Originally posted by: HM62_Xingquan_Zuo

Hi everyone!

When I use the column to generate the solution to the main problem for MIP, the values of all the dual variables obtained from the first iteration are zero. The optimal solution of the primary problem is correct, but is it correct that the dual variable value is zero? 

Is this the same question as this one?

Originally posted by: HM62_Xingquan_Zuo

yes，The optimal solution obtained by my model is no problem, but the value of the dual variable corresponding to the optimal solution is all zero. I think this is unreasonable, because this is the first iteration of the column generation and global optimal has not yet been found. , if the dual variables are all zero, then the check number is greater than 0，can you help me ?

Before thinking about whether the duals are reasonable or not, I think you have to double check whether what you are doing is actually reasonable.

If I understand correctly, you a MIP problem M. You optimize that as a MIP, then you run solveFixed(), then you query the duals. Correct? As I already noted in that other thread, this will not give you the duals for M! It will give you the duals for a different model: M with all integer variables fixed to their current solution. Are you sure this is what you want for your column generation?

Since there is no appropriate duality for MIP, the pricing for column generation algorithms has usually to be done in the tree!

Originally posted by: HM62_Xingquan_Zuo

You mean that I can relax the main problem to LP problem, and then find the integer solution with the branch bound? My question is a 0-1 integer programming problem, when I use can optimizer to solve my problem is considered an MIP problem to solve, I put the main relaxation for LP problems, and then to solve the main problems of dual information to subproblems, but many are not such to the solution of integer feasible solution, need to use branch and bound for a integer solutions? Is this step right?

Sorry, maybe it is my bad English but I don't quite understand what you are asking. Can you please try to rephrase your question? Maybe show some pseudo-code that illustrates what you are trying to do?

Originally posted by: HM62_Xingquan_Zuo

The mathematical model of the master problem in my column generation framework looks like this

The master problem was originally a pure integer programming problem. In order to obtain the information of dual variables, I relaxed the master problem into a linear programming problem and changed the value range of decision variables to [0,1].And it will lead to a solution that's probably not an integer, and then I could find an integer solution with a branch bound, is that ok? Otherwise I can't get duality information

Originally posted by: Mathsg

Hi,

I am using column generation same as your case. could you share you code with me so let i get an idea that how to implement column generation in engineering problem. I am optimizing network planning problem but i dont know how to get start of it. can you help me as you are my senior in this field. I am looking forward to hearing from you. thank you