Demonstrate when genetic algorithm is used to find the maximum of a function, but encode the design variables x1 and x2 as 8-bit binary numbers instead of 4-bit to achieve higher resolution. Function to be optimized: see photoStart your search with an assumption that x1 and x2 are somewhere between -2 and 2. Carry out the algorithm for a minimum of 5 generations. Provide output along with a list of how the maximum value of y progresses in each generation. The equation presented is as follows:\[ y = 3 + \frac{\exp(-x_1 - x_2^2)}{0.1(x_1 + 3)} \]This equation contains several components:- \( y \) is the dependent variable or the output of the function.- The constant term is \( 3 \).- The fraction denotes a transformation of an exponential function: - The numerator includes the exponential function \( \exp(-x_1 - x_2^2) \), where \( x_1 \) and \( x_2 \) are independent variables. The expression \(-x_1 - x_2^2\) serves as the exponent. - The denominator of the fraction is \( 0.1(x_1 + 3) \), which includes a linear transformation of \( x_1 \).This mathematical expression may be used in mathematical modeling, optimization problems, or data analysis in educational settings to explore interactions between variables or the characteristics of exponential decay.

To simulate the genetic algorithm for optimizing the given function y=3+exp(−x1−x22)+0.1(x1+3)…

Answered: Demonstrate when genetic algorithm is…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Demonstrate when genetic algorithm is used to find the maximum of a function, but encode the design variables x1 and x2 as 8-bit binary numbers instead of 4-bit to achieve higher resolution.
Function to be optimized:

see photo

Start your search with an assumption that x1 and x2 are somewhere between -2 and 2.
Carry out the algorithm for a minimum of 5 generations.
Provide output along with a list of how the maximum value of y progresses in each generation.

The equation presented is as follows:

\[ y = 3 + \frac{\exp(-x_1 - x_2^2)}{0.1(x_1 + 3)} \]

This equation contains several components:

- \( y \) is the dependent variable or the output of the function.
- The constant term is \( 3 \).
- The fraction denotes a transformation of an exponential function:
- The numerator includes the exponential function \( \exp(-x_1 - x_2^2) \), where \( x_1 \) and \( x_2 \) are independent variables. The expression \(-x_1 - x_2^2\) serves as the exponent.
- The denominator of the fraction is \( 0.1(x_1 + 3) \), which includes a linear transformation of \( x_1 \).

This mathematical expression may be used in mathematical modeling, optimization problems, or data analysis in educational settings to explore interactions between variables or the characteristics of exponential decay.

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