旅行商問(wèn)題
????旅行商問(wèn)題(TSP 問(wèn)題)。假設(shè)有一個(gè)旅行商人要拜訪全國(guó)31個(gè)省會(huì)城市，他需要選擇所要走的路徑，路徑的限制是每個(gè)城市只能拜訪-一次， 而且最后要回到原來(lái)出發(fā)的城市。路徑的選擇要求是:所選路徑的路程為所有路徑之中的最小值。

免疫算法原理
???? 見(jiàn)鏈接：
萬(wàn)字長(zhǎng)文了解免疫算法原理 及求解復(fù)雜約束問(wèn)題（源碼實(shí)現(xiàn)）

二進(jìn)制編碼
免疫算法（二進(jìn)制）算例（源碼實(shí)現(xiàn)）

MATLAB版求解
注意事項(xiàng)：由于旅行商問(wèn)題中，各個(gè)個(gè)體不存在相同個(gè)體，所以無(wú)需計(jì)算濃度。

%%%%%%%%%%%%%%%%%%%%%%%免疫算法求解決TSP問(wèn)題%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all; %清除所有變量 close all; %清圖 clc; %清屏 C=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;...2370 2975]; %31個(gè)省會(huì)城市坐標(biāo) N=size(C,1); %TSP問(wèn)題的規(guī)模,即城市數(shù)目 D=zeros(N); %任意兩個(gè)城市距離間隔矩陣 %%%%%%%%%%%%%%%%%%%%%求任意兩個(gè)城市距離間隔矩陣%%%%%%%%%%%%%%%%%%%%% for i=1:Nfor j=1:ND(i,j)=((C(i,1)-C(j,1))^2+(C(i,2)-C(j,2))^2)^0.5;end end NP=200; %免疫個(gè)體數(shù)目 G=1000; %最大免疫代數(shù) f=zeros(N,NP); %用于存儲(chǔ)種群 for i=1:NPf(:,i)=randperm(N); %隨機(jī)生成初始種群 end len=zeros(NP,1); %存儲(chǔ)路徑長(zhǎng)度 for i=1:NPlen(i)=func(D,f(:,i),N); %計(jì)算路徑長(zhǎng)度 end [Sortlen,Index]=sort(len); Sortf=f(:,Index); %種群個(gè)體排序 gen=0; %免疫代數(shù) Ncl=10; %克隆個(gè)數(shù) %%%%%%%%%%%%%%%%%%%%%%%%%%%免疫循環(huán)%%%%%%%%%%%%%%%%%%%%%%%%%%%%% while gen<Gfor i=1:NP/2%%%%%%%%%%%%選激勵(lì)度前NP/2個(gè)體進(jìn)行免疫操作%%%%%%%%%%%%%%%a=Sortf(:,i);Ca=repmat(a,1,Ncl);for j=1:Nclp1=floor(1+N*rand());p2=floor(1+N*rand());while p1==p2p1=floor(1+N*rand());p2=floor(1+N*rand());endtmp=Ca(p1,j);Ca(p1,j)=Ca(p2,j);Ca(p2,j)=tmp;endCa(:,1)=Sortf(:,i); %保留克隆源個(gè)體%%%%%%%%%%%%克隆抑制，保留親和度最高的個(gè)體%%%%%%%%%%%%%%for j=1:NclCalen(j)=func(D,Ca(:,j),N);end[SortCalen,Index]=sort(Calen);SortCa=Ca(:,Index); af(:,i)=SortCa(:,1);alen(i)=SortCalen(1);end%%%%%%%%%%%%%%%%%%%%%%%%%%種群刷新%%%%%%%%%%%%%%%%%%%%%%%%%%for i=1:NP/2bf(:,i)=randperm(N); %隨機(jī)生成初始種群blen(i)=func(D,bf(:,i),N); %計(jì)算路徑長(zhǎng)度end %%%%%%%%%%%%%%%%%%%%免疫種群與新種群合并%%%%%%%%%%%%%%%%%%%%%f=[af,bf];len=[alen,blen];[Sortlen,Index]=sort(len);Sortf=f(:,Index);gen=gen+1;trace(gen)=Sortlen(1); end %%%%%%%%%%%%%%%%%%%%%%%%%%輸出優(yōu)化結(jié)果%%%%%%%%%%%%%%%%%%%%%%%%%%% Bestf=Sortf(:,1); %最優(yōu)變量 Bestlen=trace(end); %最優(yōu)值 figure for i=1:N-1plot([C(Bestf(i),1),C(Bestf(i+1),1)],...[C(Bestf(i),2),C(Bestf(i+1),2)],'bo-');hold on; end plot([C(Bestf(N),1),C(Bestf(1),1)],...[C(Bestf(N),2),C(Bestf(1),2)],'ro-'); title(['優(yōu)化最短距離:',num2str(trace(end))]); figure,plot(trace) xlabel('迭代次數(shù)') ylabel('目標(biāo)函數(shù)值') title('親和度進(jìn)化曲線')%%%%%%%%%%%%%%%%%%%%%%%%%%%%計(jì)算路線總長(zhǎng)度%%%%%%%%%%%%%%%%%%%%%%%%function len=func(D,f,N)len=D(f(N),f(1));for i=1:(N-1)len=len+D(f(i),f(i+1));endend

python版求解

import numpy as np import pandas as pd from tqdm import tqdm#進(jìn)度條設(shè)置 import matplotlib.pyplot as plt from pylab import * import matplotlib; matplotlib.use('TkAgg') mpl.rcParams['font.sans-serif'] = ['SimHei'] mpl.rcParams['axes.unicode_minus'] = Falsecity_num = 31 # 城市的數(shù)量 #############1.數(shù)據(jù)集 城市坐標(biāo) C=[1304 ,2312,3639 ,1315,4177 ,2244,3712 ,1399,3488, 1535,3326, 1556,3238 ,1229,4196 ,1044,4312,790,4386,570,3007,1970,2562 ,1756,2788, 1491,2381 ,1676,1332,695,3715 ,1678,3918,2179,4061,2370,3780, 2212,3676, 2578,4029,2838,4263,2931,3429,1908,3507,2376,3394 ,2643,3439,3201,2935,3240,3140,3550,2545,2357,2778,2826,2370 ,2975] #31個(gè)省會(huì)城市坐標(biāo) C=np.array(C).reshape(-1,2)#shape=(31, 2)###############相關(guān)函數(shù)：距離和親和度函數(shù)（路程） 路徑畫圖函數(shù)####################.函數(shù)：計(jì)算城市之間的距離 def calculate_distance(X, Y):"""計(jì)算城市兩輛之間的歐式距離，結(jié)果用numpy矩陣存儲(chǔ):param X: 城市的X坐標(biāo)，np.array數(shù)組:param Y: 城市的Y坐標(biāo)，np.array數(shù)組"""distance_matrix = np.zeros((city_num, city_num))for i in range(city_num):for j in range(city_num):if i == j:continuedis = np.sqrt((X[i] - X[j]) ** 2 + (Y[i] - Y[j]) ** 2) # 歐式距離計(jì)算distance_matrix[i][j] = disreturn distance_matrix##適應(yīng)度函數(shù) 計(jì)算總距離 def fitness_func(distance_matrix, xi):"""適應(yīng)度函數(shù)，計(jì)算目標(biāo)函數(shù)值.:param distance: 城市的距離矩陣:param xi: PSO的一個(gè)解:return: 目標(biāo)函數(shù)值，即總距離"""total_distance = 0for i in range(1, city_num):start = xi[i - 1]end = xi[i]total_distance += distance_matrix[start][end]total_distance += distance_matrix[end][xi[0]] # 從最后一個(gè)城市回到出發(fā)城市return total_distance#路徑畫圖 def plot_tsp(gbest):"""繪制最優(yōu)解的圖形"""X=D[:,0]#城市坐標(biāo)的X軸Y=D[:,1]#城市坐標(biāo)的Y軸plt.scatter(X, Y, color='r')for i in range(1, city_num):start_x, start_y = X[gbest[i - 1]], Y[gbest[i - 1]]end_x, end_y = X[gbest[i]], Y[gbest[i]]plt.plot([start_x, end_x], [start_y, end_y], marker='>',alpha=0.8)start_x, start_y = X[gbest[0]], Y[gbest[0]]plt.plot([start_x, end_x], [start_y, end_y], color='b', alpha=0.8)plt.show()#############免疫算法相關(guān)函數(shù)############免疫操作函數(shù)：克隆、變異、變異抑制 def variation(Sortf):"""param Sortf:按親和度大小排序后的群體return :af 經(jīng)過(guò)克隆、變異、變異抑制后的群體#變異原理：交換個(gè)體中兩個(gè)元素的位置"""Ncl = 10 # 克隆個(gè)數(shù)af = np.zeros((np.int(NP / 2), city_num),dtype=np.int) # 存儲(chǔ)變異后的個(gè)體for i in range(np.int(NP / 2)): # 遍歷前一半個(gè)體# 選激勵(lì)度前NP/2個(gè)體進(jìn)行免疫操作a = Sortf[i] # 當(dāng)前個(gè)體 .shape(city_num,)a = a.reshape(-1, city_num) # （-1，維度city_num）Na = np.tile(a, (Ncl, 1)) # 對(duì)當(dāng)前個(gè)體進(jìn)行克隆 Na.shape=(Ncl, city_num)for j in range(Ncl): # 遍歷每一個(gè)克隆樣本p1=np.random.randint(0,city_num,1)[0] # 隨機(jī)產(chǎn)生一個(gè)整數(shù)[0,31)p2 = np.random.randint(0, city_num, 1)[0] # [0,31)while p1 == p2:p1 = np.random.randint(0, city_num, 1)[0] # 隨機(jī)產(chǎn)生一個(gè)整數(shù)[0,31)p2 = np.random.randint(0, city_num, 1)[0] # [0,31)tmp = Na[j,p1]Na[j,p1] = Na[j,p2]Na[j,p2] = tmp# 保留克隆源個(gè)體Na[0, :] = Sortf[i]#####克隆抑制，保留親和度最高的個(gè)體NaMSLL = np.zeros((Ncl, 1)) # 存儲(chǔ)變異種群親和度值for j in range(Ncl): # 遍歷每一個(gè)克隆樣本NaMSLL[j] = fitness_func(D, xi=Na[j]) # 親和度=距離Index = np.argsort(NaMSLL, axis=0) # 激勵(lì)度按升序排序Index = Index[:, 0]NaSortf = Na[Index] # 排序后的種群af[i] = NaSortf[0] # 取最優(yōu)return af#免疫操作：創(chuàng)建新生種群 def refresh():bf = np.zeros((np.int(NP/2), city_num), dtype=np.int)for i in range(np.int(NP/2)): # 遍歷每一個(gè)個(gè)體bf[i, :] = np.random.choice(list(range(0, city_num)), size=city_num, replace=False) # 群體初始化return bf#############免疫算法開(kāi)始############ D=calculate_distance(C[:,0], C[:,1])#任意兩個(gè)城市距離間隔矩陣 shape=(31, 31)NP=200 #免疫個(gè)體數(shù)目 G=600 #最大免疫代數(shù) f=np.zeros((NP,city_num),dtype=np.int) #用于存儲(chǔ)種群 shape=(200, 31) for i in range(NP):#遍歷每一個(gè)個(gè)體f[i,:]=np.random.choice(list(range(0, city_num)), size=city_num, replace=False)#群體初始化len=np.zeros((NP,1)) #存儲(chǔ)路徑長(zhǎng)度 for i in range(NP):#遍歷每一個(gè)個(gè)體len[i]=fitness_func(D, xi=f[i]) #計(jì)算初始群體每個(gè)個(gè)體的路程長(zhǎng)度###激勵(lì)度按升序排序 Index=np.argsort(len,axis=0) Index=Index[:,0] Sortf=f[Index] # #排序后的初始群體 shape=(200, 31)##############免疫循環(huán)############ trace=[] #記錄迭代激勵(lì)度最優(yōu)值 for gen in tqdm(range(G)):#遍歷每一次迭代af = variation(Sortf) # 選擇一半個(gè)體 進(jìn)行克隆、變異、變異抑制 shape=(100, 31)aflen=np.zeros((af.shape[0],1)) #存儲(chǔ)af群體路徑長(zhǎng)度 shape=(100, 1)for j in range(af.shape[0]):#遍歷af中的每一個(gè)個(gè)體aflen[j] = fitness_func(D, xi=af[j]) # 計(jì)算af群體每個(gè)個(gè)體的路程長(zhǎng)度(親和度）bf = refresh() # 創(chuàng)建一半新生種群#bf.shape=(100, 31)bflen = np.zeros((bf.shape[0], 1)) # 存儲(chǔ)bf群體路徑長(zhǎng)度 shape=(100, 1)for j in range(bf.shape[0]):#遍歷af中的每一個(gè)個(gè)體bflen[j] = fitness_func(D, xi=bf[j]) # 計(jì)算af群體每個(gè)個(gè)體的路程長(zhǎng)度(親和度）# ##########種群刷新：免疫種群與新生種群合并##f1 = np.concatenate((af, bf), axis=0) # 合并的種群 f1.shape=(50, 2) f1為子代f1len = np.concatenate((aflen, bflen), axis=0) # 合并種群激勵(lì)度值 shape=(200, 1)Index = np.argsort(f1len, axis=0)Index = Index[:, 0]Sortf = f1[Index] # shape(50, 2)trace.append(fitness_func(D, xi=f1[0])) # 記錄最優(yōu)個(gè)體的激勵(lì)度值############輸出優(yōu)化結(jié)果 Bestf=Sortf[0,:] #最優(yōu)變量 print('最優(yōu)變量',Bestf) print('最優(yōu)值',trace[-1] ) #最優(yōu)值 plt.plot(trace) plt.title('迭代曲線') plt.show() plot_tsp(Bestf)

作者：電氣 余登武

與50位技術(shù)專家面對(duì)面20年技術(shù)見(jiàn)證，附贈(zèng)技術(shù)全景圖

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