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:
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_2can also be written as0 \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: