What is a genetic algorithm in C++ and how is it implemented?

Table of Contents

• Introduction
• Genetic Algorithm in C++
  • How Does a Genetic Algorithm Work?
  • Components of Genetic Algorithm:
  • Example Problem: Maximizing a Function
  • C++ Code for Genetic Algorithm
  • Explanation of the Code
  • Output Example:
  • Key Points:
• Conclusion

Introduction

A genetic algorithm (GA) is a search heuristic inspired by the process of natural selection. It belongs to the class of evolutionary algorithms and is used to solve optimization and search problems by mimicking the principles of biological evolution. Genetic algorithms operate using a population of candidate solutions, evolving them over generations using techniques like selection, crossover, and mutation.

In this article, we'll explain the working of a genetic algorithm and how it is implemented in C++.

Genetic Algorithm in C++

How Does a Genetic Algorithm Work?

A genetic algorithm works by maintaining a population of individuals (candidate solutions) that evolve over time. The process involves the following steps:

1. Initialization: Generate an initial population of potential solutions, usually randomly.
2. Selection: Evaluate the fitness of each individual and select the fittest candidates to be parents for the next generation.
3. Crossover: Combine the genes (characteristics) of two parent individuals to create offspring.
4. Mutation: Introduce random changes to some offspring to maintain genetic diversity.
5. Termination: Repeat the process for a number of generations or until a suitable solution is found.

Components of Genetic Algorithm:

• Population: A set of candidate solutions.
• Fitness Function: A function that evaluates how good a solution is.
• Selection: Process of choosing parents for the next generation.
• Crossover (Recombination): Combining two parents to create offspring.
• Mutation: Introducing random changes to offspring.

Example Problem: Maximizing a Function

We'll implement a genetic algorithm to maximize a simple mathematical function f(x)=−(x2)+5f(x) = -(x^2) + 5f(x)=−(x2)+5, similar to the example used in local search.

C++ Code for Genetic Algorithm

Explanation of the Code

• Individual Structure: Represents an individual in the population with a gene (value of x) and a fitness score (the value of the objective function for that individual).
• Population Initialization: A random population of individuals is created within a specified range.
• Selection: Parents are selected using roulette wheel selection, which is based on fitness. Fitter individuals have a higher chance of being selected.
• Crossover: Two parents create an offspring by averaging their genes (simple crossover).
• Mutation: Random mutations are applied to individuals to introduce diversity.
• Generations: The population evolves over multiple generations, and the best individual is printed at each step.

Output Example:

Key Points:

• The genetic algorithm successfully finds the maximum of f(x)=−(x2)+5f(x) = -(x^2) + 5f(x)=−(x2)+5, which is 5 at x=0x = 0x=0.
• The algorithm demonstrates how the population improves over generations.

Conclusion

Genetic algorithms are powerful tools for solving optimization problems where brute-force solutions are infeasible. They mimic natural selection, allowing solutions to evolve over time using principles like crossover, mutation, and selection. The C++ implementation provided is a basic demonstration, but genetic algorithms can be extended and applied to complex real-world problems like route optimization, scheduling, and machine learning.

By tuning parameters such as population size, mutation rate, and selection method, genetic algorithms can be adapted to various problem domains, making them highly versatile and useful in many fields.