Genetic Algorithms(GAs) are adaptive heuristic search algorithms that belong to the larger part of evolutionary algorithms. Genetic algorithms are based on the ideas of natural selection and genetics. These are intelligent exploitation of random searches provided with historical data to direct the search into the region of better performance in solution space. They are commonly used to generate high-quality solutions for optimization problems and search problems.
Genetic algorithms simulate the process of natural selection which means those species that can adapt to changes in their environment can survive and reproduce and go to the next generation. In simple words, they simulate “survival of the fittest” among individuals of consecutive generations to solve a problem. Each generation consists of a population of individuals and each individual represents a point in search space and possible solution. Each individual is represented as a string of character/integer/float/bits. This string is analogous to the Chromosome.
Foundation of Genetic Algorithms
Genetic algorithms are based on an analogy with the genetic structure and behavior of chromosomes of the population. Following is the foundation of GAs based on this analogy -
- Individuals in the population compete for resources and mate
- Those individuals who are successful (fittest) then mate to create more offspring than others
- Genes from the “fittest” parent propagate throughout the generation, that is sometimes parents create offspring which is better than either parent.
- Thus each successive generation is more suited for their environment.
Search space
The population of individuals are maintained within search space. Each individual represents a solution in search space for given problem. Each individual is coded as a finite length vector (analogous to chromosome) of components. These variable components are analogous to Genes. Thus a chromosome (individual) is composed of several genes (variable components).
Fitness Score
A Fitness Score is given to each individual which shows the ability of an individual to “compete”. The individual having optimal fitness score (or near optimal) are sought.
The GAs maintains the population of n individuals (chromosome/solutions) along with their fitness scores.The individuals having better fitness scores are given more chance to reproduce than others. The individuals with better fitness scores are selected who mate and produce better offspring by combining chromosomes of parents. The population size is static so the room has to be created for new arrivals. So, some individuals die and get replaced by new arrivals eventually creating new generation when all the mating opportunity of the old population is exhausted. It is hoped that over successive generations better solutions will arrive while least fit die.
Each new generation has on average more “better genes” than the individual (solution) of previous generations. Thus each new generations have better “partial solutions” than previous generations. Once the offspring produced having no significant difference from offspring produced by previous populations, the population is converged. The algorithm is said to be converged to a set of solutions for the problem.
Operators of Genetic Algorithms
Once the initial generation is created, the algorithm evolves the generation using following operators -
1) Selection Operator: The idea is to give preference to the individuals with good fitness scores and allow them to pass their genes to successive generations.
2) Crossover Operator: This represents mating between individuals. Two individuals are selected using selection operator and crossover sites are chosen randomly. Then the genes at these crossover sites are exchanged thus creating a completely new individual (offspring). For example -
3) Mutation Operator: The key idea is to insert random genes in offspring to maintain the diversity in the population to avoid premature convergence. For example -
The whole algorithm can be summarized as -
1) Randomly initialize populations p
2) Determine fitness of population
3) Until convergence repeat:
a) Select parents from population
b) Crossover and generate new population
c) Perform mutation on new population
d) Calculate fitness for new population
Example problem and solution using Genetic Algorithms
Given a target string, the goal is to produce target string starting from a random string of the same length. In the following implementation, following analogies are made -
- Characters A-Z, a-z, 0-9, and other special symbols are considered as genes
- A string generated by these characters is considered as chromosome/solution/Individual
Fitness score is the number of characters which differ from characters in target string at a particular index. So individual having lower fitness value is given more preference.
C++
// C++ program to create target string, starting from
// random string using Genetic Algorithm
#include <bits/stdc++.h>
using namespace std;
// Number of individuals in each generation
#define POPULATION_SIZE 100
// Valid Genes
const string GENES = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOP"\
"QRSTUVWXYZ 1234567890, .-;:_!\"#%&/()=?@${[]}";
// Target string to be generated
const string TARGET = "I love GeeksforGeeks";
// Function to generate random numbers in given range
int random_num(int start, int end)
{
int range = (end-start)+1;
int random_int = start+(rand()%range);
return random_int;
}
// Create random genes for mutation
char mutated_genes()
{
int len = GENES.size();
int r = random_num(0, len-1);
return GENES[r];
}
// create chromosome or string of genes
string create_gnome()
{
int len = TARGET.size();
string gnome = "";
for(int i = 0;i<len;i++)
gnome += mutated_genes();
return gnome;
}
// Class representing individual in population
class Individual
{
public:
string chromosome;
int fitness;
Individual(string chromosome);
Individual mate(Individual parent2);
int cal_fitness();
};
Individual::Individual(string chromosome)
{
this->chromosome = chromosome;
fitness = cal_fitness();
};
// Perform mating and produce new offspring
Individual Individual::mate(Individual par2)
{
// chromosome for offspring
string child_chromosome = "";
int len = chromosome.size();
for(int i = 0;i<len;i++)
{
// random probability
float p = random_num(0, 100)/100;
// if prob is less than 0.45, insert gene
// from parent 1
if(p < 0.45)
child_chromosome += chromosome[i];
// if prob is between 0.45 and 0.90, insert
// gene from parent 2
else if(p < 0.90)
child_chromosome += par2.chromosome[i];
// otherwise insert random gene(mutate),
// for maintaining diversity
else
child_chromosome += mutated_genes();
}
// create new Individual(offspring) using
// generated chromosome for offspring
return Individual(child_chromosome);
};
// Calculate fitness score, it is the number of
// characters in string which differ from target
// string.
int Individual::cal_fitness()
{
int len = TARGET.size();
int fitness = 0;
for(int i = 0;i<len;i++)
{
if(chromosome[i] != TARGET[i])
fitness++;
}
return fitness;
};
// Overloading < operator
bool operator<(const Individual &ind1, const Individual &ind2)
{
return ind1.fitness < ind2.fitness;
}
// Driver code
int main()
{
srand((unsigned)(time(0)));
// current generation
int generation = 0;
vector<Individual> population;
bool found = false;
// create initial population
for(int i = 0;i<POPULATION_SIZE;i++)
{
string gnome = create_gnome();
population.push_back(Individual(gnome));
}
while(! found)
{
// sort the population in increasing order of fitness score
sort(population.begin(), population.end());
// if the individual having lowest fitness score ie.
// 0 then we know that we have reached to the target
// and break the loop
if(population[0].fitness <= 0)
{
found = true;
break;
}
// Otherwise generate new offsprings for new generation
vector<Individual> new_generation;
// Perform Elitism, that mean 10% of fittest population
// goes to the next generation
int s = (10*POPULATION_SIZE)/100;
for(int i = 0;i<s;i++)
new_generation.push_back(population[i]);
// From 50% of fittest population, Individuals
// will mate to produce offspring
s = (90*POPULATION_SIZE)/100;
for(int i = 0;i<s;i++)
{
int len = population.size();
int r = random_num(0, 50);
Individual parent1 = population[r];
r = random_num(0, 50);
Individual parent2 = population[r];
Individual offspring = parent1.mate(parent2);
new_generation.push_back(offspring);
}
population = new_generation;
cout<< "Generation: " << generation << "\t";
cout<< "String: "<< population[0].chromosome <<"\t";
cout<< "Fitness: "<< population[0].fitness << "\n";
generation++;
}
cout<< "Generation: " << generation << "\t";
cout<< "String: "<< population[0].chromosome <<"\t";
cout<< "Fitness: "<< population[0].fitness << "\n";
}
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Random;
public class GeneticAlgorithm {
// Number of individuals in each generation
private static final int POPULATION_SIZE = 100;
// Valid Genes
private static final String GENES = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ 1234567890, .-;:_!\"#%&/()=?@${[]}";
// Target string to be generated
private static final String TARGET = "I love GeeksforGeeks";
// Function to generate random numbers in given range
private static int randomNum(int start, int end) {
Random rand = new Random();
return rand.nextInt(end - start + 1) + start;
}
// Create random genes for mutation
private static char mutatedGenes() {
int len = GENES.length();
int r = randomNum(0, len - 1);
return GENES.charAt(r);
}
// Create chromosome or string of genes
private static String createGnome() {
int len = TARGET.length();
StringBuilder gnome = new StringBuilder();
for (int i = 0; i < len; i++)
gnome.append(mutatedGenes());
return gnome.toString();
}
// Class representing individual in population
private static class Individual implements Comparable<Individual> {
String chromosome;
int fitness;
Individual(String chromosome) {
this.chromosome = chromosome;
fitness = calFitness();
}
// Perform mating and produce new offspring
Individual mate(Individual par2) {
StringBuilder childChromosome = new StringBuilder();
int len = chromosome.length();
for (int i = 0; i < len; i++) {
// random probability
float p = randomNum(0, 100) / 100f;
// if prob is less than 0.45, insert gene from parent 1
if (p < 0.45)
childChromosome.append(chromosome.charAt(i));
// if prob is between 0.45 and 0.90, insert gene from parent 2
else if (p < 0.90)
childChromosome.append(par2.chromosome.charAt(i));
// otherwise insert random gene(mutate), for maintaining diversity
else
childChromosome.append(mutatedGenes());
}
// create new Individual(offspring) using generated chromosome for offspring
return new Individual(childChromosome.toString());
}
// Calculate fitness score, it is the number of characters in string which differ from target string
private int calFitness() {
int len = TARGET.length();
int fitness = 0;
for (int i = 0; i < len; i++) {
if (chromosome.charAt(i) != TARGET.charAt(i))
fitness++;
}
return fitness;
}
@Override
public int compareTo(Individual o) {
return Integer.compare(this.fitness, o.fitness);
}
}
// Driver code
public static void main(String[] args) {
// current generation
int generation = 0;
List<Individual> population = new ArrayList<>();
boolean found = false;
// create initial population
for (int i = 0; i < POPULATION_SIZE; i++) {
String gnome = createGnome();
population.add(new Individual(gnome));
}
while (!found) {
// sort the population in increasing order of fitness score
Collections.sort(population);
// if the individual having lowest fitness score i.e. 0 then we know that we have reached to the target
// and break the loop
if (population.get(0).fitness <= 0) {
found = true;
break;
}
// Otherwise generate new offsprings for new generation
List<Individual> newGeneration = new ArrayList<>();
// Perform Elitism, that mean 10% of fittest population goes to the next generation
int s = (10 * POPULATION_SIZE) / 100;
for (int i = 0; i < s; i++)
newGeneration.add(population.get(i));
// From 50% of fittest population, Individuals will mate to produce offspring
s = (90 * POPULATION_SIZE) / 100;
for (int i = 0; i < s; i++) {
int len = population.size();
int r = randomNum(0, 50);
Individual parent1 = population.get(r);
r = randomNum(0, 50);
Individual parent2 = population.get(r);
Individual offspring = parent1.mate(parent2);
newGeneration.add(offspring);
}
population = newGeneration;
System.out.print("Generation: " + generation + "\t");
System.out.print("String: " + population.get(0).chromosome + "\t");
System.out.println("Fitness: " + population.get(0).fitness);
generation++;
}
System.out.print("Generation: " + generation + "\t");
System.out.print("String: " + population.get(0).chromosome + "\t");
System.out.println("Fitness: " + population.get(0).fitness);
}
}
# Python3 program to create target string, starting from
# random string using Genetic Algorithm
import random
# Number of individuals in each generation
POPULATION_SIZE = 100
# Valid genes
GENES = '''abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOP
QRSTUVWXYZ 1234567890, .-;:_!"#%&/()=?@${[]}'''
# Target string to be generated
TARGET = "I love GeeksforGeeks"
class Individual(object):
'''
Class representing individual in population
'''
def __init__(self, chromosome):
self.chromosome = chromosome
self.fitness = self.cal_fitness()
@classmethod
def mutated_genes(self):
'''
create random genes for mutation
'''
global GENES
gene = random.choice(GENES)
return gene
@classmethod
def create_gnome(self):
'''
create chromosome or string of genes
'''
global TARGET
gnome_len = len(TARGET)
return [self.mutated_genes() for _ in range(gnome_len)]
def mate(self, par2):
'''
Perform mating and produce new offspring
'''
# chromosome for offspring
child_chromosome = []
for gp1, gp2 in zip(self.chromosome, par2.chromosome):
# random probability
prob = random.random()
# if prob is less than 0.45, insert gene
# from parent 1
if prob < 0.45:
child_chromosome.append(gp1)
# if prob is between 0.45 and 0.90, insert
# gene from parent 2
elif prob < 0.90:
child_chromosome.append(gp2)
# otherwise insert random gene(mutate),
# for maintaining diversity
else:
child_chromosome.append(self.mutated_genes())
# create new Individual(offspring) using
# generated chromosome for offspring
return Individual(child_chromosome)
def cal_fitness(self):
'''
Calculate fitness score, it is the number of
characters in string which differ from target
string.
'''
global TARGET
fitness = 0
for gs, gt in zip(self.chromosome, TARGET):
if gs != gt: fitness+= 1
return fitness
# Driver code
def main():
global POPULATION_SIZE
#current generation
generation = 1
found = False
population = []
# create initial population
for _ in range(POPULATION_SIZE):
gnome = Individual.create_gnome()
population.append(Individual(gnome))
while not found:
# sort the population in increasing order of fitness score
population = sorted(population, key = lambda x:x.fitness)
# if the individual having lowest fitness score ie.
# 0 then we know that we have reached to the target
# and break the loop
if population[0].fitness <= 0:
found = True
break
# Otherwise generate new offsprings for new generation
new_generation = []
# Perform Elitism, that mean 10% of fittest population
# goes to the next generation
s = int((10*POPULATION_SIZE)/100)
new_generation.extend(population[:s])
# From 50% of fittest population, Individuals
# will mate to produce offspring
s = int((90*POPULATION_SIZE)/100)
for _ in range(s):
parent1 = random.choice(population[:50])
parent2 = random.choice(population[:50])
child = parent1.mate(parent2)
new_generation.append(child)
population = new_generation
print("Generation: {}\tString: {}\tFitness: {}".\
format(generation,
"".join(population[0].chromosome),
population[0].fitness))
generation += 1
print("Generation: {}\tString: {}\tFitness: {}".\
format(generation,
"".join(population[0].chromosome),
population[0].fitness))
if __name__ == '__main__':
main()
using System;
using System.Collections.Generic;
using System.Linq;
public class GeneticAlgorithm
{
// Number of individuals in each generation
private const int POPULATION_SIZE = 100;
// Valid Genes
private const string GENES = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOP" +
"QRSTUVWXYZ 1234567890, .-;:_!\"#%&/()=?@${[]}";
// Target string to be generated
private const string TARGET = "I love GeeksforGeeks";
private static readonly Random random = new Random();
// Function to generate random numbers in given range
private static int RandomNum(int start, int end)
{
return random.Next(start, end + 1);
}
// Create random genes for mutation
private static char MutatedGenes()
{
int len = GENES.Length;
int r = RandomNum(0, len - 1);
return GENES[r];
}
// Create chromosome or string of genes
private static string CreateGnome()
{
int len = TARGET.Length;
char[] gnome = new char[len];
for (int i = 0; i < len; i++)
{
gnome[i] = MutatedGenes();
}
return new string(gnome);
}
// Class representing individual in population
private class Individual
{
public string Chromosome { get; }
public int Fitness { get; }
public Individual(string chromosome)
{
Chromosome = chromosome;
Fitness = CalculateFitness();
}
// Calculate fitness score, it is the number of
// characters in string which differ from target string.
private int CalculateFitness()
{
return Chromosome.Zip(TARGET, (a, b) => a == b ? 0 : 1).Sum();
}
// Perform mating and produce new offspring
public Individual Mate(Individual parent2)
{
char[] childChromosome = new char[Chromosome.Length];
for (int i = 0; i < Chromosome.Length; i++)
{
double p = random.NextDouble();
if (p < 0.45)
childChromosome[i] = Chromosome[i];
else if (p < 0.90)
childChromosome[i] = parent2.Chromosome[i];
else
childChromosome[i] = MutatedGenes();
}
return new Individual(new string(childChromosome));
}
}
// Overloading < operator
private class FitnessComparer : IComparer<Individual>
{
public int Compare(Individual ind1, Individual ind2)
{
return ind1.Fitness.CompareTo(ind2.Fitness);
}
}
// Driver code
public static void Main()
{
// current generation
int generation = 0;
List<Individual> population = new List<Individual>();
bool found = false;
// create initial population
for (int i = 0; i < POPULATION_SIZE; i++)
{
string gnome = CreateGnome();
population.Add(new Individual(gnome));
}
while (!found)
{
// sort the population in increasing order of fitness score
population.Sort(new FitnessComparer());
// if the individual having lowest fitness score ie.
// 0 then we know that we have reached the target
// and break the loop
if (population[0].Fitness == 0)
{
found = true;
break;
}
// Otherwise generate new offsprings for new generation
List<Individual> newGeneration = new List<Individual>();
// Perform Elitism, that means 10% of fittest population
// goes to the next generation
int s = (10 * POPULATION_SIZE) / 100;
for (int i = 0; i < s; i++)
newGeneration.Add(population[i]);
// From 50% of fittest population, Individuals
// will mate to produce offspring
s = (90 * POPULATION_SIZE) / 100;
for (int i = 0; i < s; i++)
{
int len = population.Count;
int r = RandomNum(0, 50);
Individual parent1 = population[r];
r = RandomNum(0, 50);
Individual parent2 = population[r];
Individual offspring = parent1.Mate(parent2);
newGeneration.Add(offspring);
}
population = newGeneration;
Console.WriteLine("Generation: " + generation + "\t" +
"String: " + population[0].Chromosome + "\t" +
"Fitness: " + population[0].Fitness);
generation++;
}
Console.WriteLine("Generation: " + generation + "\t" +
"String: " + population[0].Chromosome + "\t" +
"Fitness: " + population[0].Fitness);
}
}
// Number of individuals in each generation
const POPULATION_SIZE = 100;
// Valid Genes
const GENES = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOP" +
"QRSTUVWXYZ 1234567890, .-;:_!\"#%&/()=?@${[]}";
// Target string to be generated
const TARGET = "I love GeeksforGeeks";
// Function to generate random numbers in given range
function RandomNum(start, end) {
return Math.floor(Math.random() * (end - start + 1)) + start;
}
// Create random genes for mutation
function MutatedGenes() {
let len = GENES.length;
let r = RandomNum(0, len - 1);
return GENES.charAt(r);
}
// Create chromosome or string of genes
function CreateGnome() {
let len = TARGET.length;
let gnome = '';
for (let i = 0; i < len; i++) {
gnome += MutatedGenes();
}
return gnome;
}
// Class representing individual in population
class Individual {
constructor(chromosome) {
this.Chromosome = chromosome;
this.Fitness = this.CalculateFitness();
}
// Calculate fitness score, it is the number of
// characters in string which differ from target string.
CalculateFitness() {
let fitness = 0;
for (let i = 0; i < this.Chromosome.length; i++) {
if (this.Chromosome[i] !== TARGET[i]) {
fitness++;
}
}
return fitness;
}
// Perform mating and produce new offspring
Mate(parent2) {
let childChromosome = '';
for (let i = 0; i < this.Chromosome.length; i++) {
let p = Math.random();
if (p < 0.45)
childChromosome += this.Chromosome[i];
else if (p < 0.90)
childChromosome += parent2.Chromosome[i];
else
childChromosome += MutatedGenes();
}
return new Individual(childChromosome);
}
}
// Overloading < operator
class FitnessComparer {
static Compare(ind1, ind2) {
return ind1.Fitness - ind2.Fitness;
}
}
// Driver code
function Main() {
// current generation
let generation = 0;
let population = [];
let found = false;
// create initial population
for (let i = 0; i < POPULATION_SIZE; i++) {
let gnome = CreateGnome();
population.push(new Individual(gnome));
}
while (!found) {
// sort the population in increasing order of fitness score
population.sort((a, b) => FitnessComparer.Compare(a, b));
// if the individual having lowest fitness score ie.
// 0 then we know that we have reached the target
// and break the loop
if (population[0].Fitness === 0) {
found = true;
break;
}
// Otherwise generate new offsprings for new generation
let newGeneration = [];
// Perform Elitism, that means 10% of fittest population
// goes to the next generation
let s = Math.floor((10 * POPULATION_SIZE) / 100);
for (let i = 0; i < s; i++)
newGeneration.push(population[i]);
// From 50% of fittest population, Individuals
// will mate to produce offspring
s = Math.floor((90 * POPULATION_SIZE) / 100);
for (let i = 0; i < s; i++) {
let r = RandomNum(0, 50);
let parent1 = population[r];
r = RandomNum(0, 50);
let parent2 = population[r];
let offspring = parent1.Mate(parent2);
newGeneration.push(offspring);
}
population = newGeneration;
console.log("Generation: " + generation + "\t" +
"String: " + population[0].Chromosome + "\t" +
"Fitness: " + population[0].Fitness);
generation++;
}
console.log("Generation: " + generation + "\t" +
"String: " + population[0].Chromosome + "\t" +
"Fitness: " + population[0].Fitness);
}
// Execute the main function
Main();
Output:
Generation: 1 String: tO{"-?=jH[k8=B4]Oe@} Fitness: 18
Generation: 2 String: tO{"-?=jH[k8=B4]Oe@} Fitness: 18
Generation: 3 String: .#lRWf9k_Ifslw #O$k_ Fitness: 17
Generation: 4 String: .-1Rq?9mHqk3Wo]3rek_ Fitness: 16
Generation: 5 String: .-1Rq?9mHqk3Wo]3rek_ Fitness: 16
Generation: 6 String: A#ldW) #lIkslw cVek) Fitness: 14
Generation: 7 String: A#ldW) #lIkslw cVek) Fitness: 14
Generation: 8 String: (, o x _x%Rs=, 6Peek3 Fitness: 13
.
.
.
Generation: 29 String: I lope Geeks#o, Geeks Fitness: 3
Generation: 30 String: I loMe GeeksfoBGeeks Fitness: 2
Generation: 31 String: I love Geeksfo0Geeks Fitness: 1
Generation: 32 String: I love Geeksfo0Geeks Fitness: 1
Generation: 33 String: I love Geeksfo0Geeks Fitness: 1
Generation: 34 String: I love GeeksforGeeks Fitness: 0
Note: Every-time algorithm start with random strings, so output may differ
As we can see from the output, our algorithm sometimes stuck at a local optimum solution, this can be further improved by updating fitness score calculation algorithm or by tweaking mutation and crossover operators.
Why use Genetic Algorithms
- They are Robust
- Provide optimisation over large space state.
- Unlike traditional AI, they do not break on slight change in input or presence of noise
Application of Genetic Algorithms
Genetic algorithms have many applications, some of them are -
- Recurrent Neural Network
- Mutation testing
- Code breaking
- Filtering and signal processing
- Learning fuzzy rule base etc
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Insertion Sort Algorithm Insertion sort is a simple sorting algorithm that works by iteratively inserting each element of an unsorted list into its correct position in a sorted portion of the list. It is like sorting playing cards in your hands. You split the cards into two groups: the sorted cards and the unsorted cards. T
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Array Data Structure Guide In this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
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Sorting Algorithms A Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
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