set Cities ordered;@\Vlabel{line:back:ampl:parstart}@
set Paths := {i in Cities, j in Cities: ord(i) < ord(j)};
param cost {Paths} >= 0;@\Vlabel{line:back:ampl:parend}@

var Take {Paths} binary;@\Vlabel{line:back:ampl:var}@

param n := card {Cities};@\Vlabel{line:back:ampl:compstart}@
set SubSets := 0 .. (2**n - 1);
set PowerSet {k in SubSets} := {i in Cities: (k div 2**(ord(i)-1)) mod 2 = 1};@\Vlabel{line:back:ampl:compend}@

minimize TotalCost: sum {(i,j) in Paths} cost[i,j] * Take[i,j];@\Vlabel{line:back:ampl:goal}@

subj to Tour {i in S}:@\Vlabel{line:back:ampl:con1}@
	sum {(i,j) in Paths} Take[i,j] + sum {(j,i) in Paths} Take[j,i] = 2;

subj to SubtourElimation {k in SubSet diff {0,2**n-1}}:@\Vlabel{line:back:ampl:con2}@
	sum {i in PowerSet[k], j in Cities diff PowerSet[k]: (i,j) in Paths} X[i,j] +
	sum {i in PowerSet[k], j in Cities diff PowerSet[k]: (j,i) in Paths} X[j,i] >= 2;