遗传算法——解决M-TSP多旅行商问题（基于python基本实现）
具体的遗传算法详解请看上一篇博客
导读
MTSP_GA Multiple Traveling Salesmen Problem (M-TSP) Genetic Algorithm (GA). Finds a (near) optimal solution to the M-TSP by setting up a GA to search for the shortest route (least distance needed for the salesmen to travel to each city exactly once and return to their starting locations)
目录
- 初始化城市
- 计算城市间距离矩阵
- 初始化种群
- 适应度计算
- 选择（物竞天择）
- 交叉
- 变异
- 主逻辑代码
初始化城市
def xy():
li = []
for i in range(30):
x = np.random.randint(10, 4000)
y = np.random.randint(10, 4000)
li.append(np.array([x, y]))
li = np.array(li)
# return np.array(
# [[100, 200], [234, 1245], [423, 124], [123, 974], [578, 294], [1000, 500], [492, 2100], [320, 418], [836, 914]])
return li
计算城市间距离矩阵
def D(location1, location2):
return math.sqrt(pow(location1[0] - location2[0], 2) + pow(location1[1] - location2[1], 2))
def DMAT(locations):
length = len(locations)
distance = np.ones([length, length])
# print(distance.shape)
for i in range(length):
for j in range(length):
distance[i, j] = D(locations[i], locations[j])
return distance
初始化种群
def init_population(length, num):
li = list(range(length))
print(li)
population = []
for i in range(num):
random.shuffle(li)
population.append(copy.deepcopy(li))
return population
适应度计算
def aimFunction(entity, DMAT, break_points):
"""
目标函数
:param entity: 个体
:param DMAT: 距离矩阵
:param break_points: 切断点
:return:
"""
distance = 0
break_points.insert(0, 0)
break_points.append(len(entity))
routes = []
for i in range(len(break_points) - 1):
routes.append(entity[break_points[i]:break_points[i + 1]])
# print(routes)
for route in routes:
route.append(route[0])
for i in range(len(route)-1):
distance += DMAT[route[i],route[i+1]]
return 1.0/distance
def fitness(population, DMAT, break_points, aimFunction):
"""
适应度
:param population: 种群
:param DMAT: 距离矩阵
:param break_points:切断点
:param aimFunction: 目标函数
:return:
"""
value = []
for i in range(len(population)):
value.append(aimFunction(population[i], DMAT, copy.deepcopy(break_points)))
# weed out negative value
if value[i] < 0:
value[i] = 0
return value
选择（物竞天择）
def selection(population, value):
# 轮盘赌选择
fitness_sum = []
for i in range(len(value)):
if i == 0:
fitness_sum.append(value[i])
else:
fitness_sum.append(fitness_sum[i - 1] + value[i])
for i in range(len(fitness_sum)):
fitness_sum[i] /= sum(value)
# select new population
population_new = []
for i in range(len(value)):
rand = np.random.uniform(0, 1)
for j in range(len(value)):
if j == 0:
if 0 < rand and rand <= fitness_sum[j]:
population_new.append(population[j])
else:
if fitness_sum[j - 1] < rand and rand <= fitness_sum[j]:
population_new.append(population[j])
return population_new
交叉
def amend(entity, low, high):
"""
修正个体
:param entity: 个体
:param low: 交叉点最低处
:param high: 交叉点最高处
:return:
"""
length = len(entity)
cross_gene = entity[low:high] # 交叉基因
not_in_cross = [] # 应交叉基因
raw = entity[0:low] + entity[high:] # 非交叉基因
for i in range(length):
if not i in cross_gene:
not_in_cross.append(i)
error_index = []
for i in range(len(raw)):
if raw[i] in not_in_cross:
not_in_cross.remove(raw[i])
else:
error_index.append(i)
for i in range(len(error_index)):
raw[error_index[i]] = not_in_cross[i]
entity = raw[0:low] + cross_gene + raw[low:]
return entity
def crossover(population_new, pc):
"""
交叉
:param population_new: 种群
:param pc: 交叉概率
:return:
"""
half = int(len(population_new) / 2)
father = population_new[:half]
mother = population_new[half:]
np.random.shuffle(father)
np.random.shuffle(mother)
offspring = []
for i in range(half):
if np.random.uniform(0, 1) <= pc:
# cut1 = np.random.randint(0, len(population_new[0]))
# if cut1 >len(father[i]) -5:
# cut2 = cut1-5
# else:
# cut2 = cut1+5
cut1 = 0
cut2 = np.random.randint(0, len(population_new[0]))
if cut1 > cut2:
cut1, cut2 = cut2, cut1
if cut1 == cut2:
son = father[i]
daughter = mother[i]
else:
son = father[i][0:cut1] + mother[i][cut1:cut2] + father[i][cut2:]
son = amend(son, cut1, cut2)
daughter = mother[i][0:cut1] + father[i][cut1:cut2] + mother[i][cut2:]
daughter = amend(daughter, cut1, cut2)
else:
son = father[i]
daughter = mother[i]
offspring.append(son)
offspring.append(daughter)
return offspring
变异
def mutation(offspring, pm):
for i in range(len(offspring)):
if np.random.uniform(0, 1) <= pm:
position1 = np.random.randint(0, len(offspring[i]))
position2 = np.random.randint(0, len(offspring[i]))
# print(offspring[i])
offspring[i][position1],offspring[i][position2] = offspring[i][position2],offspring[i][position1]
# print(offspring[i])
return offspring
主逻辑代码
import numpy as np
from matplotlib import pyplot as plt
import math
import copy
import random
def show_population(population):
# x = [i / 100 for i in range(900)]
x = [i / 100 for i in range(-450, 450)]
y = [0 for i in range(900)]
for i in range(900):
y[i] = aimFunction(x[i])
population_10 = [decode(p) for p in population]
y_population = [aimFunction(p) for p in population_10]
plt.plot(x, y)
plt.plot(population_10, y_population, 'ro')
plt.show()
if __name__ == '__main__':
# x = [i / 100 for i in range(900)]
# y = [0 for i in range(900)]
locations = xy()
DMAT = DMAT(locations)
break_points = [6, 10, 16, 26]
population = init_population(len(locations), 90)
t = []
for i in range(4001):
# selection
value = fitness(population, DMAT, break_points, aimFunction)
population_new = selection(population, value)
# crossover
offspring = crossover(population_new, 0.65)
# mutation
population = mutation(offspring, 0.02)
# if i % 1 == 0:
# show_population(population)
result = []
for j in range(len(population)):
result.append(1.0 / aimFunction(population[j], DMAT, copy.deepcopy(break_points)))
t.append(min(result))
if i % 400 == 0:
min_entity = population[result.index(min(result))]
plt.scatter(locations[:, 0], locations[:, 1])
routes = []
break_points_plt = copy.deepcopy(break_points)
break_points_plt.insert(0, 0)
break_points_plt.append(len(min_entity))
for i in range(len(break_points_plt) - 1):
routes.append(min_entity[break_points_plt[i]:break_points_plt[i + 1]])
for route in routes:
route.append(route[0])
for route in routes:
x = locations[route, 0]
y = locations[route, 1]
plt.plot(x, y)
plt.show()
# print(min(result))
print(t)
plt.plot(t)
# plt.axhline(max(y), linewidth=1, color='r')
plt.show()