | 169 | \(\frac{169}{1065} = 0.16\) | 16% | | 24 | | | | | | 8 | | | | | | 16 | | | | | ### Explanation of Columns: 1. **X value (Initial Population)**: This column lists the initial population values, which are candidates for genetic algorithm processing. 2. **Initial Population Representation as Binary String**: Each initial population value is represented in binary format. This encoding is crucial for operations in genetic algorithms such as crossover and mutation. 3. **\( f_x = x^2 \)**: This is the fitness function used to evaluate each candidate in the population. For this example, the fitness function is \( f(x) = x^2 \), where each candidate's fitness value is the square of its initial population value. 4. **\( \frac{f(x)}{\text{sum of all } f(x)} \)**: This column represents the normalized fitness value. Each fitness value is divided by the sum of all fitness values in the population to determine the proportionate contribution of each candidate. 5. **Roulette Wheel (Portion that covers Each X)**: This column shows the percentage portion of the roulette wheel corresponding to each candidate, which is used for selection in the genetic algorithm. The portion is calculated based on the normalized fitness values. ### Example: For the first entry: - The X value is 13. - Its binary representation is 01101. - Using the fitness function \( f(x) = x^2 \), we get a fitness value of \( 13^2 = 169 \). - The normalized fitness value is \( \frac{169
Transcribed Image Text:### Genetic Algorithm - Initial Population and Roulette Wheel Selection This table illustrates an example of the selection process in a genetic algorithm, specifically focusing on the representation of an initial population, their fitness values, and how selection might be visualized through a roulette wheel. | X value (Initial Population) | Initial Population Representation as Binary String | \( f_x = x^2 \) | \( \frac{f(x)}{\text{sum of all } f(x)} \) | Roulette Wheel (Portion that covers Each X) | |------------------------------|----------------------------------------------------|-----------------|------------------------------------------|---------------------------------------------| | 13 | 01101 | 169 | \(\frac{169}{1065} = 0.16\) | 16% | | 24 | | | | | | 8 | | | | | | 16 | | | | | ### Explanation of Columns: 1. **X value (Initial Population)**: This column lists the initial population values, which are candidates for genetic algorithm processing. 2. **Initial Population Representation as Binary String**: Each initial population value is represented in binary format. This encoding is crucial for operations in genetic algorithms such as crossover and mutation. 3. **\( f_x = x^2 \)**: This is the fitness function used to evaluate each candidate in the population. For this example, the fitness function is \( f(x) = x^2 \), where each candidate's fitness value is the square of its initial population value. 4. **\( \frac{f(x)}{\text{sum of all } f(x)} \)**: This column represents the normalized fitness value. Each fitness value is divided by the sum of all fitness values in the population to determine the proportionate contribution of each candidate. 5. **Roulette Wheel (Portion that covers Each X)**: This column shows the percentage portion of the roulette wheel corresponding to each candidate, which is used for selection in the genetic algorithm. The portion is calculated based on the normalized fitness values. ### Example: For the first entry: - The X value is 13. - Its binary representation is 01101. - Using the fitness function \( f(x) = x^2 \), we get a fitness value of \( 13^2 = 169 \). - The normalized fitness value is \( \frac{169
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