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使用简单的遗传算法求解函数的最大值

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人工智能课上学了点遗传算法，记录搓的一段比较简单的实现代码，实现求解
$$
f(x)=xe^{sin(2\pi x)}
$$
在区间 $[0,5]$ 的最大值
(参数和算法设计不一定合理)

计算适应度函数，在此直接以 $f(x)$ 的值作为适应度

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def fitness_function(solution):
    fitness = 0
    for i in range(chromosome_length):
        fitness = fitness + solution[i] * 2**i
    # Return the fitness of a solution
    fitness = fitness/(2**chromosome_length-1)*5
    return fitness*math.exp(math.sin(2*math.pi*fitness))

染色体单点交叉函数

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def one_point_crossover(chromosome1, chromosome2):
    # Select a random crossover point
    crossover_point = random.randint(1, len(chromosome1) - 1)
    # Create two new offspring chromosomes by swapping genetic information
    offspring1 = chromosome1[:crossover_point] + chromosome2[crossover_point:]
    offspring2 = chromosome2[:crossover_point] + chromosome1[crossover_point:]
    # Return the two new offspring chromosomes
    return offspring1, offspring2

参数定义，以及初始化种群

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# Define the genetic algorithm parameters
population_size = 200
chromosome_length = 17
mutation_rate = 0.01
crossover_rate = 0.5
generations = 300

# Initialize the population
population = []
for i in range(population_size):
    chromosome = []
    for j in range(chromosome_length):
        chromosome.append(random.randint(0, 1))
    population.append(chromosome)

算法主体

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import random
import math
# Run the genetic algorithm
for generation in range(generations):
    # Evaluate the fitness of each solution in the population
    fitness_scores = []
    for chromosome in population:
        fitness_scores.append(fitness_function(chromosome))

    # Select the fittest individuals for reproduction
    selected_population = []
    for i in range(population_size//3):
        chromosome1 = random.choices(population, weights=fitness_scores)[0]
        chromosome2 = random.choices(population, weights=fitness_scores)[0]
        selected_population.append(chromosome1)
        selected_population.append(chromosome2)
        if random.random() < crossover_rate:
            offspring1, offspring2 = one_point_crossover(
                chromosome1, chromosome2)
            selected_population.append(offspring1)
            selected_population.append(offspring2)

    # Apply mutations to the selected population
    mutated_population = []
    for chromosome in selected_population:
        for i in range(chromosome_length):
            if random.random() < mutation_rate:
                chromosome[i] = 1 - chromosome[i]
        mutated_population.append(chromosome)

    # Replace the old population with the new population
    population = mutated_population

    # Print the fittest solution for each generation
    print("Generation:", generation, "Fittest solution:", max(fitness_scores))

输出示例（部分）

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Generation: 295 Fittest solution: 11.560699289395993
Generation: 296 Fittest solution: 11.560699289395993
Generation: 297 Fittest solution: 11.560720015712006
Generation: 298 Fittest solution: 11.560790129849646
Generation: 299 Fittest solution: 11.560790129849646

可见准确度在误差允许的范围内