I am having trouble modeling the last constraint for this TSP model. I have the first 3 constraints modeled properly but the last one I can’t figure out how to model in GAMS. I attached my code and a screenshot of the constraints. Specifically the last one requires me to keep track of a subset in GAMS and I am confused about how to do that. Any help would be appreciated.

hw6-1.gms (1.12 KB)

Since there are exponentially many subtours (subsets of {2…n}) you would not do this explicitly. For small n you would use the compact MTZ formulation (see https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_tsp5.html). For larger instances you should *generate* the subtour constraints that are needed using an iterative approach, see tsp1*tsp4 in the GAMS Model Library (https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_tsp1.html). For very large (and pure) TSP problems you would use a special purpose solver (not part of GAMS) like Concorde (http://www.math.uwaterloo.ca/tsp/concorde.html).

-Michael

How would I do this the naive way? Like by running the model over and over again until I got a solution.

Thanks for the response!

Look at this post: https://newforum.gams.com/t/aggregate-parameter-indices/2230/3 Here all subsets of a set are generated via the powerSetRight operator. That should help you doing it in the naive way.

-Michael

Hello there,

The Mathematical Model of Traveling Salesman Problem with Alternative Pick up and Delivery nodes. The original single/multi automated guided vehicle (AGV) scheduling problem with a specific pick up and delivery node can be formulated and solved as single/multi traveling salesman problem (TSP/MTSP).

Look at this problem post travelling salesman problem.