Add warm start, gap retrieval and better solution statuses for SCIP_PY (pyscipopt)

[supremeBaboon]

This PR aims to improve the SCIP_PY solver by :

1. Adding a boolean warmStart parameter. When True, variables set to an initial value will be used by SCIP to fasten the optimization. In particular, one can warm start only a few variables, as SCIP does not need a complete solution to start from.
2. Improving the solution statuses when a MIP reaches time or gap limit, as such cases are currently returned as LpStatusNotSolved, even when a feasible (but non optimal solution) exists. This correction is pretty similar to that of #473 for SCIP_CMD*.
3. Adding a getGap method to retrieve SCIP's gap after an optimization. As SCIP is particularly verbose, I usually disable its logs, then using this method to still get a (concise) information about the optimization.

I have not made any unit test, but I have (sucessfully) tested those additions on a custom MIP on which I am working.

*Does anyone have any news about that PR ? It has been open for ~1 year and a half now, and looks almost complete...

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1 out of 2 committers have signed the CLA.

:white_check_mark: supremeBaboon
:x: agautier

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[supremeBaboon]

I was initially pretty unsure about pyscipopt's warm start, since I've only found 2 related links : this one (whose formulation is used in this PR) and this one. Yet, after multiple tests, it seems to work just fine. The only downside I found lies in SCIP itself, as feeding it with only a few variables to warm start can 'freeze' it in finding a first solution from these initial values. In particular, SCIP can find a first solution faster without that partial initial solution (but its cost might be worse).

[supremeBaboon]

@pchtsp could you review this PR please ?

[sam-slrx]

@supremeBaboon have you run into any issues with this approach (specifically the solution statuses fix)? I'm planning on forking your fork :)

[supremeBaboon]

@sam-slrx Sorry for late answer, I've been using these changes extensively for the past 2 months and I've never encountered any issue, both for the warm-start and the solution statuses, so I assume it's safe to say they work as expected. Note however that I only tested those on MIP, not on LP.

[pchtsp]

I think you need to apply the black linter to the project, as explained here: https://coin-or.github.io/pulp/develop/contribute.html#applying-the-black-linter-formatter

[supremeBaboon]

@pchtsp done, is there anything more to do ?

[pchtsp]

looks good! It seems one contributor (agautier) has not signed the CLA. Once that's done, I can merge.

[supremeBaboon]

@pchtsp is it signed now ?

[pchtsp]

No, it's still pending.

[pchtsp]

[supremeBaboon]

But it keeps telling me it is signed

[tmaarse]

@supremeBaboon The last commit was made by agautier adrien.gautier@soprasteria.com, who hasn't signed the CLA yet. You might be able to replace their commit with one where you ran Black, or get them to sign it as well.