[Bridges] add IntegerToZeroOneBridge

[odow]

Closes #2202

Basic

• Create a new file in src/Bridges/XXX/bridges
• Define the bridge, following existing examples. The name of the bridge
  struct must end in Bridge
• Check if your bridge can be a subtype of MOI.Bridges.Constraint.SetMapBridge
• Define a new const that is a SingleBridgeOptimizer wrapping the
  new bridge. The name of the const must be the name of the bridge, less
  the Bridge suffix
• include the file in src/Bridges/XXX/bridges/XXX.jl
• If the bridge should be enabled by default, add the bridge to
  add_all_bridges at the bottom of src/Bridges/XXX/XXX.jl

Tests

• Create a new file in the appropriate subdirectory of tests/Bridges/XXX
• Use MOI.Bridges.runtests to test various inputs and outputs of the
  bridge
• If, after opening the pull request to add the bridge, some lines are not
  covered by the tests, add additional bridge-specific tests to cover the
  untested lines.

Documentation

• Add a docstring which uses the same template as existing bridges.
• Add the docstring to docs/src/submodules/Bridges/list_of_bridges.md

Final touch

If the bridge depends on run-time values of other variables and constraints in
the model:

• Implement MOI.Utilities.needs_final_touch(::Bridge)
• Implement MOI.Utilities.final_touch(::Bridge, ::MOI.ModelLike)
• Ensure that final_touch can be called multiple times in a row

[blegat]

We should probably have a utility for that shared with SplitInterval and other bridges doing this like is_infinity. In Interval we take care of Int where we never one to consider no bound while we don't do it here. At least it would make sure we are consistent

[odow]

I don't understand the SplitInterval reference. The SplitInterval bridge doesn't rely on a finite domain, it works with one-sided intervals. In comparison, we can't bridge an open set to ZeroOne (unless we pick a big M and do a 20 or 30 bit expansion?).

[blegat]

The variable bridge spirit would be to substitute x. Here it seems to be a bad idea because it x is a big sum.
This is like bridge a constrained variables x in Int by first adding the variable free and constraining it, then functionizing it and then slack bridge and then variable bridge for the slack. I'm wondering if there could be a nice way to implement this as a variable bridge but defaulting it to be used like that while allowing the user to have x be substituted as well.

[blegat]

Could you just drop a comment that it would more naturally be implemented as a variable bridge but we don't want to substitute every occurence of x so that's why we do it as a constraint bridge ?

[odow]

I'm wondering if there could be a nice way to implement this as a variable bridge

That would only be necessary for a solver supports only binary variables and not real. We don't really have any current examples, although @ccoffrin might be interested for future quantum annealing formulations. (They have some pretty specific structure restrictions though, which mean doing it naively might be the wrong thing to do.)

[odow]

Is there anything else to do here?