Hi Ted,<br><br>Thanks for your reply. You understood correctly. In essence, we try to use column generation to solve an IP without using Branch-and-Price. That is, we generate columns outside of B&B tree. <br><br>
Here's an outline of our column generation algorithm:<br>1. Formulate a Restricted Master Problem (RMP) with subset of columns from the original problem.<br>2. Solve the above RMP in B&B to IP optimal. <br>3. Use the optimal IP solution, to price and generate columns.
<br>4. Solve the RMP + additional columns generated in B&B to optimality.<br>5. Repeat 3 and 4, until no more columns are generated.<br><br>Now, in Step 3, we need dual information to price the columns. And I guess here's where I confused you. I used to work with CPLEX; in CPLEX it allows users to obtain dual info of the optimal IP solution (or more correctly, of the LP relaxation solution at the optimal B&B node) by changing the problem type from IP to LP-fixed, in which, all variables are fixed at the IP solution. I think what CPLEX does (to fix those variables) is to solve LP relaxation with the conditions at that B&B node to reproduce the integer solution and hence dual info. That is, it does not literally fix the variables. (So, I confused you when I said we tried to fix the variables.)
<br><br>So, the question is, can we do the same thing with SYMPHONY/CLP?<br><br>Many thanks for your help. I appreciate you time and help.<br><br>Cheers,
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