输出结果如下

DE.gif

实现代码如下

# 差分进化算法
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from PIL import Image
import shutil
import os
import glob 
import random

plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号

def plot_jpg(start, point_best, err, m, n, lower, upper, title):
    point_g = min(start.tolist(), key=target)
    
    plt.figure(figsize=(8, 12))
    gs = gridspec.GridSpec(3, 2)
    
    ax1 = plt.subplot(gs[:2, :2])
    ax1.scatter(start[:, 0], start[:, 1], alpha=0.3, color='green', s=20, label='当前位置')  # 当前位置
    ax1.scatter(point_g[0], point_g[1], alpha=1, color='blue', s=20, label='当前最优点')  # 全局最优点
    ax1.scatter(point_best[0], point_best[1], alpha=0.3, color='red', label='目标点')  # 最优点

    for i in range(n):
        ax1.text(start[i][0]+2, start[i][1]+2, f'{i}', alpha=0.3, fontsize=10, color='red')
    
    ax1.grid(True, color='gray', linestyle='-.', linewidth=0.5)
    ax1.set_xlim(lower[0]*1.2, upper[0]*1.2)
    ax1.set_ylim(lower[1]*1.2, upper[1]*1.2)
    ax1.set_xlabel(f'iter:{m}  dist: {err[-1]:.8f}'  )
    ax1.set_title(title)
    ax1.legend(loc='lower right', bbox_to_anchor=(1, 0), ncol=1)

    ax2 = plt.subplot(gs[2, :])
    ax2.plot(range(len(err)), err, marker='o', markersize=5)
    ax2.grid(True, color='gray', linestyle='-.', linewidth=0.5)
    ax2.set_xlim(0, max_iter)
    ax2.set_ylim(0, np.ceil(max(err)))
    ax2.set_xticks(range(0, max_iter, 5))
    
    plt.savefig(rf'./tmp/tmp_{m:04}.png')
    plt.close()


# 目标函数
def target(point):
    return (point[0]-a)**2 + (point[1]-b)**2


# 越界值处理
def get_out_bound_value(value):
    value = np.where((np.array(lower_lim) - value) > 0, np.array(lower_lim), value)
    value = np.where((value - np.array(upper_lim)) > 0, np.array(upper_lim), value) 
    return value


# 变异
def mutation(population, F):
    result = []
    for i in range(n):
        lis = list(range(n))
        lis.pop(i)
        p1, p2, p3 = random.sample(lis, 3)
        value = population[p1] + F*(population[p2] - population[p3])
        value = get_out_bound_value(value)
        result.append(value)
    return np.array(result)


# 交叉
def cross(population, population_new, CR):
    for i in range(n):
        if random.random() > CR:
            ind = random.randint(0, d-1)
            tmp = population_new[i][ind]
            population_new[i] = population[i]
            population_new[i][ind] = tmp
    return population_new
        

# 选择
def select(population, population_new):
    # 进化后变优了，那么就将基因保留到下一代，否则放弃进化
    population = np.array([min([population[i], population_new[i]], key=target) for i in range(n)]) 
    return population


def de():
    # 初始化种群
    population = np.random.random(size=(n, d))
    for _ in range(d):
        population[:, _] = population[:, _]*(upper_lim[_]-lower_lim[_])+lower_lim[_]
    
    if os.path.exists(tmp_path):
        shutil.rmtree(tmp_path) 
    os.makedirs(tmp_path, exist_ok=True)
    
    errors = [target(min(population.tolist(), key=target))**0.5]
    for _ in range(max_iter):
        title = f'DE\nn:{n} F:{F} CR:{CR} max_iter:{max_iter}'
        plot_jpg(population, point_best, errors, _, n, lower_lim, upper_lim, title)
        population_new = mutation(population, F)
        population_new = cross(population, population_new, CR)
        population = select(population, population_new)
        errors.append(target(min(population.tolist(), key=target))**0.5)
    plot_jpg(population, point_best, errors, max_iter, n, lower_lim, upper_lim, title)
    return errors


F = 0.5  # 放缩因子
CR = 0.3  # 交叉率

n = 20  # 粒子数量
d = 2  # 粒子维度
max_iter = 50  # 迭代次数

# 搜索区间  
lower_lim = [-100, -100]
upper_lim = [100, 100]

# 目标点
a, b = 0, 0
point_best = (a, b)

# 临时文件路径
tmp_path = r'./tmp/'

err = de()

images = [Image.open(png) for png in glob.glob(os.path.join(tmp_path, '*.png'))]
im = images.pop(0)
im.save(r"./DE.gif", save_all=True, append_images=images, duration=200)

im = Image.open(r"./DE.gif")
im.show()
im.close()