The following code solves the TSP with no subtours, using an idea

that is somewhat similar to the MTZ constraints.

$($a$)$ Explain how the code ensures there are no subtours in the

solution.

$($b$)$ What is the code in arcs, $t$ in $N$:$x[i,j,t]>0.$

doing? Why?

$($c$)$ Run this code using the gurobi solver for different numbers

of cities $n$ using the data provided in LNP$2024$dat.txt$,$ but

only consider a small number of cities. Do the results look

reasonable?

Note that this code will produce an 'error', which is that some

invalid subscripts are discarded. AMPL is just removing the

diagonal data $d_{ii}$ which are not required for this code, but it

is not a problem because AMPL will still compute a solution.

$($It is possible to remove the diagonals but they are required

for other code, so I've left them in$.)$