data = np.array([16.47, 96.10, 16.47, 94.44, 20.09, 92.54,
                     22.39, 93.37, 25.23, 97.24, 22.00, 96.05, 20.47, 97.02,
                     17.20, 96.29, 16.30, 97.38, 14.05, 98.12, 16.53, 97.38,
                     21.52, 95.59, 19.41, 97.13, 20.09, 92.55]).reshape((14, 2))

import numpy as np
import matplotlib.pyplot as plt
Population_Size = 100
Iteration_Number = 200
Cross_Rate = 0.8
Mutation_Rate = 0.003
Dna_Size = 10
X_Range=[0,5]
def F(x):
    '''
    目標(biāo)函數(shù)，需要被優(yōu)化的函數(shù)
    :param x:
    :return:
    '''
    return np.sin(10 * x) * x + np.cos(2 * x) * x
def CrossOver(Parent,PopSpace):
    '''
    交叉DNA，我們直接在種群里面選擇一個(gè)交配
    然后就生出孩子了
    :param parent:
    :param PopSpace:
    :return:
    '''
    if(np.random.rand()) < Cross_Rate:
        cross_place = np.random.randint(0, 2, size=Dna_Size).astype(np.bool)
        cross_one = np.random.randint(0, Population_Size, size=1) #選擇一位男/女士交配
        Parent[cross_place] = PopSpace[cross_one,cross_place]
    return Parent
def Mutate(Child):
    '''
    變異
    :param Child:
    :return:
    '''
    for point in range(Dna_Size):
        if np.random.rand() < Mutation_Rate:
            Child[point] = 1 if Child[point] == 0 else 0
    return Child
def TranslateDNA(PopSpace):
    '''
    把二進(jìn)制轉(zhuǎn)化為十進(jìn)制方便計(jì)算
    :param PopSpace:
    :return:
    '''
    return PopSpace.dot(2 ** np.arange(Dna_Size)[::-1]) / float(2 ** Dna_Size - 1) * X_Range[1]
def Fitness(pred):
    '''
    這個(gè)其實(shí)是對(duì)我們得到的F(x)進(jìn)行換算，其實(shí)就是選擇的時(shí)候
    的概率，我們需要處理負(fù)數(shù)，因?yàn)楦怕什荒転樨?fù)數(shù)呀
    pred 這是一個(gè)二維矩陣
    :param pred:
    :return:
    '''
    return pred + 1e-3 - np.min(pred)
def Select(PopSpace,Fitness):
    '''
    選擇
    :param PopSpace:
    :param Fitness:
    :return:
    '''
    '''
    這里注意的是，我們先按照權(quán)重去選擇我們的優(yōu)良個(gè)體，所以我們這里選擇的時(shí)候允許重復(fù)的元素出現(xiàn)
    之后我們就可以去掉這些重復(fù)的元素，這樣才能實(shí)現(xiàn)保留良種去除劣種。100--》70（假設(shè)有30個(gè)重復(fù)）
    如果不允許重復(fù)的話，那你相當(dāng)于沒(méi)有篩選
    '''
    Better_Ones = np.random.choice(np.arange(Population_Size), size=Population_Size, replace=True,
                           p=Fitness / Fitness.sum())
    # np.unique(Better_Ones) #這個(gè)是我后面加的
    return PopSpace[Better_Ones]
if __name__ == '__main__':
    PopSpace = np.random.randint(2, size=(Population_Size, Dna_Size))  # initialize the PopSpace DNA
    plt.ion() 
    x = np.linspace(X_Range, 200)
    # plt.plot(x, F(x))
    plt.xticks([0,10])
    plt.yticks([0,10])
    for _ in range(Iteration_Number):
        F_values = F(TranslateDNA(PopSpace))  
        # something about plotting
        if 'sca' in globals():
            sca.remove()
        sca = plt.scatter(TranslateDNA(PopSpace), F_values, s=200, lw=0, c='red', alpha=0.5)
        plt.pause(0.05)
        # GA part (evolution)
        fitness = Fitness(F_values)
        print("Most fitted DNA: ", PopSpace[np.argmax(fitness)])
        PopSpace = Select(PopSpace, fitness)
        PopSpace_copy = PopSpace.copy()
        for parent in PopSpace:
            child = CrossOver(parent, PopSpace_copy)
            child = Mutate(child)
            parent[:] = child
    plt.ioff()
    plt.show()

from math import floor
import numpy as np
import matplotlib.pyplot as plt
class Gena_TSP(object):
    """
    使用遺傳算法解決TSP問(wèn)題
    """
    def __init__(self, data, maxgen=200,
                 size_pop=200, cross_prob=0.9,
                 pmuta_prob=0.01, select_prob=0.8
                 ):
        self.maxgen = maxgen            # 最大迭代次數(shù)
        self.size_pop = size_pop        # 群體個(gè)數(shù)，（一次性瞎蒙多少個(gè)解）
        self.cross_prob = cross_prob    # 交叉概率
        self.pmuta_prob = pmuta_prob    # 變異概率
        self.select_prob = select_prob  # 選擇概率
        self.data = data        # 城市的坐標(biāo)數(shù)據(jù)
        self.num = len(data)    # 有多少個(gè)城市，對(duì)應(yīng)多少個(gè)坐標(biāo)，對(duì)應(yīng)染色體的長(zhǎng)度（我們的解叫做染色體）
        """
        計(jì)算城市的距離，我們用矩陣表示城市間的距離
        """
        self.__matrix_distance = self.__matrix_dis()
        self.select_num = int(self.size_pop * self.select_prob)
        # 通過(guò)選擇概率確定子代的選擇個(gè)數(shù)
        """
        初始化子代和父代種群，兩者相互交替
        """
        self.parent = np.array([0] * self.size_pop * self.num).reshape(self.size_pop, self.num)
        self.child = np.array([0] * self.select_num * self.num).reshape(self.select_num, self.num)
        """
        負(fù)責(zé)計(jì)算每一個(gè)個(gè)體的（瞎蒙的解）最后需要多少距離
        """
        self.fitness = np.zeros(self.size_pop)
        self.best_fit = []
        self.best_path = []
        # 保存每一步的群體的最優(yōu)路徑和距離
    def __matrix_dis(self):
        """
        計(jì)算14個(gè)城市的距離，將這些距離用矩陣存起來(lái)
        :return: 
        """
        res = np.zeros((self.num, self.num))
        for i in range(self.num):
            for j in range(i + 1, self.num):
                res[i, j] = np.linalg.norm(self.data[i, :] - self.data[j, :])
                res[j, i] = res[i, j]
        return res
    def rand_parent(self):
        """
        初始化種群
        :return:
        """
        rand_ch = np.array(range(self.num))
        for i in range(self.size_pop):
            np.random.shuffle(rand_ch)
            self.parent[i, :] = rand_ch
            self.fitness[i] = self.comp_fit(rand_ch)
    def comp_fit(self, one_path):
        """
        計(jì)算，咱們這個(gè)路徑的長(zhǎng)度，例如A-B-C-D
        :param one_path:
        :return:
        """
        res = 0
        for i in range(self.num - 1):
            res += self.__matrix_distance[one_path[i], one_path[i + 1]]
        res += self.__matrix_distance[one_path[-1], one_path[0]]
        return res
    def out_path(self, one_path):
        """
        輸出我們的路徑順序
        :param one_path:
        :return:
        """
        res = str(one_path[0] + 1) + '-->'
        for i in range(1, self.num):
            res += str(one_path[i] + 1) + '-->'
        res += str(one_path[0] + 1) + '\n'
        print(res)
    def Select(self):
        """
        通過(guò)我們的這個(gè)計(jì)算的距離來(lái)計(jì)算出概率，也就是當(dāng)前這些個(gè)體DNA也就瞎蒙的解
        之后我們?cè)谕ㄟ^(guò)概率去選擇個(gè)體，放到child里面
        :return:
        """
        fit = 1. / (self.fitness)  # 適應(yīng)度函數(shù)
        cumsum_fit = np.cumsum(fit)
        pick = cumsum_fit[-1] / self.select_num * (np.random.rand() + np.array(range(self.select_num)))
        i, j = 0, 0
        index = []
        while i < self.size_pop and j < self.select_num:
            if cumsum_fit[i] >= pick[j]:
                index.append(i)
                j += 1
            else:
                i += 1
        self.child = self.parent[index, :]
    def Cross(self):
        """
        模仿DNA交叉嘛，就是交換兩個(gè)瞎蒙的解的部分的解例如
        A-B-C-D
        C-D-A-B
        我們選幾個(gè)交叉例如這樣
        A-D-C-B
        1,3號(hào)交換了位置，當(dāng)然這里注意可不能重復(fù)啊
        :return:
        """
        if self.select_num % 2 == 0:
            num = range(0, self.select_num, 2)
        else:
            num = range(0, self.select_num - 1, 2)
        for i in num:
            if self.cross_prob >= np.random.rand():
                self.child[i, :], self.child[i + 1, :] = self.intercross(self.child[i, :],
                                                                             self.child[i + 1, :])
    def intercross(self, ind_a, ind_b):
        """
        這個(gè)是我們兩兩交叉的具體實(shí)現(xiàn)
        :param ind_a:
        :param ind_b:
        :return:
        """
        r1 = np.random.randint(self.num)
        r2 = np.random.randint(self.num)
        while r2 == r1:
            r2 = np.random.randint(self.num)
        left, right = min(r1, r2), max(r1, r2)
        ind_a1 = ind_a.copy()
        ind_b1 = ind_b.copy()
        for i in range(left, right + 1):
            ind_a2 = ind_a.copy()
            ind_b2 = ind_b.copy()
            ind_a[i] = ind_b1[i]
            ind_b[i] = ind_a1[i]
            x = np.argwhere(ind_a == ind_a[i])
            y = np.argwhere(ind_b == ind_b[i])
            if len(x) == 2:
                ind_a[x[x != i]] = ind_a2[i]
            if len(y) == 2:
                ind_b[y[y != i]] = ind_b2[i]
        return ind_a, ind_b
    def Mutation(self):
        """
        之后是變異模塊，這個(gè)就是按照某個(gè)概率，去替換瞎蒙的解里面的其中幾個(gè)元素。
        :return:
        """
        for i in range(self.select_num):
            if np.random.rand() <= self.cross_prob:
                r1 = np.random.randint(self.num)
                r2 = np.random.randint(self.num)
                while r2 == r1:
                    r2 = np.random.randint(self.num)
                self.child[i, [r1, r2]] = self.child[i, [r2, r1]]
    def Reverse(self):
        """
        近化逆轉(zhuǎn)，就是說(shuō)下一次瞎蒙的解如果沒(méi)有更好的話就不進(jìn)入下一代，同時(shí)也是隨機(jī)選擇一個(gè)部分的
        我們不是一次性全部替換
        :return: 
        """
        for i in range(self.select_num):
            r1 = np.random.randint(self.num)
            r2 = np.random.randint(self.num)
            while r2 == r1:
                r2 = np.random.randint(self.num)
            left, right = min(r1, r2), max(r1, r2)
            sel = self.child[i, :].copy()
            sel[left:right + 1] = self.child[i, left:right + 1][::-1]
            if self.comp_fit(sel) < self.comp_fit(self.child[i, :]):
                self.child[i, :] = sel
    def Born(self):
        """
        替換，子代變成新的父代
        :return:
        """
        index = np.argsort(self.fitness)[::-1]
        self.parent[index[:self.select_num], :] = self.child
def main(data):
    Path_short = Gena_TSP(data)     # 根據(jù)位置坐標(biāo)，生成一個(gè)遺傳算法類(lèi)
    Path_short.rand_parent()        # 初始化父類(lèi)
    ## 繪制初始化的路徑圖
    fig, ax = plt.subplots()
    x = data[:, 0]
    y = data[:, 1]
    ax.scatter(x, y, linewidths=0.1)
    for i, txt in enumerate(range(1, len(data) + 1)):
        ax.annotate(txt, (x[i], y[i]))
    res0 = Path_short.parent[0]
    x0 = x[res0]
    y0 = y[res0]
    for i in range(len(data) - 1):
        plt.quiver(x0[i], y0[i], x0[i + 1] - x0[i], y0[i + 1] - y0[i], color='r', width=0.005, angles='xy', scale=1,
                   scale_units='xy')
    plt.quiver(x0[-1], y0[-1], x0[0] - x0[-1], y0[0] - y0[-1], color='r', width=0.005, angles='xy', scale=1,
               scale_units='xy')
    plt.show()
    print('初始染色體的路程: ' + str(Path_short.fitness[0]))
    # 循環(huán)迭代遺傳過(guò)程
    for i in range(Path_short.maxgen):
        Path_short.Select()     # 選擇子代
        Path_short.Cross()      # 交叉
        Path_short.Mutation()   # 變異
        Path_short.Reverse()    # 進(jìn)化逆轉(zhuǎn)
        Path_short.Born()      # 子代插入
        # 重新計(jì)算新群體的距離值
        for j in range(Path_short.size_pop):
            Path_short.fitness[j] = Path_short.comp_fit(Path_short.parent[j, :])
        index = Path_short.fitness.argmin()
        if (i + 1) % 50 == 0:
            print('第' + str(i + 1) + '步后的最短的路程: ' + str(Path_short.fitness[index]))
            print('第' + str(i + 1) + '步后的最優(yōu)路徑:')
            Path_short.out_path(Path_short.parent[index, :])  # 顯示每一步的最優(yōu)路徑
        # 存儲(chǔ)每一步的最優(yōu)路徑及距離
        Path_short.best_fit.append(Path_short.fitness[index])
        Path_short.best_path.append(Path_short.parent[index, :])
    return Path_short  # 返回遺傳算法結(jié)果類(lèi)
if __name__ == '__main__':
    data = np.array([16.47, 96.10, 16.47, 94.44, 20.09, 92.54,
                     22.39, 93.37, 25.23, 97.24, 22.00, 96.05, 20.47, 97.02,
                     17.20, 96.29, 16.30, 97.38, 14.05, 98.12, 16.53, 97.38,
                     21.52, 95.59, 19.41, 97.13, 20.09, 92.55]).reshape((14, 2))
    main(data)