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Yup. & when you get a model that works matched up with an industrial scale decision problem that's valuable to solve, arguably it's only of academic interest if
by shoo 3y ago
Yup. & when you get a model that works matched up with an industrial scale decision problem that's valuable to solve, arguably it's only of academic interest if you can solve it "optimally". The problem is only a simplified model of reality anyway -- it's often better to get a quick close-enough approximate solution to a problem that's a good approximation of the situation than an exact optimal solution to a simpler problem that's a poorer approximation.
If you're lucky enough to get a problem that's basically stable over time, where the problem structure doesn't change, then maybe you can get improved solutions rapidly at industrial scale replacing use of a black-box MIP solver like Gurobi/CPLEX with a decomposition that exploits the problem structure, where sub-problems can be solved by some specialized graph algorithm or heuristic or brute force (if they all have bounded size), and the general purpose MIP/LP solver can be left with the job of figuring out how to deal with the shared resources and constraints that bind the subproblems together. The downside to a highly specialised custom solver is that it usually isn't flexible to changing requirements (unless you get very lucky) -- a slight change in business rule can break the problem structure that underpins the entire solution approach.
- 7thaccount 3y agoI disagree with the first statement for some industries. My industry has several companies that have amongst the hardest MILP problems in the world that have millions of variables and constraints and need to be globally optimal for the sake of fairness and to save many millions of dollars per year. Electricity markets are extremely complicated and although it would be amazing to simplify things, the decisions and prices need to be correct. Also, performance is critical as these auctions are running 24/7. They're also always being changed as well, so black-box globally optimal solutions are a need to have.