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### Help in Modeling travelling salesman problem.

Posted: **Wed Mar 13, 2019 2:47 am**

by **thegorila78**

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.

### Re: Help in Modeling travelling salesman problem.

Posted: **Wed Mar 13, 2019 5:13 am**

by **bussieck**

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/ ... _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/ ... _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

### Re: Help in Modeling travelling salesman problem.

Posted: **Wed Mar 13, 2019 2:26 pm**

by **thegorila78**

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!

### Re: Help in Modeling travelling salesman problem.

Posted: **Thu Mar 14, 2019 6:09 am**

by **bussieck**

Look at this post:

viewtopic.php?f=9&t=10428&p=24102. Here all subsets of a set are generated via the powerSetRight operator. That should help you doing it in the naive way.

-Michael