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  1. 123

    A genetic algorithm (GA) is a search heuristic inspired by natural selection. Below is an implementation of a GA in Python to evolve a binary string where all bits are set to 1.

    Steps to Implement the Genetic Algorithm

    1. Initialize Population: Create a random population of binary strings.

    2. Fitness Function: Evaluate how close each individual is to the target (all ones).

    3. Selection: Choose the fittest individuals for reproduction.

    4. Crossover: Combine parents to produce offspring.

    5. Mutation: Introduce random changes to maintain diversity.

    6. Repeat: Iterate until the target is achieved or a maximum number of generations is reached.

    Python Implementation

    import random

    # Parameters
    POPULATION_SIZE = 20
    CHROMOSOME_LENGTH = 10
    MUTATION_RATE = 0.1
    GENERATIONS = 100

    # Generate initial population
    def initialize_population():
    return [[random.randint(0, 1) for _ in range(CHROMOSOME_LENGTH)] for _ in range(POPULATION_SIZE)]

    # Fitness function: Count the number of ones
    def fitness(individual):
    return sum(individual)

    # Selection: Roulette Wheel Selection
    def select(population, fitnesses):
    total_fitness = sum(fitnesses)
    probabilities = [f / total_fitness for f in fitnesses]
    return population[random.choices(range(len(population)), probabilities)[0]]

    # Crossover: Single-point crossover
    def crossover(parent1, parent2):
    point = random.randint(1, CHROMOSOME_LENGTH - 1)
    return parent1[:point] + parent2[point:], parent2[:point] + parent1[point:]

    # Mutation: Flip bits with a certain probability
    def mutate(individual):
    return [bit if random.random() > MUTATION_RATE else 1 - bit for bit in individual]

    # Main Genetic Algorithm Loop
    def genetic_algorithm():
    population = initialize_population()
    for generation in range(GENERATIONS):
    fitnesses = [fitness(ind) for ind in population]
    if max(fitnesses) == CHROMOSOME_LENGTH:
    print(f"Solution found in generation {generation}")
    break

    new_population = []
    for _ in range(POPULATION_SIZE // 2):
    parent1 = select(population, fitnesses)
    parent2 = select(population, fitnesses)
    child1, child2 = crossover(parent1, parent2)
    new_population.extend([mutate(child1), mutate(child2)])

    population = new_population

    # Print the best solution
    best_individual = max(population, key=fitness)
    print("Best Individual:", best_individual)
    print("Fitness:", fitness(best_individual))

    # Run the algorithm
    genetic_algorithm()
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