Genetic Algorithm – Sum of Squares Minimization

This project implements a Genetic Algorithm (GA) in Python to minimize the mathematical function:

[ f(x) = sum(xi ^ 2) ]

The goal is to find the vector x where each element is close to 0, which minimizes the overall sum of squares.

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🧠 Algorithm Overview

This GA uses the following steps:

• Initialization: Random population within the domain [-5.12, 5.12]
• Selection: Binary tournament selection
• Crossover: Single-point crossover with 80% probability
• Mutation: Random mutation with 20% probability
• Evaluation: Fitness = sum of squares

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⚙️ How to Run

Make sure you have Python and matplotlib installed. Then run:

python ga_sum_of_squares.py

A plot will be saved to:

genetic/output_plot.png

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🔧Parameters

You can customize these parameters at the bottom of the script:

POP_SIZE = 50          # Number of individuals in the population
LOWER_BOUND = -5.12    # Minimum value of each gene
UPPER_BOUND = 5.12     # Maximum value of each gene
GENERATIONS = 100      # Number of generations
NUM_VARIABLES = 5      # Number of genes in each chromosome

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📈Sample Output

in generation 100 --> the best fitness in each section: 0.0008, the best chromosome in each section: [0.0031, -0.0012, 0.0005, 0.0007, -0.0020]

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