《模擬退火(SA)求解TSP問題》

問題：柏林有52座城市，每座城市的座標數據在coordinates中，求TSP的解答。

a = 0.99;
T0 = 97; Tf = 3; t = T0;
MarkovLength = 10000;

coordinates = [
1    565.0   575.0; 2     25.0   185.0; 3    345.0   750.0; 
4    945.0   685.0; 5    845.0   655.0; 6    880.0   660.0; 
7     25.0   230.0; 8    525.0  1000.0; 9    580.0  1175.0; 
10   650.0  1130.0; 11  1605.0   620.0; 12  1220.0   580.0; 
13  1465.0   200.0; 14  1530.0     5.0; 15   845.0   680.0; 
16   725.0   370.0; 17   145.0   665.0; 18   415.0   635.0; 
19   510.0   875.0; 20   560.0   365.0; 21   300.0   465.0; 
22   520.0   585.0; 23   480.0   415.0; 24   835.0   625.0; 
25   975.0   580.0; 26  1215.0   245.0; 27  1320.0   315.0; 
28  1250.0   400.0; 29   660.0   180.0; 30   410.0   250.0; 
31   420.0   555.0; 32   575.0   665.0; 33  1150.0  1160.0; 
34   700.0   580.0; 35   685.0   595.0; 36   685.0   610.0; 
37   770.0   610.0; 38   795.0   645.0; 39   720.0   635.0; 
40   760.0   650.0; 41   475.0   960.0; 42    95.0   260.0; 
43   875.0   920.0; 44   700.0   500.0; 45   555.0   815.0; 
46   830.0   485.0; 47  1170.0    65.0; 48   830.0   610.0; 
49   605.0   625.0; 50   595.0   360.0; 51  1340.0   725.0; 
52  1740.0   245.0; 
];

coordinates(:,1) = [];
amount = size(coordinates, 1);
%使用矩陣方法計算巧妙得到距離矩陣
distMatrix = zeros(amount, amount);

coorXTemp1 = coordinates(:,1) * ones(1,amount);
coorXTemp2 = coorXTemp1';

coorYTemp1 = coordinates(:,2) * ones(1,amount);
coorYTemp2 = coorYTemp1';

distMatrix = sqrt((coorXTemp1-coorXTemp2).^2 + (coorYTemp1-coorYTemp2).^2);

newSol =1:amount;
curResult = inf; bestResult = inf;
curSol = newSol; bestSol = newSol;

p=1;
while t >= Tf
    for r = 1:MarkovLength
        %產生隨機擾動
        if rand<0.5
            %兩交換
            index1 = 0; index2 = 0;
            while index1 == index2
                index1 = ceil(rand*amount);
                index2 = ceil(rand*amount);
            end
            %三段式交換
            tmp = newSol(index1);
            newSol(index1) = newSol(index2);
            newSol(index2) = tmp;
        else
            %三交換
            index1 = 0; index2 = 0; index3 = 0;
            while (index1 == index2)||(index1 == index3)||(index2 == index3)||(abs(index1-index2) == 1)
                index1 = ceil(rand*amount);
                index2 = ceil(rand*amount);
                index3 = ceil(rand*amount);
            end

            tmp1 = index1; tmp2 = index2; tmp3 = index3;

            %確保index1 < index2 < index3
            if(index1 < index2)&&(index2<index3);
            elseif (index1 < index3)&&(index3<index2)
                index2 = tmp3; index3 = tmp2;
            elseif (index2 < index1)&&(index1<index3)
                index1 = tmp2; index2 = tmp1;
            elseif (index2 < index3)&&(index3<index1)
                index1 = tmp2; index2 = tmp3; index3 = tmp1;
            elseif (index3 < index1)&&(index1<index2)
                index1 = tmp3; index2 = tmp1; index3 = tmp2;
            elseif (index3 < index2)&&(index2<index1);
                index1 = tmp3; index3 = tmp1;
            end

            tmpRoute = newSol((index1+1):(index2-1));
            newSol((index1+1):(index1 + index3-index2 + 1)) = newSol(index2:index3);
            newSol((index1 + index3 - index2 + 2):index3) = tmpRoute;
        end

        newResult = 0;
        for i = 1:(amount-1)
            newResult = newResult + distMatrix(newSol(i),newSol(i+1));
        end
        newResult = newResult + distMatrix(newSol(amount), newSol(1));

        if newResult < curResult
            curResult = newResult;
            curSol = newSol;
            if newResult < bestResult
                bestResult = newResult;
                bestSol = newSol;
            end
        else
            if rand < exp(-(newResult - curResult)/t)
                curResult = newResult;
                curSol = newSol;
            else
                newSol = curSol;
            end
        end
    end
    t = t * a;  
end

disp('最優解爲：');
disp(bestSol);
disp('最短距離爲：');
disp(bestResult);

運行結果

最優解爲：
1 至 23 列

19 41 8 9 10 43 33 51 11 52 14 13 47 26 27 28 12 25 4 6 15 5 24

24 至 46 列

48 38 37 40 39 36 35 34 44 46 16 29 50 20 23 30 2 7 42 21 17 3 18

47 至 52 列

31 22 1 49 32 45

最短距離爲：
7.5444e+03