【TSP】改进的禁忌搜索算法之求解旅行商问题【Matlab 170期】

一、简介

旅行商问题(TSP问题)。假设有一个旅行商人要拜访全国31个省会城市,他需要选择所要走的路径,路径的限制是每个城市只能拜访一次，而且最后要回到原来出发的城市。路径的选择要求是所选路径的路程为所有路径之中的最小值。
在这里插入图片描述

二、源代码

%%%%%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;                        %清除所有变量
close all;                        %清图 
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个省会城市坐标
N=size(C,1);                      %TSP问题的规模,即城市数目
D=zeros(N);                       %任意两个城市距离间隔矩阵
%%%%%%%%%%%%%%%%%%%%%求任意两个城市距离间隔矩阵%%%%%%%%%%%%%%%%%%%%%
for i=1:N
    for j=1:N
        D(i,j)=((C(i,1)-C(j,1))^2+...
            (C(i,2)-C(j,2))^2)^0.5;
    end
end
Tabu=zeros(N);                      %禁忌表
TabuL=round((N*(N-1)/2)^0.5);       %禁忌长度
Ca=200;                             %候选集的个数(全部领域解个数)
CaNum=zeros(Ca,N);                  %候选解集合
S0=randperm(N);                     %随机产生初始解
bestsofar=S0;                       %当前最佳解
BestL=Inf;                          %当前最佳解距离
figure(1);
p=1;
Gmax=1000;                          %最大迭代次数   
%%%%%%%%%%%%%%%%%%%%%%%%%%%禁忌搜索循环%%%%%%%%%%%%%%%%%%%%%%%%%%
while p<Gmax
    ALong(p)=func1(D,S0);            %当前解适配值
    %%%%%%%%%%%%%%%%%%%%%%%%%%%交换城市%%%%%%%%%%%%%%%%%%%%%%%%%%
    i=1;
    A=zeros(Ca,2);                   %解中交换的城市矩阵
    %%%%%%%%%%%%%%%%%求领域解中交换的城市矩阵%%%%%%%%%%%%%%%%%%%%%
    while i<=Ca
        M=N*rand(1,2);
        M=ceil(M);         
        if M(1)~=M(2)
            A(i,1)=max(M(1),M(2));
            A(i,2)=min(M(1),M(2));
            if i==1
                isa=0;
            else
                for j=1:i-1
                    if A(i,1)==A(j,1) && A(i,2)==A(j,2)
                        isa=1;
                        break;
                    else
                        isa=0;
                    end
                end
            end
            if ~isa
                i=i+1;
            else
            end
        else
        end
    end
    %%%%%%%%%%%%%%%%%%%%%%%%%产生领域解%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%保留前BestCaNum个最好候选解%%%%%%%%%%%%%%%%%%%
    BestCaNum=Ca/2;
    BestCa=Inf*ones(BestCaNum,4);
    F=zeros(1,Ca);
    for i=1:Ca
        CaNum(i,:)=S0;
        CaNum(i,[A(i,2),A(i,1)])=S0([A(i,1),A(i,2)]);
        F(i)=func1(D,CaNum(i,:));
        if i<=BestCaNum
            BestCa(i,2)=F(i);
            BestCa(i,1)=i;
            BestCa(i,3)=S0(A(i,1));
            BestCa(i,4)=S0(A(i,2));
        else
            for j=1:BestCaNum
                if F(i)<BestCa(j,2)
                    BestCa(j,2)=F(i);
                    BestCa(j,1)=i;
                    BestCa(j,3)=S0(A(i,1));
                    BestCa(j,4)=S0(A(i,2));
                    break;
                end
            end
        end
    end

三、运行结果

在这里插入图片描述

四、备注

【TSP】改进的禁忌搜索算法之求解旅行商问题【Matlab 170期】

一、简介

二、源代码

三、运行结果

四、备注

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