七、附录
附录1：
sets:
dian/1..9/:x,y,z; qian/1..9/:w; endsets data:
x=22 8 5 52 38 16 81 18 62; y=38 13 81 32 11 12 63 45 12; z=17 40 60 25 30 15 50 8 35; enddata
w(1)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(1)-x(j))+@abs(y(1)-y(j)))*z(j)*(@abs(x(1)-x(j))+@abs(y(1)-y(j))));
w(2)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(2)-x(j))+@abs(y(2)-y(j)))*z(j)*(@abs(x(2)-x(j))+@abs(y(2)-y(j))));
w(3)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(3)-x(j))+@abs(y(3)-y(j)))*z(j)*(@abs(x(3)-x(j))+@abs(y(3)-y(j))));
w(4)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(4)-x(j))+@abs(y(4)-y(j)))*z(j)*(@abs(x(4)-x(j))+@abs(y(4)-y(j))));
w(5)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(5)-x(j))+@abs(y(5)-y(j)))*z(j)*(@abs(x(5)-x(j))+@abs(y(5)-y(j))));
w(6)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(6)-x(j))+@abs(y(6)-y(j)))*z(j)*(@abs(x(6)-x(j))+@abs(y(6)-y(j))));
w(7)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(7)-x(j))+@abs(y(7)-y(j)))*z(j)*(@abs(x(7)-x(j))+@abs(y(7)-y(j))));
w(8)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(8)-x(j))+@abs(y(8)-y(j)))*z(j)*(@abs(x(8)-x(j))+@abs(y(8)-y(j))));
w(9)=@sum(dian(j)|j#ge#1 #and#
j#le#9:(@abs(x(9)-x(j))+@abs(y(9)-y(j)))*z(j)*(@abs(x(9)-x(j))+@abs(y(9)-y(j))));
9
Feasible solution found.
Total solver iterations: 0
Variable Value X( 1) 22.00000 X( 2) 8.000000 X( 3) 5.000000 X( 4) 52.00000 X( 5) 38.00000 X( 6) X( 7) X( 8) X( 9) Y( 1) Y( 2) Y( 3) Y( 4) Y( 5) Y( 6) Y( 7) Y( 8) Y( 9) Z( 1) Z( 2) Z( 3) Z( 4) Z( 5) Z( 6) Z( 7) Z( 8) Z( 9) W( 1) W( 2) W( 3) W( 4) W( 5) W( 6) W( 7) W( 8) W( 9) Row 1 2 10
16.00000 81.00000 18.00000 62.00000 38.00000 13.00000 81.00000 32.00000 11.00000 12.00000 63.00000 45.00000 12.00000 17.00000 40.00000 60.00000 25.00000 30.00000 15.00000 50.00000 8.000000 35.00000 886298.0 1335914. 1924178. 1046714. 1243946. 1255578. 2041850. 913322.0 1513034. 0.000000 0.000000
Slack or Surplus
3 0.000000 4 0.000000 5 0.000000 6 0.000000 7 0.000000 8 0.000000 9 0.000000
附录2：
min=k*((22-x)^2+(38-y)^2)*17+k*((8-x)^2+(13-y)^2)*40+k*((5-x)^2+(81-y)^2)*60+k*((52-x)^2+(32-y)^2)*25+k*((38-x)^2+(11-y)^2)*30+
k*((16-x)^2+(12-y)^2)*15+k*((81-x)^2+(63-y)^2)*50+k*((18-x)^2+(45-y)^2)*8+k*((62-x)^2+(12-y)^2)*35;
x>=-100; x<=100; y>=-100; y<=100; k>=1;
Local optimal solution found.
Objective value: 455120.1 Extended solver steps: 5 Total solver iterations: 80
Variable Value Reduced Cost K 1.000000 0.000000 X 35.85000 0.000000 Y 40.23571 0.000000
Row Slack or Surplus Dual Price 1 455120.1 -1.000000 2 135.8500 0.000000 3 64.15000 0.000000 4 140.2357 0.000000 5 59.76429 0.000000 6 0.000000 -455120.1
附录3：
x=[22 8 5 52 38 16 81 18 62]
11
x =
22 8 5 52 38 16 81 18 62
>> y=[38 13 81 32 11 12 63 45 12] y =
38 13
>> plot(x,y)
附录4：
>> clear >> A=[22 38 8 13 5 81 52 32 38 11 16 12 81 63 18 45 62 12 ]
A =
22 38 8 13 5 81 52 32 38 11 16 12 81 63 18 45 62 12
>> X = A(:,1); Y = A(:,2);
N = length(X); D = zeros(N,N);
81 32 11 12 63 45 12
12
for I = 2:N for J = 1:I-1
D(I,J) = sqrt((X(I) - X(J))*(X(I) - X(J)) + (Y(I) - Y(J))*(Y(I) - Y(J))); end
end
>> D % 任意两点间距离 D1 = D+D' % 任意两点间距离 D =
Columns 1 through 7
0 0 28.6531 0 46.2385 68.0661 30.5941 47.9270 31.3847 30.0666 26.6833 8.0623 64.0781 88.4816 8.0623 33.5261 47.7074 54.0093
Columns 8 through 9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 55.0000 0 D1 =
Columns 1 through 7
0 28.6531
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 67.8970 0 0 0 0 77.3886 25.2389 0 0 0 69.8713 41.1825 22.0227 0 0 78.1025 42.4500 67.4759 82.6196 0 38.2753 36.4005 39.4462 33.0606 65.5210 89.4986 22.3607 24.0208 46.0000 54.4243 46.2385 30.5941 31.3847 26.6833 64.0781
13