Finding the alignment of a set of sequences (which consecutive symbols match to which, while maybe allowing gaps), minimizes the number of missmatches.

https://www.wikiwand.com/en/Multiple_sequence_alignment?wprov=sfla1

As explained here: Sequence Alignment and Dynamic Programming, the problem can be solved as a minimum-distance-like Dynamic programming algorithm. The main insight is expressing alignments as paths in a certain matrix. (vid)