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Genetic Algorithm for Function Optimization

This repository contains an implementation of a Genetic Algorithm (GA) for optimizing a specific function. The GA is used to minimize the function g(x) by finding the optimal values of the variables x₁ and x₂.

Overview

The goal of this project is to demonstrate the application of a Genetic Algorithm to optimize a given mathematical function. The function to be optimized is defined as:

g(x) = ∑ ([1.5, 2.25, 2.625] - x₁ + x₁ * (x₂^[1, 2, 3]))²

The fitness of an individual is calculated as:

fitness(x) = 1 / (g(x) + 1)

The GA aims to find the values of x₁ and x₂ that minimize the function g(x), thereby maximizing the fitness.

Implementation Details

The code is structured as follows:

  • decode_chromosome: Decodes a binary chromosome into real-valued variables.
  • cross: Performs crossover between two parent individuals to produce offspring.
  • evaluate_individual: Evaluates the fitness of an individual.
  • initialize_population: Initializes a population of individuals randomly.
  • mutate: Performs mutation on an individual.
  • run_function_optimization: Main function that runs the genetic algorithm.
  • tournament_select: Implements tournament selection to select an individual based on fitness.

Parameters

The parameters for the genetic algorithm are specified in the script and include:

  • number_of_runs: Number of runs for the batch experiments.
  • population_size: Number of individuals in the population.
  • maximum_variable_value: Maximum absolute value for the variables.
  • number_of_genes: Number of genes in each chromosome.
  • number_of_variables: Number of variables to be optimized.
  • number_of_generations: Number of generations to run the algorithm.
  • tournament_size: Size of the tournament for selection.
  • tournament_probability: Probability of selecting the better individual in the tournament.
  • crossover_probability: Probability of performing crossover.
  • mutation_probabilities: List of mutation probabilities to be tested.

Usage

  1. Clone the repository:

    git clone https://github.com/Nekros0day/Genetic-Algorithm.git
cd Genetic-Algorithm

  2. Run the script:

    python GA.py

  3. View the results: The script will output the fitness and variable values for each run, and plot the median fitness values as a function of mutation probability.

A plot will be generated showing the median performance as a function of mutation probability.

Dependencies

  • numpy
  • matplotlib

Install the dependencies using:

pip install numpy matplotlib