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shoo 3 days ago

Agreed - adaptability to changing requirements is a very strong advantage for real-world work.

The first attempt to formalise some practical problem into a mathematical optimisation problem is often not quite right. You discover new things that change the problem statement after reviewing example solutions with experts who exclaim "that solution couldn't possibly work, because <discovery of additional requirements>".

A neat dynamic programming solution is a glorious thing, but dynamic programming relies on a mathematical problem with some elegant recursive substructure that you can exploit. Sometimes such elegant recursive substructure is going to be broken by additional requirements or side constraints that you discover during the project -- so the real valuable problem you actually need to solve has no such substructure, and you need to throw out your dynamic programming approach and go back to a blank sheet of paper to design a viable attack on the real valuable messy problem.

For lower-risk delivery of useful outcomes, it probably makes the most sense to use general purpose flexible black box solvers like constraint or MIP solvers early in the project, and focus efforts on rapidly discovering and extracting all the requirements, so you zero in on the real problem quicker. You don't want to prematurely invest a lot of time and effort building a highly efficient bespoke elegant solution to the wrong problem, then discover a month before a delivery deadline that everything needs to be thrown out.