Why does PuLP send two distinct steps of commands to the CPLEX_CMD solver for solving MILPs?

[twissocq]

Hello,

When using the CPLEX_CMD solver (i.e., without relying on the CPLEX API), I noticed a peculiar behavior in how it handles MILP problems. Three commands are sent to cplex : mipopt, change problem fixed and finally optimize.

See on file cplex_apy.py starting at line 97

if lp.isMIP():
      if self.mip:
            cplex_cmds += "mipopt\n"
            cplex_cmds += "change problem fixed\n"
      else:
      cplex_cmds += "change problem lp\n"
cplex_cmds += "optimize\n"
cplex_cmds += "write " + tmpSol + "\n"
cplex_cmds += "quit\n"

If self.mip is True, then we run mipopt (line 97) then optimize (at line 103).
To my knowledge, when using the official cplex python api, (with solver= CPLEX_PY()), only a single solve is performed.

My questions are:

• What is the purpose of running a second optimization after fixing the integer variables (with change problem fixed)?
• Does this double optimization have any significant impact on performance or the final solution accuracy?
• Are there historical or technical reasons for this specific behavior in PuLP with CPLEX_CMD?

Thank you in advance for any insights!

[pchtsp]

That's a very good question. These commands have been there for a long time and the CPLEX_CMD has always solved the problem once (except very weird unexplained cases). Do you have a reference URL that clearly shows which options to send to CPLEX in each case? I see https://www.ibm.com/docs/en/cofz/12.10.0?topic=optimizer-invoking-mip-model and https://www.ibm.com/docs/en/cofz/12.10.0?topic=cplex-table-commands-interactive-optimizer but the documentation is not very explicit.

Would you care to make a PR? Unfortunately we do not have CPLEX set up in the github CI so there's no way to easily test the differences though. If you know of a way to add cplex to the github CI that would be welcome too!

[twissocq]

Thanks, Franco, for your answer.
The optimize command is only for LP, mipopt is the good command for MILP. (if you try use the optimize command, cplex optimizer will fail)

After exploring the links you provided, especially here: IBM Documentation: Working with a fixed MIP problem, there could be a benefit from this approach, when we need access to dual information.
Therefore, I think it’s best not to modify the code.

Regarding GitHub CI with CPLEX:

For cplex_py(), there’s a Python package available on PyPI: https://pypi.org/project/cplex/. Maybe you could give it a try?
For cplex_cmd(), honestly, I’m not sure.