LPL - A Mathematical Modeling Language

model Icosian "Hamiltonian's Game";
  set i,j    "set of vertices";
      e{i,j} "set of edges";
  parameter d{i,j} "distances"; 
  binary variable x{i,j|i<>j};
  constraint
    A{i}: sum{j} x = 1;
    B{j}: sum{i} x = 1;
    F{i,j|j>i}: x[i,j] + x[j,i] <= 1;
    G: x[14,7] "This is enough to make a single tour";
  minimize obj: sum{i,j} d*x "minimize a round trip";
  if obj then Write('No tour length of zero exists\n');
  else Write('An Icosian tour exists, see graph.\n'); 
 end;
  draw;

model data "The Icosian Game Instance"; 
    i:=[1..20];
    e{i,j}:= [(1,2) (2,3) (3,4) (4,5) (5,1) (1,6) (2,7) 
      (3,8) (4,9) (5,10) (6,14) (14,7) (7,15) (15,8) 
      (8,11) (11,9) (9,12) (12,10) (10,13) (13,6) 
      (14,19) (15,20) (11,16) (12,17) (13,18) (16,17) 
      (17,18) (18,19) (19,20) (20,16)];
    d{i,j}:= if(e[i,j] or e[j,i],0,1);
  end

model draw;
    parameter r:=6; PI:=4*Arctan(1);
      X{i}:=if(i<6,1,i<11,0.75,i<16,0.5,0.3)*r*
             Cos(3*PI/if(i<11,2,6)+(i-1)*2*PI/5)+r+.3; 
      Y{i}:=if(i<6,1,i<11,0.75,i<16,0.5,0.3)*r*
             Sin(3*PI/if(i<11,2,6)+(i-1)*2*PI/5)+r+.3;
    Draw.Scale(50,50);
    for{i,j|e} do Draw.Line(X[i],Y[i],X[j],Y[j]);  end;
    for{i,j|x} do Draw.Line(X[i],Y[i],X[j],Y[j],3,5);  end;
    --for{i,j|x} do Draw.CLine(X[i],Y[i],X[j],Y[j],1,3,5);  end;
    for{i} do Draw.Circle(i&'',X,Y,.35,1,0) ; end;
  end;  
end

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