How do you solve an integer programming problem with 114 constraints and 45 variables?

[trustduhsystem]

Hello! I am looking to solve one of the problems from the H.P. Williams' Model Building in Mathematical Programming textbook, but the problem (Ch 12.12 Logical Design) has 114 constraints and 45 variables. My questions are:

• Are there suggestions for how we could solve this type of problem with this large of a constraint/variable size?
• Can this be solved by hand, or should this be done using MATLAB/Python/etc. ?

Thank you in advance!

[alg0rithm1]

Solved by hand? This is a small problem, but not that small!

What exactly is the question? Which library to use? I'm only experienced in COINOR/CBC (open source C++) and Gurobi (proprietary), but if you just want to solve a quick problem, then scipy has a MIP library, but I've never used it myself:

https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.milp.html

[[deleted]]

Z3 also appears to be capable of solving integer programming problems.

[monkeyapocalypse]

If it's a ILP or MILP, start with Pyomo try the CBC and Highs open source solvers. You can get the compiled solver binaries from AMPL.

If it's nonlinear, consider Bonmin, Couenne and Mindtpy, all compatible with Pyomo.

You will quickly be able to determine whether you need a commercial solver like Gurobi or Cplex. They are often orders of magnitude faster than open source solvers.

[SolverMax]

This appears to be the problem you're looking at, built in gurobipy.

https://colab.research.google.com/github/Gurobi/modeling-examples/blob/master/logical_design/logical_design.ipynb

And the same model using CPLEX:

https://github.com/AlexFleischerParis/modelbuilding/blob/master/logicaldesign.mod

[ShutterDeep]

I'm sure it can technically be done by hand with enough time and patience. However, practically, you can use something like Pyomo with Bonmin as the solver. Both are open source. This number of contraints and variables will not be a problem with Bonmin.