用Floyd算法解决选址问题（附完整matlab代码）

  以2021年五一建模比赛中的消防站选址为例，此问题为重心性加权最优选址问题。可考虑各区域的出警次数和人口密度，并对其进行加权分析处理。

  首先用Floyd算法求出距离矩阵，在考虑出警次数和人口密度的前提下找出已知距离图的15个重心点，数值最小点即为新建消防站点。若要在2021-2029年每隔3年新建1个消防站，则根据所求的15个顶点从最优到次优进行排序选址。

直接上代码：

function [D,R] = floyd(A)

n=size(a,1);D=a;

for i=1:n

    for j=1:n

        R(i,j)=j;

    end

end

for k=1:n

    for i=1:n

        for j=1:n

            if D(i,k)+D(k,j)

上面是Floyd函数的代码，下面是构建矩阵图的MATLAB代码，数据参考五一建模的消防选址题目。

a = [0 11.1 inf 11.4 inf inf inf inf inf inf inf inf 8.2 inf inf ;

    11.1 0 8.2 12.8 inf inf inf inf inf inf inf inf inf inf inf;

    inf 8.2 0 7.7 11.1 9.4 inf inf inf inf inf inf inf inf inf ;

    11.4 12.8 7.7 0 inf 6.9 inf inf inf 12.7 inf inf 14.3 10 8.5 ;

    inf inf 11.1 inf  0 7.4 inf inf inf inf inf inf inf inf inf;

    inf inf 9.4 6.9 7.4 0 inf inf inf inf inf inf inf inf inf ;

    inf inf inf inf inf inf 0 inf inf 12.9 13.4 14.5 inf 10.6 inf;

    inf inf inf inf inf inf inf 0 9 inf inf 12.3 inf inf inf ;

    inf inf inf inf inf inf inf 9 0 inf inf inf inf inf inf ;

    inf inf inf 12.7 inf inf 12.9 inf inf 0 9.5 inf 9.6 6.9 4.2 ;

    inf inf inf inf inf inf 13.4 inf inf 9.5 0 4.4 15 inf inf ;

    inf inf inf inf inf inf 14.5 12.3 inf inf 4.4 0 inf inf inf ;

    8.2 inf inf 14.3 inf inf inf inf inf 9.6 15 inf 0 inf inf ;

    inf inf inf 10 inf 11.2 10.6 inf inf 6.9 inf inf inf 0 5.9 ;

    inf inf inf 8.5 inf inf inf inf inf 4.2 inf inf inf 5.9 0];

q=[0.0578  0.052  0.0436  0.061  0.0745  0.0593  0.0607  0.0467  0.0405  0.0575  0.0573  0.0364  0.0702  0.0551  1.0256]

[D,R] =floyd(a)

s=q*D