[OFF-TOPIC] State of the art (mixed) integer optimization algorithm

[G]

Hello,

I was wondering what are the algorithm implemented in the best solvers? Branch and bound, Gomory's cut, what else?
What are the best reference can I find about that?

P.S. Sorry for this very general and off-topic question. I ask in this group to have some opinion, I am afraid that asking on some solver's group I won't get any answer :)

Cheers

[Johan Löfberg]

They all use branch&bound + cuts.

You can see the vast number of cuts available by simply looking in the options structures. Here is an excerpt from gurobi options

 Cuts: -1
           CliqueCuts: -1
            CoverCuts: -1
        FlowCoverCuts: -1
         FlowPathCuts: -1
         GUBCoverCuts: -1
          ImpliedCuts: -1
           MIPSepCuts: -1
              MIRCuts: -1
             ModKCuts: -1
          NetworkCuts: -1
           SubMIPCuts: -1
         ZeroHalfCuts: -1
         CutAggPasses: -1
            CutPasses: -1
         GomoryPasses: -1

gurobi displays the number of cuts (and which ones) it used after it finishes

There are numerous presentations and papers to read. Just google mixed integer linear programming bixby, and you will find interesting stuff by cplex developers, or mixed integer linear programming rothberg to find equally interesting stuff from gurobi, etc