[Cbc] MILP: Solving LP followed by minimizing L1-norm

[Sam Mathew]

Hi everyone,

I've started to use Cbc and have found it quite useful for solving some
Integer LP problems.

For a hard minimization problem, I experienced that *solving an LP followed
by L1-norm minimization of the integer solution* w.r.t. the LP solution of
variables (while *maintaining the same constraints* as the original ILP),
at least gave a feasible integer solution within a few seconds.

In short,
1. solving the relaxed problem to get X_lp
2. Solve a new ILP with original constraints and new objective:
               minimize | X- X_lp |

Otherwise, while solving the original ILP (400 variables and 62
constraints), Cbc was not even giving any solution (also CPLEX, SCIP and
MIPCL gave up, saying that the problem is infeasible). Only Gurobi gave an
optimal solution after around 5 seconds.

Is there any means or option within Cbc that does this already? I guess
feasibility pump is not the same, is it?

I would be glad for some insight how this feasible integer solution was
arrived at, so quickly?

Regards,

Sam

-- 
Senior Process Engineer

*Gyan Data Pvt. Ltd.*
*IITM Research Park*
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