模擬退火演算法解決TSP(python實現 110+行程式碼)【gif生成】
阿新 • • 發佈:2018-12-19
簡述
程式碼我是基於我之前寫的兩篇,一篇是遺傳演算法TSP的Python實現,一篇是模擬退火演算法的解決TSP的C++實現。
效果演示
對比
相比於遺傳演算法來說沒有保持歷史中的較優資料,但是通過退火的演算法思維,很鄰近點搜尋的想法,任然能保持較為正確的收斂結果
程式碼
import numpy as np
import random
import matplotlib.pyplot as plt
import os
import shutil
import imageio
def create_data(N, xu=25, yu=25, xd=-25, yd=-25):
fx = lambda: random.random() * (xu - xd) + xd
fy = lambda: random.random() * (yu - yd) + yd
calDistance = lambda x, y: np.sqrt((x[0] - y[0]) ** 2 + (x[1] - y[1]) ** 2)
points = [(0, 0)] * N
for i in range(N):
points[i] = (fx(), fy())
Mat = np.zeros((N, N))
for i in range(N):
for j in range(i + 1, N):
dv = calDistance(points[i], points[j])
Mat[i][j], Mat[j][i] = dv, dv
return points, Mat
def calpathValue(path):
global Mat
temp = Mat[ 0][path[0]]
for i in range(len(path) - 1):
temp += Mat[path[i]][path[i + 1]]
temp += Mat[path[-1]][0]
return temp
def initial():
global N
init = list(range(1, N, 1))
random.shuffle(init)
packValue = calpathValue(init)
return init, packValue
def draw(path, pv):
global points, N, TIMESIT, PNGFILE, PNGLIST
plt.cla()
plt.title('cross=%.4f' % pv)
xs = [p[0] for p in points]
ys = [p[1] for p in points]
plt.scatter(xs, ys, color='b')
xs = np.array(xs)
ys = np.array(ys)
plt.plot(xs[[0, path[0]]], ys[[0, path[0]]], color='r')
for i in range(N - 2):
plt.plot(xs[[path[i], path[i + 1]]], ys[[path[i], path[i + 1]]], color='r')
plt.plot(xs[[path[N - 2], 0]], ys[[path[N - 2], 0]], color='r')
plt.scatter(xs[0], ys[0], color='k', linewidth=10)
for i, p in enumerate(points):
plt.text(*p, '%d' % i)
plt.savefig('%s/%d.png' % (PNGFILE, TIMESIT))
PNGLIST.append('%s/%d.png' % (PNGFILE, TIMESIT))
TIMESIT += 1
if __name__ == '__main__':
# N, Mat = read_data()
TIMESIT = 0
PNGFILE = './png/'
PNGLIST = []
if not os.path.exists(PNGFILE):
os.mkdir(PNGFILE)
else:
shutil.rmtree(PNGFILE)
os.mkdir(PNGFILE)
N = 30
points, Mat = create_data(N)
T = 1000 # 起始溫度
alpha = 0.995 # T_{k+1} = alpha * T_k方式更新溫度
limitedT = 1. # 最小值的T
iterTime = 1000 # 每個溫度下迭代的次數
K = 0.8 # 係數K
p = 0
path, value = initial()
tempPath, tempValue = [], 0
global_Best = value # 畫圖
while T > limitedT:
print(T)
for i in range(iterTime):
tempPath = path.copy()
tx = random.randint(0, N - 2)
ty = random.randint(0, N - 2)
if tx != ty:
tempPath[tx], tempPath[ty] = tempPath[ty], tempPath[tx]
tempValue = calpathValue(tempPath)
if tempValue <= value:
path = tempPath.copy()
value = tempValue.copy()
else:
p = np.exp((value - tempValue) / (K * T))
if random.random() < p:
path = tempPath.copy()
value = tempValue.copy()
if value < global_Best:
global_Best = value
draw(path, value)
T *= alpha
print(value)
print(0, end='-->')
for i in path:
print(i, end='-->')
generated_images = []
for png_path in PNGLIST:
generated_images.append(imageio.imread(png_path))
shutil.rmtree(PNGFILE) # 可刪掉
generated_images = generated_images + [generated_images[-1]] * 5
imageio.mimsave('TSP-SAA.gif', generated_images, 'GIF', duration=0.5)