Many fine answers have already been provided fort this question. Here are some additional frequently solved optimization problems.
Neural network training for image recognition, or whatever. Not by number of problems solved, but by total amount of computing (those babies can burn weeks on high end GPUs and TPUs)
Oil Refining. In the old days (through the '70s and into at least the early 80s), LPs to optimize oil refining, solved by some variant of the Simplex Method, were the most frequently solved optimization problems, and were responsible for a large portion of the total worldwide floating point computations.
MILPs largely supplanted LPs, to include in oil refining, by the 90s when MILP solvers started greatly maturing and becoming commercially available.
Even in the 70s, there was some oil refining optimization done using Nonlinear Programming (or in some case, just Nonlinear Equation Solving). But I think such optimizations were more commonly performed by oil company researchers in Operations Research colloquiums, such as I attended at Stanford in the early 80s, than they were in practice at the oil companies which employed them.