```MODEL: ! DUPLEX, OBJ= 674; ! Find minimum set of links so that there are two paths, of at most two links, between every node pair; ! Keywords: telecommunications, network design, routing, hub network, redundant network; SETS: NODE:; ENDSETSDATA: NODE = A B C D E F G H I J; ENDDATA SETS: LINK( NODE, NODE) | &1 #LT# &2: COST, X; LXN( LINK, NODE) | (&1 #NE# &3) #AND# ( &2 #NE# &3): C; ENDSETSDATA: COST = 66 46 87 21 19 39 51 38 35 95 48 29 53 72 83 28 48 38 39 51 19 34 42 73 44 19 33 82 49 35 57 95 83 24 55 28 45 32 53 53 84 24 99 11 36; ENDDATA !-----------------------------------------; ! Minimize the cost of links chosen; MIN = @SUM( LINK: COST * X); ! Each node pair (I,J) must have at least two paths; @FOR( LINK( I, J): X( I, J) + @SUM( LXN( I, J, K): C( I, J, K)) >= 2; @BIN( X( I, J)); ); ! If the 2-link path C(I,J,K), between I and J, via K is used, both component links must be on; @FOR( LXN( I, J, K)| K #GT# J: C( I, J, K) <= X( I, K); C( I, J, K) <= X( J, K); ); @FOR( LXN( I, J, K)| K #LT# I: C( I, J, K) <= X( K, I); C( I, J, K) <= X( K, J); ); @FOR( LXN( I, J, K)| K #GT# I #AND# K #LT# J: C( I, J, K) <= X( I, K); C( I, J, K) <= X( K, J); ); END ```