lingo 住宅小区服务中心选址：某地新建一个生活住宅区,共有20栋住宅楼,小区内所有道路都是东西或南北走向,开发商拟在小区内修建一个服务中心,地址选在离所有楼房的总路程最小的地方.为

Question

lingo
住宅小区服务中心选址：某地新建一个生活住宅区,共有20栋住宅楼,小区内所有道路都是东西或南北走向,开发商拟在小区内修建一个服务中心,地址选在离所有楼房的总路程最小的地方.为保证建筑物之间有足够的空间,服务中心的位置与其他楼房位置之间的距离不能少于30米（已经考虑了所有建筑的占地面积）,请你确定服务中心的位置.
设初始点X0=[20,20],设（ai,bi）(i=1,.,20)为第i栋住宅楼的坐标：a=[29.74 4.9 69.32 65.0 98.3 55.27 40.0 19.8 62.5 73.3 37.58 0.98 41.98 75.37 79.38 92.0 84.47 36.77 62.08 73.13],b=[19.39 90.48 56,92 63.18 23.44 54.88 93.16 33.5 65.5 39.19 62.73 69.9 39.72 41.37 65.52 43.5 34.6 75.2 12.32 86.7].
model:
sets:
fw/A/:px,py;
zl/1..20/:x,y;
endsets
data:
x=29.74,4.9,69.32,65.0,98.3,55.27,40.0,19.8,62.5,73.3,37.58,0.98,41.98,75.37,79.38,92.0,84.47,36.77,62.08,73.13;
y=19.39,90.48,56.92,63.18,23.44,54.88,93.16,33.5,65.5,39.19,62.73,69.9,39.72,41.37,65.52,43.5,34.6,75.2,12.32,86.7;
enddata
min=@sum(zl(i):(((x(i)-px)^2)^(1/2)+((y(i)-py)^2)^(1/2));
@for(zl(i):-((x(i)-px)^2+(y(i)-py)^2)^(1/2)

Answer 1

model:
sets:
zl/1..20/:x,y;
endsets
data:
x=29.74,4.9,69.32,65.0,98.3,55.27,40.0,19.8,62.5,73.3,37.58,0.98,41.98,75.37,79.38,92.0,84.47,36.77,62.08,73.13;
y=19.39,90.48,56.92,63.18,23.44,54.88,93.16,33.5,65.5,39.19,62.73,69.9,39.72,41.37,65.52,43.5,34.6,75.2,12.32,86.7;
enddata
min=@sum(zl(i):(((x(i)-px)^2)^(1/2)+((y(i)-py)^2)^(1/2)));
@for(zl(i):(x(i)-px)^2+(y(i)-py)^2>=900);
end