遗传算法求解TSP问题-python实现
遗传算法求解TSP问题
1. TSP问题简介
旅行商人要拜访n个城市，并最终回到出发城市，要求每个城市只能拜访一次，优化目标是最小化路程之和。
2. 例子求解结果
20个城市坐标：(88, 16),(42, 76),(5, 76),(69, 13),(73, 56),(100, 100),(22, 92),(48, 74),(73, 46),(39, 1),(51, 75),(92, 2),(101, 44),(55, 26),(71, 27),(42, 81),(51, 91),(89, 54),(33, 18),(40, 78）
结果路径图和迭代效果如下：
3. 遗传算法设计
自然数编码、锦标赛选择、顺序交叉、基本位变异、一对一生存者竞争。python编程。算法详细情况可参考Geatpy进化算法介绍 （Geatpy也是一个实用的Python遗传算法工具箱）
3.1 适应度函数
def calFitness(line,dis_matrix):
dis_sum = 0
dis = 0
for i in range(len(line)):
if i<len(line)-1:
dis = dis_matrix.loc[line[i],line[i+1]]#计算距离
dis_sum = dis_sum+dis
else:
dis = dis_matrix.loc[line[i],line[0]]
dis_sum = dis_sum+dis
return round(dis_sum,1)
3.2 锦标赛选择
def tournament_select(pops,popsize,fits,tournament_size):
new_pops,new_fits = [],[]
while len(new_pops)<len(pops):
tournament_list = random.sample(range(0,popsize),tournament_size)
tournament_fit = [fits[i] for i in tournament_list]
#转化为df方便索引
tournament_df = pd.DataFrame([tournament_list,tournament_fit]).transpose().sort_values(by=1).reset_index(drop=True)
#选出获胜者
fit = tournament_df.iloc[0,1]
pop = pops[int(tournament_df.iloc[0,0])]
new_pops.append(pop)
new_fits.append(fit)
return new_pops,new_fits
3.3 顺序交叉
def crossover(popsize,parent1_pops,parent2_pops,pc):
child_pops = []
for i in range(popsize):
#初始化
child = [None]*len(parent1_pops[i])
parent1 = parent1_pops[i]
parent2 = parent2_pops[i]
if random.random() >= pc:
child = parent1.copy()#随机生成一个（或者随机保留父代中的一个）
random.shuffle(child)
else:
#parent1
start_pos = random.randint(0,len(parent1)-1)
end_pos = random.randint(0,len(parent1)-1)
if start_pos>end_pos:
tem_pop = start_pos
start_pos = end_pos
end_pos = tem_pop
child[start_pos:end_pos+1] = parent1[start_pos:end_pos+1].copy()
# parent2 -> child
list1 = list(range(end_pos+1,len(parent2)))
list2 = list(range(0,start_pos))
list_index = list1+list2
j = -1
for i in list_index:
for j in range(j+1,len(parent2)):
if parent2[j] not in child:
child[i] = parent2[j]
break
child_pops.append(child)
return child_pops
3.4 基本位变异
随机选出两个位置进行交换
def mutate(pops,pm):
pops_mutate = []
for i in range(len(pops)):
pop = pops[i].copy()
#随机多次成对变异
t = random.randint(1,5)
count = 0
while count < t:
if random.random() < pm:
mut_pos1 = random.randint(0,len(pop)-1)
mut_pos2 = random.randint(0,len(pop)-1)
if mut_pos1 != mut_pos2:
tem = pop[mut_pos1]
pop[mut_pos1] = pop[mut_pos2]
pop[mut_pos2] = tem
pops_mutate.append(pop)
count +=1
return pops_mutate
#另一种实现方式
# def mutate(pops,pm):
# pops_mutate = []
# for i in range(len(pops)):
# pop = pops[i].copy()
# for j in range(len(pop)):
# if random.random() < pm:
# mut_pos = random.randint(0,len(pop)-1)
# if j != mut_pos:
# tem = pop[j]
# pop[j] = pop[mut_pos]
# pop[mut_pos] = tem
# pops_mutate.append(pop)
# return pops_mutate
3.5 主函数
import math
import random
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.pylab import mpl
mpl.rcParams['font.sans-serif'] = ['SimHei'] # 添加这条可以让图形显示中文
#画路径图
def draw_path(line,CityCoordinates):
x,y= [],[]
for i in line:
Coordinate = CityCoordinates[i]
x.append(Coordinate[0])
y.append(Coordinate[1])
x.append(x[0])
y.append(y[0])
plt.plot(x, y,'r-', color='#4169E1', alpha=0.8, linewidth=0.8)
plt.xlabel('x')
plt.ylabel('y')
plt.show()
if __name__ == '__main__':
#参数
CityNum = 20#城市数量
MinCoordinate = 0#二维坐标最小值
MaxCoordinate = 101#二维坐标最大值
#GA参数
generation = 100 #迭代次数
popsize = 100 #种群大小
tournament_size = 5 #锦标赛小组大小
pc = 0.95 #交叉概率
pm = 0.1 #变异概率
#随机生成城市数据,城市序号为0,1,2,3...
CityCoordinates = [(random.randint(MinCoordinate,MaxCoordinate),random.randint(MinCoordinate,MaxCoordinate)) for i in range(CityNum)]
# CityCoordinates = [(88, 16),(42, 76),(5, 76),(69, 13),(73, 56),(100, 100),(22, 92),(48, 74),(73, 46),(39, 1),(51, 75),(92, 2),(101, 44),(55, 26),(71, 27),(42, 81),(51, 91),(89, 54),(33, 18),(40, 78)]#随机生成的例子
#计算城市之间的距离
dis_matrix = pd.DataFrame(data=None,columns=range(len(CityCoordinates)),index=range(len(CityCoordinates)))
for i in range(len(CityCoordinates)):
xi,yi = CityCoordinates[i][0],CityCoordinates[i][1]
for j in range(len(CityCoordinates)):
xj,yj = CityCoordinates[j][0],CityCoordinates[j][1]
dis_matrix.iloc[i,j] = round(math.sqrt((xi-xj)**2+(yi-yj)**2),2)
iteration = 0
#初始化,随机构造
pops = [random.sample([i for i in list(range(len(CityCoordinates)))],len(CityCoordinates)) for j in range(popsize)]
#计算适应度
fits = [None]*popsize
for i in range(popsize):
fits[i] = calFitness(pops[i],dis_matrix)
#保留当前最优
best_fit = min(fits)
best_pop = pops[fits.index(best_fit)]
print('初代最优值 %.1f' % (best_fit))
best_fit_list = []
best_fit_list.append(best_fit)
while iteration <= generation:
#锦标赛赛选择
pop1,fits1 = tournament_select(pops,popsize,fits,tournament_size)
pop2,fits2 = tournament_select(pops,popsize,fits,tournament_size)
#交叉
child_pops = crossover(popsize,pop1,pop2,pc)
#变异
child_pops = mutate(child_pops,pm)
#计算子代适应度
child_fits = [None]*popsize
for i in range(popsize):
child_fits[i] = calFitness(child_pops[i],dis_matrix)
#一对一生存者竞争
for i in range(popsize):
if fits[i] > child_fits[i]:
fits[i] = child_fits[i]
pops[i] = child_pops[i]
if best_fit>min(fits):
best_fit = min(fits)
best_pop = pops[fits.index(best_fit)]
best_fit_list.append(best_fit)
print('第%d代最优值 %.1f' % (iteration, best_fit))
iteration += 1
#路径顺序
print(best_pop)
#路径图
draw_path(best_pop,CityCoordinates)
#迭代图
iters = list(range(len(best_fit_list)))
plt.plot(iters, best_fit_list, 'r-', color='#4169E1', alpha=0.8, linewidth=0.8)
plt.xlabel('迭代次数')
TSP系列目录
| 智能优化算法类别 | 启发式算法求解TSP问题系列博文 |
|---|---|
| 进化算法 | 遗传算法求解TSP问题 |
| 仿人智能优化算法 | 禁忌搜索算法求解TSP问题 |
| 仿自然优化算法 | 模拟退火算法求解TSP问题 |
| 群智能优化算法 | 蚁群算法求解TSP问题 |
| 群智能优化算法 | 粒子群算法求解TSP问题 |
| 总结篇 | 五种常见启发式算法求解TSP问题 |
| 改进篇 | 遗传-粒子群算法&遗传-禁忌搜索算法求解TSP问题 |
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