You say there is no trick to avoid looking at all possible paths. However, I think you are thinking of the Traveling Salesman Problem, where we must visit every node in an efficient manner. When traveling from point A to point B there certainly are useful tricks and shortcuts. Dijkstra’s Algorithm is a common approach, and is much faster than looking at all possibilities.
Of course, the ‘multivariate’ case gets more complicated. I’m only disagreeing with that one sentence.

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