一个简单的遗传算法

代码

import random


class GeneticAlgorithm:
    def __init__(self, population_size, chromosome_length, mutation_rate, generations):
        """
        初始化遗传算法参数
        :param population_size: 种群大小
        :param chromosome_length: 染色体长度（二进制编码位数）
        :param mutation_rate: 变异概率
        :param generations: 迭代次数
        """
        self.pop_size = population_size
        self.chromo_len = chromosome_length
        self.mutation_rate = mutation_rate
        self.generations = generations
        self.population = []

        # 初始化种群
        self.initialize_population()

    def initialize_population(self):
        """生成随机的二进制编码种群"""
        self.population = [
            ''.join(random.choice('01') for _ in range(self.chromo_len))
            for _ in range(self.pop_size)
        ]

    @staticmethod
    def decode(binary_str, search_min=0, search_max=15):
        """将二进制字符串解码为实际数值"""
        int_val = int(binary_str, 2)
        return search_min + (int_val / (2 ** len(binary_str) - 1)) * (search_max - search_min)

    def fitness_function(self, x):
        """适应度函数（值越小越好，这里取倒数）"""
        return 1 / (x ** 2 + 1e-6)  # 避免除以0

    def tournament_selection(self, tournament_size=3):
        """锦标赛选择"""
        selected = []
        for _ in range(self.pop_size):
            # 随机选择 tournament_size 个个体进行竞争
            competitors = random.sample(list(zip(self.population, self.fitness_scores)), tournament_size)
            # 选择适应度最高的（因为我们的适应度函数是倒数）
            winner = max(competitors, key=lambda x: x[1])[0]
            selected.append(winner)
        return selected

    def crossover(self, parent1, parent2):
        """单点交叉"""
        point = random.randint(1, self.chromo_len - 1)
        child1 = parent1[:point] + parent2[point:]
        child2 = parent2[:point] + parent1[point:]
        return child1, child2

    def mutate(self, individual):
        """按位变异"""
        mutated = list(individual)
        for i in range(len(mutated)):
            if random.random() < self.mutation_rate:
                mutated[i] = '0' if mutated[i] == '1' else '1'
        return ''.join(mutated)

    def run(self):
        """执行遗传算法"""
        for gen in range(self.generations):
            # 计算适应度
            self.fitness_scores = [
                self.fitness_function(self.decode(ind))
                for ind in self.population
            ]

            # 选择
            selected = self.tournament_selection()

            # 交叉生成新种群
            new_population = []
            for i in range(0, self.pop_size, 2):
                parent1 = selected[i]
                parent2 = selected[i + 1] if i + 1 < self.pop_size else selected[0]
                child1, child2 = self.crossover(parent1, parent2)
                new_population.extend([child1, child2])

            # 变异
            self.population = [self.mutate(ind) for ind in new_population[:self.pop_size]]

            # 跟踪最佳解
            best_ind = max(zip(self.population, self.fitness_scores), key=lambda x: x[1])
            best_x = self.decode(best_ind[0])
            print(f"Generation {gen + 1}: Best x = {best_x:.4f}, f(x) = {best_x ** 2:.4f}")

        # 返回最终结果
        best_ind = max(zip(self.population, self.fitness_scores), key=lambda x: x[1])
        return self.decode(best_ind[0])


# 参数设置
ga = GeneticAlgorithm(
    population_size=20,  # 种群大小
    chromosome_length=8,  # 二进制编码位数（精度更高）
    mutation_rate=0.01,  # 变异概率
    generations=30  # 迭代次数
)

# 运行算法
best_solution = ga.run()
print(f"\nOptimal Solution: x = {best_solution:.4f}, f(x) = {best_solution ** 2:.4f}")

输出示例

Generation 1: Best x = 1.4118, f(x) = 1.9931
Generation 2: Best x = 3.7647, f(x) = 14.1730
Generation 3: Best x = 0.5294, f(x) = 0.2803
Generation 4: Best x = 0.2941, f(x) = 0.0865
Generation 5: Best x = 0.1765, f(x) = 0.0311
Generation 6: Best x = 0.0000, f(x) = 0.0000
Generation 7: Best x = 0.0000, f(x) = 0.0000
Generation 8: Best x = 0.0000, f(x) = 0.0000
Generation 9: Best x = 3.7647, f(x) = 14.1730
Generation 10: Best x = 0.0000, f(x) = 0.0000
Generation 11: Best x = 0.0000, f(x) = 0.0000
Generation 12: Best x = 0.0000, f(x) = 0.0000
Generation 13: Best x = 0.0000, f(x) = 0.0000
Generation 14: Best x = 7.5294, f(x) = 56.6920
Generation 15: Best x = 0.0000, f(x) = 0.0000
Generation 16: Best x = 0.0000, f(x) = 0.0000
Generation 17: Best x = 0.1176, f(x) = 0.0138
Generation 18: Best x = 0.0000, f(x) = 0.0000
Generation 19: Best x = 0.0000, f(x) = 0.0000
Generation 20: Best x = 0.0000, f(x) = 0.0000
Generation 21: Best x = 0.0000, f(x) = 0.0000
Generation 22: Best x = 0.0000, f(x) = 0.0000
Generation 23: Best x = 0.0000, f(x) = 0.0000
Generation 24: Best x = 0.0000, f(x) = 0.0000
Generation 25: Best x = 0.0000, f(x) = 0.0000
Generation 26: Best x = 0.0000, f(x) = 0.0000
Generation 27: Best x = 0.0000, f(x) = 0.0000
Generation 28: Best x = 0.0000, f(x) = 0.0000
Generation 29: Best x = 0.0000, f(x) = 0.0000
Generation 30: Best x = 0.0000, f(x) = 0.0000

Optimal Solution: x = 0.0000, f(x) = 0.0000