N-Queens Genetic Algorithm

An implementation of the N-Queens problem using a Genetic Algorithm (GA) to find valid solutions for different board sizes.

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📝 Table of Contents

• Features
• Prerequisites
• Usage
• Algorithm Overview
• Technical Implementation

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✨ Features

• Scalable Solution: Supports customizable N×N board sizes.
• Genetic Algorithm Optimization:
  • Implements selection, crossover, and mutation techniques.
  • Prioritizes valid solutions with minimal computation.

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📋 Prerequisites

• Python 3.7 or higher
• NumPy

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💻 Usage

Run the program to solve the N-Queens problem:

python n_queens_ga.py

Follow the prompts to:

1. Set the board size (e.g., N = 8 for an 8x8 chessboard).
2. Choose Genetic Algorithm parameters (mutation rate, population size, etc.).

Output:

• Prints the solved board in a matrix format.

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🔧 Algorithm Overview

• Selection: Chooses the fittest individuals based on a fitness function that minimizes conflicts.
• Crossover: Combines parent solutions to produce offspring.
• Mutation: Introduces randomness to explore diverse solutions.
• Fitness Evaluation: Calculates the number of conflicts for each solution and prioritizes the least conflicting ones.

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🔬 Technical Implementation

Key Functions:

• Initialization:

  def initialize_population(size, n):
      return [random_permutation(n) for _ in range(size)]

• Fitness Function: Evaluates the number of queens attacking each other.

  def calculate_fitness(board):
      # Counts row, column, and diagonal conflicts

• Crossover and Mutation: Introduces variety and combines solutions to find optimal configurations.