Travelling Salesman Problem where a subset of the nodes must be visited in a particular order I’m curious whether there is any work on the variant of the Travelling Salesman Problem where a subset of the nodes must be visited in a particular order. I haven’t found anything with searches or in survey articles, but that may just mean I haven’t found the right search terms or the right surveys.

If there are $n$ nodes in the graph, and a list $a_1, \dots, a_k$ of nodes that must be visited in that order, I can transform the problem to an instance of ATSP with $2k(n-k)+k$ nodes. The result is asymmetric even if the original edge-weights were symmetric, so we lose another factor of $2$ if we want to reduce it to a symmetric instance. I would be interested to know if there is a more efficient reduction.

Edited to add: On further reflection I think I can improve the reduction to $k(n-k)+k$ nodes.
This is a special case of the precedence-constrained TSP which has been studied quite a lot. For instance, there are a polyhedral analysis by Balas, Fischetti and Pulleyblank, and a branch-and-cut algorithm by Ascheuer, Jünger and Reinelt.