Genetic Algorithm to Solve TSP Problem

The TSP problem (Travelling Salesman Problem) is one of the famous problems in the field of mathematics. Suppose there is a traveling merchant who wants to visit n cities, he must choose the path he wants to take. The limit of the path is that each city can only be visited once, and finally he has to return to the original city. The path selection goal is to require the path distance to be the minimum value among all paths.

Reference: Using Genetic Algorithms to Solve TSP Problems
Related Blogs

Since the results on the Internet only have a path map, and the distance value is not specified, there is no way to refer to it.

""" 
@author: zoutai
@file: TSP_Solve.py 
@time: 2018/04/22 
@description: 旅行商问题求解
"""
import math
import random
import matplotlib.pyplot as plt

def geneticoptimize(popsize=50, step=1, mutprob=0.2, elite=0.2, mixiter=80000):

    # # 生成随机DNA
    # list1 = [i for i in range(lengthDNA)]
    # random.shuffle(list1)
    # print(list1)

    # 变异(交换)
    def mutate(list1):
        index1 = random.randint(0,lengthDNA - 1)
        index2 = random.randint(0,lengthDNA - 1)
        list1[index1], list1[index2] = list1[index2], list1[index1]
        return list1
    # 重组
    def cross(list1, list2):
        index1 = random.randint(0, lengthDNA - 1)
        index2 = random.randint(index1, lengthDNA - 1)
        tempGene = list2[index1:index2]
        newDNA = []
        temp = 0
        for gene in list1:
            if index1==temp:
                newDNA.extend(tempGene)
                temp+=1
            if gene not in tempGene:
                newDNA.append(gene)
                temp+=1
        return newDNA
    # 距离
    def distance(list1):
        distance = 0.0
        # i从-1到32,-1是倒数第一个
        if not isinstance(list1, list):
            print()
        index1, index2 = 0,0
        for i in range(len(list1)-1):
            index1, index2 = list1[i], list1[i + 1]
            # print(index1,index2)
            # print(i)
            distance += math.sqrt((float(cities[index1][4]) - float(cities[index2][5])) ** 2 + (float(cities[index1][6]) - float(cities[index2][7])) ** 2)

        # index2 = list1[len(list1)-1]
        distance += math.sqrt(
            (float(cities[index2][8]) - float(cities[0][9])) ** 2 + (float(cities[index2][10]) - float(cities[0][11])) ** 2)

        return distance


    cities = []
    for line in open('distanceMatrix.txt', 'r', encoding="utf8"):
        # 按照tab键分割
        cities.append(line.strip().split('\t'))
    lengthDNA = len(cities)

    # 开始
    # 第一步：初始化种群
    pop = []
    for i in range(popsize):
        list1 = [j for j in range(lengthDNA)]
        random.shuffle(list1)
        pop.append(list1.copy())

    # 进化选择数
    toplite = int(popsize * elite)

    # 进化选择，排序
    for i in range(mixiter):
        # 排序，进行物种进化选择
        distances = [(distance(v),v) for v in pop]
        distances.sort()
        ranked = [v for (s,v) in distances]

        pop = ranked[:toplite]
        while len(pop)<popsize:
            if random.random()<mutprob:
                c = random.randint(0,toplite)
                pop.append(mutate(ranked[c]))
            else:
                c1 = random.randint(0,toplite)
                c2 = random.randint(0,toplite)
                pop.append(cross(ranked[c1],ranked[c2]))
        print(distances[0][0])

    list1, distance = distances[0][12],distances[0][0]

    # 画图
    plt.figure()
    xlist = []
    ylist = []
    for i in list1:
        xlist.append(float(cities[i][13]))
        ylist.append(float(cities[i][14]))
    xlist.append(float(cities[list1[0]][15]))
    ylist.append(float(cities[list1[0]][16]))
    plt.plot(xlist,ylist,color='r')
    plt.scatter(xlist, ylist, color='b')
    plt.title('TSP_gen:'+str(distance))
    plt.show()
    return distances[0][17],distances[0][0]

list1, distance = geneticoptimize()
print(distance,list1)