I'm facing trouble in counting linked nodes in Mathprog while trying to solve a quite-big TSP problem: let's say I have
set C := 0..645; # a set of nodes
set A := {i in C, j in C: i!=j}; # a set of edges
a distance function d(c1,c2)
var a{(i,j) in A}, binary; # binary variables that mean "go through edge i-j"
minimize walk: sum{(i,j) in A} d[i,j] * a[i,j]; # an objective function
and some other conditions
subject to get_out {i in C}: sum{(i,j) in A} a[i,j] = 1;
subject to get_in {j in C}: sum{(i,j) in A} a[i,j] = 1;
Making all possible cuts to solve the circuit requires the powerset and some other stuff but on more than 20 nodes the problem is too greedy and I can't get a solution.
So I thought I would constrain the solver to concatenate all a[i,j] imposing
a[i,j], a[j,k], a[k,w], ..., a[z,i] =1 with i!= {j,k,w,...,z} and j!={k,w,...,z} and ...
which is the same as
check(a[i,C]) {
while C is empty
take j: a[i,j]=1;
check( a[j,{C diff {i}}] )
}
which may not lead to a solution but is quite frustrating not to be able to implement such a simple thing... is there a way to implement such pseudo-code in mathprog (gmpl)?
