set NODES ordered;
param hpos {NODES} >= 0;
param vpos {NODES} >= 0;

set PAIRS := {i in NODES, j in NODES: i != j};

param dist {(i,j) in PAIRS}
   := sqrt((hpos[j]-hpos[i])**2 + (vpos[j]-vpos[i])**2);

var X {PAIRS} binary;

minimize Tour_Length: sum {(i,j) in PAIRS} dist[i,j] * X[i,j];

subject to LeaveOnce {i in NODES}:
   sum {(i,j) in PAIRS} X[i,j] = 1;

subject to VisitOnce {j in NODES}:
   sum {(i,j) in PAIRS} X[i,j] = 1;

# subtour elimination:

param n := card(NODES);
param start symbolic := first(NODES);
var u{i in NODES}, >= 0;

# Miller, Tucker and Zemlin (MTZ) (1960)
subject to MTZ{(i,j) in PAIRS: i != start}:
   u[i]-u[j]+(n-1)*X[i,j] <= n-2;

# Desrochers and Laporte (1991)
subject to  DL{(i,j) in PAIRS: i != start}:
   u[i]-u[j]+(n-1)*X[i,j]+(n-3)*X[j,i] <= n-2;