Allow generation of relaxations as MILP

People could find it useful to use the reformulation mechanism of bridges to get a relaxation that can be solved really fast: this relaxation could have better properties than the usual LP relaxation of the equivalent MIP (maybe tighter, more probably smaller). It should not be much harder to implement than the current bridges, but these new bridges would never be used without the user explicitly asking for it.

A similar thing would be to have less tight formulations that are not MIP relaxations, but smaller. I'm mostly thinking about the 2-way constraint to encode an AND: y = x_1 \land x_2 can also be written as 0 \leq x_1 + x_2 - 2 y\leq 1; the integer solutions are the same, but the formulation is not tight anymore.

A few references/tutorials:

• https://www.sciencedirect.com/science/article/abs/pii/S1574652606800192, section 15.6
• http://egon.cheme.cmu.edu/ewo/docs/HookerCP.pdf
• https://people.eng.unimelb.edu.au/pstuckey/papers/cp2016a.pdf ?

Start by reading the repository's current bridge and reformulation mechanisms to understand how existing bridges are selected. Define the explicitly requested relaxation behavior, including the MILP and potentially smaller non-tight formulations, and determine how the referenced formulations should fit the existing design; the issue does not name files or tests.