Mentally I tend to further categorise heuristics into "construction" and "improvement" heuristics. Your "shortest path" is a construction heuristic that I normally call "nearest neighbour". Other common heuristics are "greedy" (iteratively add the shortest feasible edge) and "farthest insertion" (iteratively add the farthest point from the subtour to the best position). There's an interesting synergy between construction and improvement strategies, e.g. 2-opt might be more worthwhile after nearest neighbour than greedy. It would be extra awesome to be able to choose both construction as well as improvement and see how it pans out.
Mentally I tend to further categorise heuristics into "construction" and "improvement" heuristics. Your "shortest path" is a construction heuristic that I normally call "nearest neighbour". Other common heuristics are "greedy" (iteratively add the shortest feasible edge) and "farthest insertion" (iteratively add the farthest point from the subtour to the best position). There's an interesting synergy between construction and improvement strategies, e.g. 2-opt might be more worthwhile after nearest neighbour than greedy. It would be extra awesome to be able to choose both construction as well as improvement and see how it pans out.