Evolutionary Algorithm README

Overview

This script implements an evolutionary algorithm to optimize a simple fitness function ( f(x, y) = x^2 + y^2 ). The algorithm evolves a population of candidate solutions through selection, crossover, and mutation over multiple iterations.

Prerequisites

Ensure you have Python installed. No additional packages are required for this script.

Script Explanation

Fitness Function

The fitness function ( f(x, y) ) calculates the fitness of an individual based on their ( x ) and ( y ) values:

def f(x, y):
    return x**2 + y**2

Parameters

POP_SIZE: The number of individuals in the population.
NUM_ITER: The number of iterations for the evolutionary algorithm.

Initial Population

The initial population is defined with random ( x ) and ( y ) values between -5 and 5. You can use a predefined population or randomly initialize it:

population = [[1, 2], [-2, 3], [4, -1], [5, 2], [-3, 3]]
# Or use the following for random initialization:
# population = [[random.uniform(-5, 5), random.uniform(-5, 5)] for _ in range(POP_SIZE)]

Evolutionary Process

The script evolves the population over the specified number of iterations (NUM_ITER).

Selection

Parents are selected using binary tournament selection. Two parents are chosen based on their fitness:

p1 = random.choice(population)
p2 = random.choice(population)
parent1 = p1 if f(*p1) > f(*p2) else p2

p1 = random.choice(population)
p2 = random.choice(population)
parent2 = p1 if f(*p1) > f(*p2) else p2

Crossover and Mutation

Four offspring are generated from each pair of parents using crossover and mutation:

Crossover: The ( x ) value from parent 1 and the ( y ) value from parent 2 are combined.
Mutation: With a 50% chance, the ( x ) and ( y ) values are swapped.

child = [parent1[0], parent2[1]]
if random.random() < 0.5:
    child[0], child[1] = child[1], child[0]
offspring.append(child)

Survivor Selection

The population is updated by selecting the best individuals from the offspring based on their fitness:

population = sorted(offspring, key=lambda ind: -f(*ind))[:POP_SIZE]

Output

The script prints the best individual of each generation, showing their ( x ), ( y ) values, and fitness:

print(f"Best individual in iteration {iter+1}: x = {bestIndividual[0]}, y = {bestIndividual[1]}, fitness = {f(*bestIndividual)}")

Running the Script

Save the script to a Python file, e.g., evolutionary_algorithm.py.
Open a terminal or command prompt.
Navigate to the directory containing evolutionary_algorithm.py.
Run the script:

python evolutionary_algorithm.py

Ali11502/evolutionary_algorithm