编程实现QDF和骨架粒子群算法（给出骨架粒子群算法的源代码）

QDF（Quantum-behaved Differential Evolution）算法实现：

import numpy as np
import random

# QDF算法的超参数
POPULATION_SIZE = 50
CROSSOVER_PROBABILITY = 0.5
SCALE_FACTOR = 0.5

# 目标函数，需要根据实际问题进行定义
def objective_function(x):
    return np.sum(x**2)

# QDF算法
def QDF(max_iterations):
    # 生成初始种群
    population = np.random.uniform(low=-5.12, high=5.12, size=(POPULATION_SIZE, 30))
    # 计算初始种群中每个个体的适应度值
    fitness = np.array([objective_function(individual) for individual in population])
    # 记录最优的个体和适应度值
    best_individual = population[np.argmin(fitness)]
    best_fitness = np.min(fitness)
    # 迭代
    for i in range(max_iterations):
        # 生成新的种群
        new_population = np.zeros_like(population)
        for j in range(POPULATION_SIZE):
            # 随机选择三个不同的个体
            a, b, c = random.sample(range(POPULATION_SIZE), 3)
            # 生成新的个体
            trial = np.zeros(30)
            for k in range(30):
                if np.random.uniform() < CROSSOVER_PROBABILITY:
                    trial[k] = population[a, k] + SCALE_FACTOR * (population[b, k] - population[c, k])
                else:
                    trial[k] = population[j, k]
            # 计算新个体的适应度值
            trial_fitness = objective_function(trial)
            # 更新最优的个体和适应度值
            if trial_fitness < best_fitness:
                best_individual = trial
                best_fitness = trial_fitness
            # 选择更优的个体进入新的种群
            if trial_fitness < fitness[j]:
                new_population[j] = trial
            else:
                new_population[j] = population[j]
        # 更新种群和适应度值
        population = new_population
        fitness = np.array([objective_function(individual) for individual in population])
    # 返回最优的个体和适应度值
    return best_individual, best_fitness

骨架粒子群算法实现：

import numpy as np
import random

# 骨架粒子群算法的超参数
POPULATION_SIZE = 50
MAX_ITERATIONS = 100
W = 0.729
C1 = 1.49445
C2 = 1.49445

# 目标函数，需要根据实际问题进行定义
def objective_function(x):
    return np.sum(x**2)

# 骨架粒子群算法
def Skeleton_Particle_Swarm_Optimization(max_iterations):
    # 生成初始种群
    population = np.random.uniform(low=-5.12, high=5.12, size=(POPULATION_SIZE, 30))
    # 计算初始种群中每个个体的适应度值
    fitness = np.array([objective_function(individual) for individual in population])
    # 初始化个体的最优位置和最优适应度值
    p_best = population.copy()
    p_best_fitness = fitness.copy()
    # 初始化全局最优位置和最优适应度值
    g_best = population[np.argmin(fitness)]
    g_best_fitness = np.min(fitness)
    # 迭代
    for i in range(max_iterations):
        # 更新速度和位置
        for j in range(POPULATION_SIZE):
            r1 = np.random.uniform()
            r2 = np.random.uniform()
            velocity = W * population[j] + C1 * r1 * (p_best[j] - population[j]) + C2 * r2 * (g_best - population[j])
            population[j] = population[j] + velocity
            # 约束处理
            population[j] = np.maximum(population[j], -5.12)
            population[j] = np.minimum(population[j], 5.12)
        # 计算新位置的适应度值
        fitness = np.array([objective_function(individual) for individual in population])
        # 更新个体的最优位置和最优适应度值
        for j in range(POPULATION_SIZE):
            if fitness[j] < p_best_fitness[j]:
                p_best[j] = population[j]
                p_best_fitness[j] = fitness[j]
        # 更新全局最优位置和最优适应度值
        if np.min(fitness) < g_best_fitness:
            g_best = population[np.argmin(fitness)]
            g_best_fitness = np.min(fitness)
    # 返回全局最优位置和最优适应度值
    return g_best, g_best_fitness