基于遗传算法解决旅行商问题(Python代码)

大家好！本文为大家提供了遗传算法解决TSP问题的一种python实现。有兴趣的同学可以通过“蚁群算法解决TSP问题”，看看蚁群算法与遗传算法的不同之处。

import math
import numpy as np
import matplotlib.pyplot as plt

# 随机生成城市信息
nCity = 10
City = np.random.uniform(-10, 10, [nCity, 2])
Dis = {
     }
for i in range(nCity):
    for j in range(nCity):
        if i > j:
            dis = ((City[i][0] - City[j][0]) ** 2 + (City[i][1] - City[j][1]) ** 2) ** 0.5
            Dis[(i, j)] = dis
            Dis[(j, i)] = dis

Data_BestFit =[]   #用于保存每一代蚂蚁的最优适应度

#适应度计算函数 适应值 = 1 / 路径距离
def Cal_Fit(X):
    total_dis = Dis[(X[-1],X[0])]
    for i in range(nCity-1):
        total_dis += Dis[(X[i],X[i+1])]
    return 1 / total_dis

def GA_TSP():
    # 定义基本参数
    nPop = 100  # 种群大小
    Maxit = 100 # 最大迭代次数
    Pm = 0.15   # 变异概率
    Pc = 0.7    # 交叉概率

    #种群初始化
    X = [list(np.random.permutation(nCity)) for i in range(nPop)]
    Fit = np.zeros([nPop])
    Best_X = None
    Best_Fit = -math.inf
    for i in range(nPop):
        Fit[i] = Cal_Fit(X[i])
        if Fit[i] > Best_Fit:
            Best_Fit = Fit[i]
            Best_X = X[i].copy()

    #迭代求解
    for j in range(Maxit):
        # 变异-在一个解中随机选取两座不同的城市交换遍历顺序
        for k in range(nPop):
            if np.random.random() < Pm:
                point1 = int(np.random.random() * nCity)
                point2 = int(np.random.random() * nCity)
                while point1 == point2:
                    point1 = int(np.random.random() * nCity)
                    point2 = int(np.random.random() * nCity)
                X[k][point1],X[k][point2] = X[k][point2],X[k][point1]
                
        #交叉-交换解的部分序列
        k = 0
        while k < nPop:
            if np.random.random() < Pc:
                point = int(np.random.random() * nCity)
                x1 = X[k][0:point+1]
                x2 = X[k][point+1:nCity]
                x2.extend(x1)
                X[k] = x2
            k += 1

        #选择 以适应度占比为概率选取下一代个体(有的个体会被重复选取)
        for i in range(nPop):
            Fit[i] = Cal_Fit(X[i])
            if Fit[i] > Best_Fit:
                Best_Fit = Fit[i]
                Best_X = X[i].copy()
        fit = Fit.copy()
        P = fit / sum(fit)
        swarm = np.random.choice(range(nPop),size = nPop,replace=True,p = P)
        x = X.copy()
        for k in range(nPop):
            X[k] = x[swarm[k]]

        Data_BestFit.append(Best_Fit)

    return Best_X ,Best_Fit

# 绘制路径与迭代曲线
def Draw_City(City, X ,Best_Fit):
    X = list(X)
    X.append(X[0])
    coor_x = []
    coor_y = []
    for i in X:
        i = int(i)
        coor_x.append(City[i][0])
        coor_y.append(City[i][1])

    plt.plot(coor_x, coor_y, 'r-o')
    plt.title('TSP with Genetic Algorithm\n'+'total_dis = '+str(round(Best_Fit,3)))
    plt.show()

    plt.plot(range(len(Data_BestFit)), Data_BestFit)
    plt.title('Iteration_BestFit')
    plt.xlabel('iteration')
    plt.ylabel('fitness')
    plt.show()

if __name__ == '__main__':
    Best_X, Best_Fit = GA_TSP()
    Draw_City(City ,Best_X ,(Best_Fit)**-1)