python实现Memetic算法程序设计及应用并生成3D图像

下面是一个使用Python实现Memetic算法，并生成3D图像的例子，以求解函数f(x,y) = sin(x+y) + (x-y)^2 - 1.5x + 2.5y + 1为例：

import random
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 目标函数
def f(x, y):
    return np.sin(x+y) + (x-y)**2 - 1.5*x + 2.5*y + 1

# 产生初始种群
def init_population(pop_size, x_range, y_range):
    return [(random.uniform(x_range[0], x_range[1]), random.uniform(y_range[0], y_range[1])) for i in range(pop_size)]

# 适应度评价
def evaluate(population):
    return [f(x, y) for x, y in population]

# 交叉操作
def crossover(parents, pc):
    children = []
    for i in range(len(parents)-1):
        if random.random() < pc:
            child1 = (parents[i][0], parents[i+1][1])
            child2 = (parents[i+1][0], parents[i][1])
            children.append(child1)
            children.append(child2)
    return children

# 变异操作
def mutation(children, pm, x_range, y_range):
    mutants = []
    for child in children:
        if random.random() < pm:
            mutant1 = (child[0] + random.uniform(-0.1, 0.1), child[1])
            mutant2 = (child[0], child[1] + random.uniform(-0.1, 0.1))
            if mutant1[0] < x_range[0]:
                mutant1 = (x_range[0], mutant1[1])
            elif mutant1[0] > x_range[1]:
                mutant1 = (x_range[1], mutant1[1])
            if mutant2[1] < y_range[0]:
                mutant2 = (mutant2[0], y_range[0])
            elif mutant2[1] > y_range[1]:
                mutant2 = (mutant2[0], y_range[1])
            mutants.append(mutant1)
            mutants.append(mutant2)
    return mutants

# 局部搜索操作
def local_search(children):
    new_children = []
    for child in children:
        x, y = child
        fx = f(x, y)
        for i in range(10):
            delta1 = random.uniform(-0.1, 0.1)
            delta2 = random.uniform(-0.1, 0.1)
            x_new = x + delta1
            y_new = y + delta2
            fx_new = f(x_new, y_new)
            if fx_new < fx:
                x = x_new
                y = y_new
                fx = fx_new
        new_children.append((x, y))
    return new_children

# Memetic算法
def memetic_algorithm(pop_size, x_range, y_range, pc, pm, max_gen):
    population = init_population(pop_size, x_range, y_range)
    for i in range(max_gen):
        fitness = evaluate(population)
        best_fitness = min(fitness)
        best_index = fitness.index(best_fitness)
        best_individual = population[best_index]
        print("Generation {}: best_fitness = {}, best_individual = {}".format(i+1, best_fitness, best_individual))
        parents = [population[i] for i in range(pop_size) if fitness[i] < best_fitness*1.1]
        children = crossover(parents, pc)
        mutants = mutation(children, pm, x_range, y_range)
        new_children = local_search(mutants)
        population = parents + new_children
    return best_individual, best_fitness

# 绘制3D图像
def plot_3d(x_range, y_range):
    x = np.linspace(x_range[0], x_range[1], 100)
    y = np.linspace(y_range[0], y_range[1], 100)
    X, Y = np.meshgrid(x, y)
    Z = f(X, Y)
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    ax.plot_surface(X, Y, Z, cmap='jet')
    plt.show()

# 测试
best_individual, best_fitness = memetic_algorithm(50, [-5, 5], [-5, 5], 0.8, 0.1, 100)
print("Best individual: {}, best fitness: {}".format(best_individual, best_fitness))
plot_3d([-5, 5], [-5, 5])

该程序使用了随机生成初始种群、适应度评价、交叉操作、变异操作、局部搜索操作等Memetic算法的基本操作，求解了函数f(x,y)的最小值，并生成了3D图像。