量子遗传算法 python 代码

以下是一个基于Python的量子遗传算法示例代码。

import numpy as np
import random

#定义遗传算法参数
POPULATION_SIZE = 50 # 种群大小
CROSSOVER_PROBABILITY = 0.8 # 交叉概率
MUTATION_PROBABILITY = 0.05 # 变异概率
TOURNAMENT_SELECTION_SIZE = 3 # 锦标赛选择策略大小
NUM_GENERATIONS = 100 # 迭代次数

#定义量子遗传算法参数
NUM_QUBITS = 4 # 量子比特数
NUM_INDIVIDUALS = 2**(NUM_QUBITS) # 个体数目
NUM_PARENTS = 2 # 父代个数
NUM_CHILDREN = 2 # 子代个数
NUM_GENERATIONS_QGA = 5 # 量子遗传算法迭代次数

#定义函数
def fitness_function(individual):
    x = individual[0]*2**3 + individual[1]*2**2 + individual[2]*2**1 + individual[3]*2**0
    return (x-10)**2

#定义遗传算法
def genetic_algorithm():
    #初始化种群
    population = []
    for i in range(POPULATION_SIZE):
        individual = []
        for j in range(NUM_QUBITS):
            individual.append(random.randint(0,1))
        population.append(individual)

    #开始迭代
    for i in range(NUM_GENERATIONS):
        #计算适应度
        fitness_values = []
        for individual in population:
            fitness_values.append(fitness_function(individual))

        #进行选择
        parents = []
        for j in range(NUM_PARENTS):
            tournament = random.sample(range(POPULATION_SIZE), TOURNAMENT_SELECTION_SIZE)
            winner = tournament[0]
            for k in tournament[1:]:
                if fitness_values[k] < fitness_values[winner]:
                    winner = k
            parents.append(population[winner])

        #进行交叉
        children = []
        for j in range(NUM_CHILDREN):
            if random.random() < CROSSOVER_PROBABILITY:
                crossover_point = random.randint(0, NUM_QUBITS-1)
                child1 = parents[0][:crossover_point] + parents[1][crossover_point:]
                child2 = parents[1][:crossover_point] + parents[0][crossover_point:]
                children.append(child1)
                children.append(child2)

        #进行变异
        for j in range(len(children)):
            for k in range(NUM_QUBITS):
                if random.random() < MUTATION_PROBABILITY:
                    children[j][k] = 1 - children[j][k]

        #替换最差的个体
        fitness_values = []
        for individual in population:
            fitness_values.append(fitness_function(individual))
        worst_individual = np.argmax(fitness_values)
        population[worst_individual] = children[0]

    #返回最优解
    fitness_values = []
    for individual in population:
        fitness_values.append(fitness_function(individual))
    best_individual = np.argmin(fitness_values)
    return population[best_individual]

#定义量子遗传算法
def quantum_genetic_algorithm():
    #初始化状态
    state = np.ones(NUM_INDIVIDUALS)/np.sqrt(NUM_INDIVIDUALS)

    #开始迭代
    for i in range(NUM_GENERATIONS_QGA):
        #计算适应度
        fitness_values = []
        for j in range(NUM_INDIVIDUALS):
            individual = [int(x) for x in list('{0:0b}'.format(j).zfill(NUM_QUBITS))]
            fitness_values.append(fitness_function(individual))
        fitness_values = np.array(fitness_values)

        #计算平均适应度
        mean_fitness = np.mean(fitness_values)

        #计算Q值
        q_values = np.zeros(NUM_INDIVIDUALS)
        for j in range(NUM_INDIVIDUALS):
            for k in range(NUM_INDIVIDUALS):
                if j != k:
                    q_values[j] += (fitness_values[k] - mean_fitness) * np.conj(state[k]) * state[j]

        #进行旋转
        angle = 2 * np.arccos(np.sqrt(1/NUM_INDIVIDUALS))
        for j in range(NUM_INDIVIDUALS):
            state[j] = np.cos(angle/2) * state[j] - 1j * np.sin(angle/2) * q_values[j]

    #返回最优解
    best_individual = np.argmax(np.abs(state)) 
    return [int(x) for x in list('{0:0b}'.format(best_individual).zfill(NUM_QUBITS))]

#测试
print("遗传算法结果：", genetic_algorithm())
print("量子遗传算法结果：", quantum_genetic_algorithm())

这个代码实现了一个简单的四位二进制数的最小化函数的优化。其中遗传算法和量子遗传算法均被实现，可以进行比较。