Are there any known heuristics for the following variation of the traveling salesman problem: given $n$ sets of points $S_1,\dots,S_n$, and $n$ integers $k_i$ such that $k_i \leq |S_i|$, find the shortest path that visits $k_i$ points from each $S_i$? The case $k_i=1$ is reasonably well-studied but I have not seen this variant.
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