Change the problem: 18XX token placement
It's surprising how often you can translate one problem into another problem, for which there are known solutions and/or algorithms. For example, with Green's theorem you can choose between solving a line integral or a double integral, and select whichever option is simplest to solve. The necessary ingredients are:
- Being aware of the equivalence between two problems; and
- Knowing how to solve (at least) one of these problems.
One example that I found (by accident) was that preserving the connectivity of all placed tokens when upgrading a tile in an 18XX board game is equivalent to solving a maximum flow problem.