Why are Mixed integer programming solvers focused on finding cuts and not so much on search?

The big difference is that search is problem specific and MILP solvers don’t know nearly as much about the domain. Minimax search is a fun case where the problem is recursive so at every level, the solution to the problem is trivial if you’ve solved the problem 1 layer down. This means that in Chess, you only need 1 search strategy and it will massively improve everything. In MILP, by contrast there isn’t a clean structure, so any search needs to find connected subsets with a given structure and any improvement will only be useful for a very small number of places.

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