優化算法之模擬退火算法

clear all;clc;close all
%模擬退火算法求解旅行商問題
%{
日期：
20190912_ZD
%}
t0 = clock;%計時
Inter = 1;%迭代次數初始化
a = 0.99;%溫度衰減係數
Ts = 120;%初始溫度
Te = 1;%截止溫度
T = Ts;
Markov = 1000;%Markov鏈長度
C = [1,2;70,90;80,60;10,100;800,200;800,100;90,80;200,600;230,4;500,90];
N = size(C,1);
D = zeros(N,N);
%計算各個城市之間的距離
for i = 1:N
    for j = 1:N
        D(i,j) = sqrt( sum((C(i,:) - C(j,:) ).^2));
    end
end
%隨機生成路徑
Route = randperm(N);
Route_new = [];
BestLength = inf;
BestRoute = [];
Length = inf;
%模擬退火過程
while T>= Te
    for j = 1:Markov
        %產生新路徑
        ind1 = (ceil(rand*10));
        ind2 = (ceil(rand*10));
        %交換兩個索引位置的城市座標
        tmp = Route(ind1);
        Route(ind1) = Route(ind2);
        Route(ind2) = tmp;
        Route_new = Route;
        %計算路徑距離
        Length_new = 0;
        Route_new1 = [Route_new,Route_new(1)];
        for i = 1:N
            Length_new = Length_new + D(Route_new1(i),Route_new1(i+1));
        end
        %判斷路徑長度
        if Length_new < Length
            Route = Route_new;
            Length = Length_new;
            if Length < BestLength
                BestLength = Length;
                BestRoute = Route;
                Inter = Inter + 1;
            end
        else
            %一定概率選擇較差的解
            if rand < exp(-(Length_new - Length) / T)
                Route = Route_new;
                Length = Length_new;
            end
        end
    end
    T = T*a;
end
%顯示結果
time = etime(clock,t0);
disp('計算時間爲：')
disp(time)
RouteFinal = [BestRoute,BestRoute(1)];
plot([C(RouteFinal,1)],[C(RouteFinal,2)],'Linewidth',3,'Marker','o','MarkerSize',10);
disp('最優路徑爲：')
disp(BestRoute)
disp('最短路徑爲：')
disp(BestLength)
for i = 1:N
    text(C(i,1),C(i,2),['      ',num2str(i)]);
end
xlabel('城市位置橫座標')
ylabel('城市位置縱座標')
title(['模擬退火算法(最短距離）:' num2str(BestLength) ''])

運行結果：