I know the Floyd–Warshall, but this thread discusses CHR^rp (CHR with rule priorities), and Dijkstra’s algorithm is a good example of using the CHR^rp system .
There are many ways to compute shortest path, such as Dijkstra, Floyd–Warshall, A*, etc. Each has pros and cons. For instance, Dijkstra often computes single source shortest paths, whereas Floyd-Warshall computes shortest paths between all pairs of vertices.
You can do Floyd–Warshall for your situation, but Dijkstra has its own applicable scenarios. It is not feasible for one algorithm to completely replace another.
Back to the CHR^rp system, because the priority queue behavior in Dijkstra’s algorithm can be elegantly expressed via rule priority in CHR^rp, that’s why I was discussing it here. For other algorithms, they are not within the scope of discussion unless they are relevant to the CHR^rp system.