[SCIP] LP dual solution accuracy

[Shin, Jungeun]

Hi,

I have been using SCIP framework with its own solver(Soflex) to implement Branch and Price, which requires dual solutions of the restricted master problem to calculate the reduced costs of additional columns.
After running a few sample instances, I started doubt the accuracy of the dual solutions because Pricer keeps generating columns at the root node with the negative reduced costs but the lower bound of the node didn't reduce.  ( Sometimes it even increased very little bit (1e-10), but I guess its because of the optimality tolerance setting)

I looked up this SCIP archive and found the related one:   http://listserv.zib.de/pipermail/scip/2019-November/003806.html
According to the answer, I set   presolving/maxrestarts = 0   , propagating/maxrounds=0 and  propagating/maxroundsroot=0 , but still the dual solution seems not accurate.

I have tested the dual solutions in multiple ways.  For example, I let SCIP and CPLEX solver read the same .lp file and obtained the dual solutions using each lp solver, respectively. Then, solved the same subproblem using two different sets of dual solutions.  With the dual solutions of SCIP(Soflex), the subproblem found a column with the negative reduced costs  whereas the subproblem objective value using dual solutions of Cplex was positive.


As far as I know, there are many researchers using SCIP framework for Branch and Price algorithm, so I believe there should be a way to resolve this problem.
One thing I tried to do to resolve this problem is that writing .lp file of RMP within the Pricer plugin and reading it with CPLEX to solve the LP relaxation and get the dual solutions. However, it didn't include the constraints generated from branching in the parents nodes and wasn't able to have the right LP model to solve.

Long story in short,

1) I set presolving/maxrestarts = 0   , propagating/maxrounds=0 and  propagating/maxroundsroot=0  to get dual solutions, but it is not accurate. What else should I do to get the correct dual solutions of LP ?
2) Is there a way to use Cplex to solve RMP LP relaxation within Branch and Price framework?
3) Would it be resolved if I install SCIP with CPLEX as lp solver?


Thank you!
Jungeun

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://listserv.zib.de/pipermail/scip/attachments/20200526/6f47425b/attachment.html>