Yes, yes, yes. I've made this comment a few times on here but tools like MIP solvers are vastly unknown since they didn't take on a sexy name when they started out. However, they can outperform most heuristic based algorithms, and even solve some of the largest problems. It's how the NFL makes their schedules oh, and you can imagine how complicated that is.

Fun fact. Most power grids in the developed world are run off of some of the largest MILP and LP problems. We're talking about millions of constraints to commit units and hundreds of thousands to dispatch them. These run around the clock 24/7.

I've only recently learned about SAT type solvers as MILP/LP problems are very fast and globally optimal, unlike things like A* or Genetic Algorithms. I think GA's are cool because you can write one in less than 1/2 page of Python, where MIP solvers are usually large black-box C codesets (Ex: GLPK, CPLEX, GUROBI, XPRESS, Open-Solver).

GA does not belong anywhere near real problems. They are toy solutions with zero guarantees.

Fun to code though!

Sadly, I've mostly come to the same conclusion in that I at least need a MIP Gap to tell me how far I am from the optimal solution.

My only issue with LP and MILP solvers is scalibility. You have none! Multicore doesn't really seem to help any.

Ssshhh ... Stop telling everyone. I have rewritten various problems as MILP it finds a solution and people think I’m smart!

My favorite MILP is commercial and perhaps somewhat obscure for general population - Mosek. Any recommendations in regards to other good options? perhaps open source that might be in same or better league.

Gurobi, CPLEX and XPRESS are the obvious commercial ones. GLPK and Cbc will also do MILP.

For more information, see this page: http://plato.asu.edu/guide.html

Thank you so much. Very nice collection of information.

I think it was this year I learned they exist. They told me a few to check out. I still don't have a list of applications. What areas were you thinking about when you said underused?