Nice Topic! I agree that the general advice of "avoid integers in a MIP!" is today superceded by improvements in hardware, solvers, and even problem decomposition and formulation savvy. However if the decision variable really does not care (e.g. quantities that are large), then I'd personally still rely on the LP vs. the IP for large problems. Not to miss the main point: totally agree that for many areas "solve LP and round" is really problematic: e.g. assigning personnel, containers, or quantities that are both discrete and can be relatively small counts. Try to see if you can formulate with IP and get reasonable solve times. Also concur with your similar comments on quadratic terms, where the leading commercial solvers now have special algorithms to solve problems with non-convex quadratic objectives and constraints. Great series Mike.. keep em coming! :)
Great point. Agree to Ehsan's point that experimenting and testing helps, and also regarding quadratic terms. To make production or shipment variables integers, not sure if that something will hold true on a repeatable basis. Will try and share my experience in large scale models. But yes, its a golden age for optimization
Sarang. Thanks for sharing. I agree that there is some nuance with large-scale models, models in production, and models that are part of commercial packages where the users can enter what they want. (I have a good story on the latter that we can use on a blog post if you'd like.)
Nice Topic! I agree that the general advice of "avoid integers in a MIP!" is today superceded by improvements in hardware, solvers, and even problem decomposition and formulation savvy. However if the decision variable really does not care (e.g. quantities that are large), then I'd personally still rely on the LP vs. the IP for large problems. Not to miss the main point: totally agree that for many areas "solve LP and round" is really problematic: e.g. assigning personnel, containers, or quantities that are both discrete and can be relatively small counts. Try to see if you can formulate with IP and get reasonable solve times. Also concur with your similar comments on quadratic terms, where the leading commercial solvers now have special algorithms to solve problems with non-convex quadratic objectives and constraints. Great series Mike.. keep em coming! :)
Great point. Agree to Ehsan's point that experimenting and testing helps, and also regarding quadratic terms. To make production or shipment variables integers, not sure if that something will hold true on a repeatable basis. Will try and share my experience in large scale models. But yes, its a golden age for optimization
Sarang. Thanks for sharing. I agree that there is some nuance with large-scale models, models in production, and models that are part of commercial packages where the users can enter what they want. (I have a good story on the latter that we can use on a blog post if you'd like.)