用lingo解决“最短路径问题”

求城市A到城市D的最短路径？

用ligno解决的代码，如下：

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model:
!A到D的最短路径;
!We hava a network of 7 cities.
 we want to find the length of the shortest route form city 1 to city 7;

sets:
 !Here is our primitive set of seven cities;
 cities /A,B1,B2,C1,C2,C3,D/ ;
 !The Derived set "roads" lists the roads that
   exist between the cities ;
 roads(cities,cities)/
   A,B1 A,B2 B1,C1 B1,C2 B1,C3 B2,C1 B2,C2 B2,C3
   C1,D C2,D C3,D/: w,x;
endsets

data:
 !Here are  the distances that correspond to above links;
 w= 2 4 3 3 1 2 3 1 1 3 4;
enddata

n= @size(cities); !The number of cities;
min= @sum(roads: w*x);
@for(cities(i)|i #ne# 1 #and# i #ne# n:
   @sum(roads(i,j): x(i,j))= @sum(roads(j,i): x(j,i)));
@sum(roads(i,j)|i #eq# 1: x(i,j))=1;
end

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结果如下：

解释如下：

   即最短路径为A→B1→C1→D，最短路长为6个单位。