Any solvers which can be integrated in python where we can quickly solve if we have integer and binary variables alone in our model other than normal solvers for MIP, MILP?
For binary only there are the following classes of solvers:
- SAT Solvers and MaxSat for optimization
- Pseudo Boolean Programming or Pseudo Boolean optimization
For integer valued there are the following approaches:
- Constraint Programming
- Rephrasing as Boolean Problem provided the search space is finite
- SMT solvers and Optimization modulo theory
As well as local solvers which might be able to solve both.
As for whether such software is callable from Python:
- SAT solvers: yes, for example Lingeling
- Pseudo Boolean solvers: no, as far as i know, but you can generate a problem file a solver like RoundingSAT could work on and read it's output files.
- Contraint programming: yes, see Python constraint
- SMT solvers, yes see Z3Py
- Local solvers, yes see LocalSolver
All those solvers use different proof systems from MILP solvers, so it is possible that they solve certain formulations of certain problems better than MILP solvers. However there is no single approach that dominates MILP on every task.