What do we call a greedy algorithm that tracks the best $n > 1$ solutions? A naive greedy algorithm tries to find an optimal solution based on the best solution so far, hence it may get stuck in local optima.

To avoid this problem, we may keep track of the best $n &gt; 1$ solutions (instead of the best only). What is the name(s) of this algorithm?

Surprisingly, I can't seem to find the answer from Google. It'd be great if you could also list some resources on extensions to the naive greedy algorithm.
You might be interested in beam search, which could be viewed as working in more or less this way.