text: Update: see the comments below for some helpful hints. If you are unable to run this with your version of Solver Foundation and Gurobi, consider installing the lp_solve plugin for MSF. More details on this thread.
  Here’s an example that I walked through during yesterday’s INFORMS session. Erwin has two blog postings about Solver Foundation and the traveling salesman problem, but I want to throw in my two cents because I want to emphasize a couple of points:
  - By combining C# and Solver Foundation Services it is possible to express complex models clearly and succinctly.
  - It is very easy to build powerful, reusable model libraries using C# and Solver Foundation Services.
  - Solver Foundation Services code can be used in many different application environments (ASP.Net, silverlight, DB, command line apps, WPF, …) with minimal changes.
  The traveling salesman problem is a classical problem in computer science, and you should bow your head in shame if you don’t know about it (and turn in your conference badge if you happen to be in Phoenix). William Cook’s book on the traveling salesman problem is a wonderful read.; namespace Microsoft.SolverFoundation.Samples { class TravelingSalesman { //:
  - Assign[i,j]: this is equal to 1 if the optimal tour contains a trip (or arc) from city i to city j.
  - Rank[i]: this is equal to the number of cities visited after arriving at city i.
  We have one parameter in our model:
  - Distance[I,j]: the distance from city i to city j.
  With that in mind, here’s the model. Explanation of the goals and constraints follow.
  public static void Run() { SolverContext context = SolverContext.GetContext(); context.ClearModel();1", Model.ForEach(city, i => Model.Sum(Model.ForEachWhere(city, j => assign[i, j], j => i != j)) == 1)); model.AddConstraint("assign2", Model.ForEach(city, j => Model.Sum(Model.ForEachWhere(city, i => assign[i, j], i => i != j)) == 1)); model.AddConstraint("A1", Model.ForEach(city, i => Model.Sum(Model.ForEachWhere(city, j => assign[i, j], j => i != j)) == 1)); model.AddConstraint("A2", Model.ForEach(city, j => Model.Sum(Model.ForEachWhere(city, i => assign[i, j], i => i != j)) == 1)); // Forbid subtours (Miller, Tucker, Zemlin - 1960...) model.AddConstraint("nosubt.
  Getting the cost is very easy using goal.ToDouble(). We can get the tour using either Assign or Rank. I have chosen to use Assign because it gives me another opportunity to use LINQ. When you call GetValues() on a decision, you get arrays that contain the value along with the indexes for each decision. In this case, the last entry in the array is the one we are interested in. There are other ways to conveniently query decsision results, I’ll save that for another time.
  The next post will show how we can use Solver Foundation’s plug-in model to tune the behavior of the Gurobi MIP solver.
  Dear Nathan,
  Thank you very much for the sources and explanation. I’ve got a question, the obtained solution is optimal? Solver Foundation provide exact solution and it is not a heuristic?
  Best regards,
  Sergey
  Hi Sergey, thanks for your comment. Yes, the obtained solution is provably optimal. Results returned by the linear and mixed integer linear solvers are globally optimal (unless the solution status says otherwise, for example if the problem is infeasible).
  Nate
  Dear Nathan,
  Thank you for the answer.
  The code works perfectly well as it gives optimal result. But the sequence seems not to be correct. E.g. optimal is: 335, but when I summarize the distances between the obtained nodes in sequence, then it is 783.
  I think the optimality is found correct, I tested this code and compared results with Brute-force algorithms, for 6 points. But likely there is an error of extracting the right tour from the solver. It seems like extracted tour is not last found or so.
  I would be very grateful if you could give any suggestions.
  Best regards,
  Sergey
  The solution printed to Console does not appear to be correct or is at least misleading. The output:
  5 -> 10 -> 15 -> …
  implies you travel from city5 to city10 to city15…
  But the output code appears to be written as a list of destinations ordered by origin city with no such that:
  city5 comes after 0, city10 comes after 1, city15 comes after 3, etc.
  -Ed
  Dear Nathan,
  I used the report command:
  “Report report = solution.GetReport();
  Console.Write(“{0}”, report);”
  And it is possible to extract the right sequence out of there from “assign”.
  Could you recommend any other elegant way?
  Strange, but
  ” var tour = from p in assign.GetValues() where (double)p[0] > 0.9 select p[2];”
  gives something wrong.
  Best regards,
  Sergey
  The problem is in the display of the result. This seems to work:
  var tour = from p in assign.GetValues() where (double)p[0] > 0.9 select p;
  foreach (var t in tour)
  {
  Console.WriteLine(“{0} -> {1}”, t[1], t[2]);
  }
  -Ed
  Ed – thanks for identifying the problem!
  That works. Ed and Nathan, thanks for proposed solution!
  I tried to run this for 25 cities, but it exceeded the Gurobi solver throttle. Is there a way to tell SFS to use a different solver? Is there a good FOSS solver out there with a plugin for SFS?
  Thanks,
  -Ed
  I faced the same problem, I also tried to follow thes instructions (), but it did not work out.
  Best regards,
  Sergey
  You can try the lpsolve connector. This thread has more:
  Thanks you for the answer. I attached Ipsolver into the project.
  I got this from report:
  “Solve Time (ms): 15412
  Total Time (ms): 15593
  Solve Completion Status: Optimal
  Solver Selected: Microsoft.SolverFoundation.Solvers.SimplexSolver”
  This is for 15 cities configuration. Gurobi solved it within 500 ms. IPSolver 30 times slower.
  Ed, how is it in your example? Slow too?
  Best regards,
  Sergey
  Somehow I managed to force Gurobi Solver to work with 30 cities.
  May be the last time I did something wrong, or now it works, because I got an academic license.
  The time needed for 30 points is:
  Solve Time (ms): 46261
  Total Time (ms): 46460
  Solve Completion Status: Optimal
  Solver Selected: SolverFoundation.Plugin.Gurobi.GurobiSolver
  The academic license does not have problem size limitations, which is why it works now.
  Hi Sergey,
  I have not yet been able to solve using the LPSolve plugin. If I figure it out, I’ll follow up with performance observations. Right now I’m getting the following:
  “A call to PInvoke function ‘LpSolvePlugIn!LpSolveNativeInterface.lpsolve::set_timeout’ has unbalanced the stack. This is likely because the managed PInvoke signature does not match the unmanaged target signature. Check that the calling convention and parameters of the PInvoke signature match the target unmanaged signature.”
  It is occuring in the plugin code at:
  lpsolve.set_timeout(_lp, prms._LpSolveTimeout);
  Thanks,
  -Ed
  I got it going, and I’m seeing a similar performance difference. The Gurobi solved 20 cities in about 2 seconds, and the LP took about 23.
  Ed, I would recommend you to get an academic license from Gurobi (in case if it suits you) and try with it. But I did not use DLL from their package, but rather from here:
  It seems that this library also start to work, when you got a license.
  In case if it does not work, try these DLLs:
  And put them here:
  C:\Program Files\Microsoft Solver Foundation\3.0.2.10889\Plugins
  Although I have 64bit PC, this win32 library works fine. Have no idea how does it work.
  Let me know, when you download libs, so that I can delete them from DropBox.
  Thanks Sergey,
  I’d prefer to find/use a good open source solver and it turns out that the LPSolve is actually working marginally faster for me than Gurobi in the hacked up test case with which I’m playing. Here are two runs on 20 cities:
  Version: Microsoft Solver Foundation 3.0.2.10889 Express Edition
  Model Name: DefaultModel
  Capabilities Applied: MILP
  Solve Time (ms): 45
  Total Time (ms): 466
  Solve Completion Status: Optimal
  Solver Selected: SolverFoundation.Plugin.LpSolve.LpSolveSolver
  Version: Microsoft Solver Foundation 3.0.2.10889 Express Edition
  Model Name: DefaultModel
  Capabilities Applied: MILP
  Solve Time (ms): 76
  Total Time (ms): 534
  Solve Completion Status: Optimal
  Solver Selected: SolverFoundation.Plugin.Gurobi.GurobiSolver
  I’m going to go back through the sample and try to identify the minimal changes to get the LPSolve performing similar to the Gurboi, but two things that may have helped are changing the distance parameter from Domain.Real to Domain.IntegerNonnegative and adding this directive:
  context.Solve(new SolverFoundation.Plugin.LpSolve.LpSolveDirective());
  -Ed
  Hi, Nate, how can one change the code so that it solves the classic TSP, where the salesperson begins and ends in city 0, so that we would have something like 0->3 -> 8 -> … ->0?
  Thanks in advance!
  Oh, now I got it. This is the piece of code I was looking for:
  var tour = from p in assign.GetValues() where (double)p[0] > 0.9 select p[2];
  Console.Write(“0 -> “);
  int indice = 0;
  int currentCity;
  for (int i = 0; i < data.Length; i++)
  {
  currentCity = Convert.ToInt32(tour.ToArray()[indice]);
  Console.Write("{0}" + ((i ” :””), currentCity);
  indice = currentCity;
  }
  Console.WriteLine();
  The result is the correct sequence of cities:
  0 -> 1 -> 13 -> 2 -> 3 -> 4 -> 5 -> 11 -> 6 -> 12 -> 7 -> 10 -> 8 -> 9 -> 0
  Hi Ricardo,
  But what is the difference, where to start from?
  Imagine the sequences: 0-1-2-3-4-0 and 1-2-3-4-0-1
  I assume that the tour is actualy the same. You can start anywhere you’d like to.
  Am I right?
  Best regards,
  Sergey
  Hi, Sergey, you are mathematically correct. But if the salesman lives in city 0, it is only natural for him to start and finish in his own city :)
  After you obtain a tour, you can just make some manipulations with the order and assign any starting point you want. :)
  Hi Nathan,
  This is excellent code and solved something I truly over complicated. I am using this for solving production line changeover matrixes that are asymmetrical–i.e. if you are making pudding, the line can change over from vanilla to chocolate with a 15 minute wipe down but when going from chocolate to vanilla it takes 8 hours of clean up.
  Anyway, my 20X20 matrix ran great and actually cut 13% off of what I thought was the optimal!
  What do you think the scalability for this is. We are building up a 43X43 matrix now and want to make sure we are capable of doing 100X100.
  Do you or any of the other readers think this will be a problem or have any suggestions before we attempt this?
  Steve
  I tried your solution on a Graph with some not existed edges and your code did not provide any useful output. Can u please present a TSP solution for situation like I face?