LPL - A Mathematical Modeling Language

model IntersectingLines "Paths in a Grid";
  set i   "A set of rows";
      j   "A set of columns";
      k   "A set of paths";
  parameter a{i,j} "Initial assignment";
  binary variable x{k,i,j} "paths points"; 
  constraint
    I{k,i,j|a[i,j]=k}: x[k,i,j]=1;
    N{k,i,j|a=k}: x[k,i,j+1]+x[k,i-1,j]
                 +x[k,i,j-1]+x[k,i+1,j]=1;
    L{k,i,j|a[i,j]<>k}: x[k,i,j] -> 
      (x[k,i,j+1]+x[k,i-1,j]+x[k,i,j-1]+x[k,i+1,j]=2);
    E{i,j}: sum{k} x <=1;
  minimize pathL: sum{k,i,j} x[k,i,j];

Write('path length = %2d\n', pathL);
  Draw.Scale(40,40);
  {i} Draw.Line(1,i,#j,i,9); {j} Draw.Line(j,1,j,#i,9);
  {i,j,k|x and x[k,i+1,j]} Draw.Line(j,i,j,i+1,0,4,2);
  {i,j,k|x and x[k,i,j+1]} Draw.Line(j,i,j+1,i,0,4,2);
  {i,j|~a} Draw.Circle(j,i,.04);
  {i,j|a} Draw.Circle(a&'',j,i,.2,1,0);

model data "A feasible layout";

i:= [1..8]; j:=[1..8]; k:=[1..5];
    a{i,j}:= [(1,1)=1 (4,5)=1  (1,3)=2 (7,5)=2, (2,5)=3 
              (6,7)=3, (3,3)=4 (3,8)=4, (6,2)=5 (4,8)=5];
  end 
end

Mathematical Modeling with LPL : Explain and run a Model