旅行商問題（Travelling Salesman Problem，即TSP問題）是數學領域中著名問題之一。假設有一個旅行商人要拜訪n個城市，他必須選擇所要走的路徑，路經的限制是每個城市只能拜訪一次，而且最後要回到原來出發的城市。路徑的選擇目標是要求得的路徑路程為所有路徑之中的最小值。
TSP問題是一個組合優化問題，也是一個NP完全問題，使用通常的解法往往需要耗費大量的時間，不過我們也可以使用遺傳算法，在較短的時間裡找到一個可接受（不一定是最優）的解。
下面是我的代碼，一共有三個文件。
1、TSP.py
# -*- coding: utf-8 -*-
"""TSP.py
TSP問題
"""
import sys
import random
import math
import Tkinter
import threading
from GA import GA
class MyTSP(object):
"TSP"
def __init__(self, root, width = 800, height = 600, n = 32):
self.root = root
self.width = width
self.height = height
self.n = n
self.canvas = Tkinter.Canvas(
root,
width = self.width,
height = self.height,
bg = "#ffffff",
xscrollincrement = 1,
yscrollincrement = 1
)
self.canvas.pack(expand = Tkinter.YES, fill = Tkinter.BOTH)
self.title("TSP")
self.__r = 5
self.__t = None
self.__lock = threading.RLock()
self.__bindEvents()
self.new()
def __bindEvents(self):
self.root.bind("q", self.quite)
self.root.bind("n", self.new)
self.root.bind("e", self.evolve)
self.root.bind("s", self.stop)
def title(self, s):
self.root.title(s)
def new(self, evt = None):
self.__lock.acquire()
self.__running = False
self.__lock.release()
self.clear()
self.nodes = [] # 節點坐標
self.nodes2 = [] # 節點圖片對象
for i in range(self.n):
x = random.random() * (self.width - 60) + 30
y = random.random() * (self.height - 60) + 30
self.nodes.append((x, y))
node = self.canvas.create_oval(x - self.__r,
y - self.__r, x + self.__r, y + self.__r,
fill = "#ff0000",
outline = "#000000",
tags = "node",
)
self.nodes2.append(node)
self.ga = GA(
lifeCount = 50,
mutationRate = 0.05,
judge = self.judge(),
mkLife = self.mkLife(),
xFunc = self.xFunc(),
mFunc = self.mFunc(),
save = self.save()
)
self.order = range(self.n)
self.line(self.order)
def distance(self, order):
"得到當前順序下連線總長度"
distance = 0
for i in range(-1, self.n - 1):
i1, i2 = order[i], order[i + 1]
p1, p2 = self.nodes[i1], self.nodes[i2]
distance += math.sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2)
return distance
def mkLife(self):
def f():
lst = range(self.n)
random.shuffle(lst)
return lst
return f
def judge(self):
"評估函數"
return lambda lf, av = 100: 1.0 / self.distance(lf.gene)
def xFunc(self):
"交叉函數"
def f(lf1, lf2):
p1 = random.randint(0, self.n - 1)
p2 = random.randint(self.n - 1, self.n)
g1 = lf2.gene[p1:p2] + lf1.gene
# g2 = lf1.gene[p1:p2] + lf2.gene
g11 = []
for i in g1:
if i not in g11:
g11.append(i)
return g11
return f
def mFunc(self):
"變異函數"
def f(gene):
p1 = random.randint(0, self.n - 2)
p2 = random.randint(self.n - 2, self.n - 1)
gene[p1], gene[p2] = gene[p2], gene[p1]
return gene
return f
def save(self):
def f(lf, gen):
pass
return f
def evolve(self, evt = None):
self.__lock.acquire()
self.__running = True
self.__lock.release()
while self.__running:
self.ga.next()
self.line(self.ga.best.gene)
self.title("TSP - gen: %d" % self.ga.generation)
self.canvas.update()
self.__t = None
def line(self, order):
"將節點按 order 順序連線"
self.canvas.delete("line")
def line2(i1, i2):
p1, p2 = self.nodes[i1], self.nodes[i2]
self.canvas.create_line(p1, p2, fill = "#000000", tags = "line")
return i2
reduce(line2, order, order[-1])
def clear(self):
for item in self.canvas.find_all():
self.canvas.delete(item)
def quite(self, evt):
self.__lock.acquire()
self.__running = False
self.__lock.release()
sys.exit()
def stop(self, evt):
self.__lock.acquire()
self.__running = False
self.__lock.release()
def mainloop(self):
self.root.mainloop()
if __name__ == "__main__":
MyTSP(Tkinter.Tk()).mainloop()
2、2、GA.py
# -*- coding: utf-8 -*-
"""GA.py
遺傳算法類
"""
import random
from Life import Life
class GA(object):
def __init__(self, xRate = 0.7, mutationRate = 0.005, lifeCount = 50, geneLength = 100, judge = lambda lf, av: 1, save = lambda: 1, mkLife = lambda: None, xFunc = None, mFunc = None):
self.xRate = xRate
self.mutationRate = mutationRate
self.mutationCount = 0
self.generation = 0
self.lives = []
self.bounds = 0.0 # 得分總數
self.best = None
self.lifeCount = lifeCount
self.geneLength = geneLength
self.__judge = judge
self.save = save
self.mkLife = mkLife # 默認的產生生命的函數
self.xFunc = (xFunc, self.__xFunc)[xFunc == None] # 自定義交叉函數
self.mFunc = (mFunc, self.__mFunc)[mFunc == None] # 自定義變異函數
for i in range(lifeCount):
self.lives.append(Life(self, self.mkLife()))
def __xFunc(self, p1, p2):
# 默認交叉函數
r = random.randint(0, self.geneLength)
gene = p1.gene[0:r] + p2.gene[r:]
return gene
def __mFunc(self, gene):
# 默認突變函數
r = random.randint(0, self.geneLength - 1)
gene = gene[:r] + ("0", "1")[gene[r:r] == "1"] + gene[r + 1:]
return gene
def __bear(self, p1, p2):
# 根據父母 p1, p2 生成一個後代
r = random.random()
if r < self.xRate:
# 交叉
gene = self.xFunc(p1, p2)
else:
gene = p1.gene
r = random.random()
if r < self.mutationRate:
# 突變
gene = self.mFunc(gene)
self.mutationCount += 1
return Life(self, gene)
def __getOne(self):
# 根據得分情況，隨機取得一個個體，機率正比於個體的score屬性
r = random.uniform(0, self.bounds)
for lf in self.lives:
r -= lf.score
if r <= 0:
return lf
def __newChild(self):
# 產生新的後代
return self.__bear(self.__getOne(), self.__getOne())
def judge(self, f = lambda lf, av: 1):
# 根據傳入的方法 f ，計算每個個體的得分
lastAvg = self.bounds / float(self.lifeCount)
self.bounds = 0.0
self.best = Life(self)
self.best.setScore(-1.0)
for lf in self.lives:
lf.score = f(lf, lastAvg)
if lf.score > self.best.score:
self.best = lf
self.bounds += lf.score
def next(self, n = 1):
# 演化至下n代
while n > 0:
# self.__getBounds()
self.judge(self.__judge)
newLives = []
newLives.append(Life(self, self.best.gene)) # 將最好的父代加入競爭
# self.bestHistory.append(self.best)
while (len(newLives) < self.lifeCount):
newLives.append(self.__newChild())
self.lives = newLives
self.generation += 1
#print("gen: %d, mutation: %d, best: %f" % (self.generation, self.mutationCount, self.best.score))
self.save(self.best, self.generation)
n -= 1
3、Life.py
# -*- coding: utf-8 -*-
"""Life.py
生命類
"""
import random
class Life(object):
def __init__(self, env, gene = None):
self.env = env
if gene == None:
self.__rndGene()
elif type(gene) == type([]):
self.gene = []
for k in gene:
self.gene.append(k)
else:
self.gene = gene
def __rndGene(self):
self.gene = ""
for i in range(self.env.geneLength):
self.gene += str(random.randint(0, 1))
def setScore(self, v):
self.score = v
def addScore(self, v):
self.score += v
運行TSP.py，即可開始程序。幾個快捷鍵說明如下：
n: 開始新的計算（隨機產生32個新的城市）
e: 開始進化
s: 停止
q: 退出
程序沒有設置終止進化條件，進化一旦開始，如果不手動停止，會一直計算下去。
遺傳算法主要是一種思想，並沒有很具體的代碼，在解決大多數問題時，最難解決的部分主要是編碼（如何將問題轉化為合適的方便操作的“基因”）、評價（如何評價各個“基因”的得分）部分。在本例中，我們將城市的順序做為基因編碼，路徑總長度的倒數為基因的得分。這種做法不一定是最好的，不過是有效的。
下面是我運行時的一次截圖：
初始狀態。
第153代。
第624代，可以看到，已經比初始狀態好多了。
第2331代，除了下方有一些交叉外，已經基本差不多了。
第3710代，完成。
