Here is all we can find in the Lightning Network whitepaper about payment routing process that it is completely unclear to me (at least it is not enough to know what happens exactly at time of finding the best optimized path for a payment between two users):
"It is theoretically possible to build a route map implicitly from observing 2-of-2 multisigs on the blockchain to build a routing table. Note, however, this is not feasible with pay-to-script-hash transaction outputs, which can be resolved out-of-band from the bitcoin protocol via a third party routing service. Building a routing table will become necessary for large operators (e.g. BGP, Cjdns). Eventually, with optimizations, the network will look a lot like the correspondent banking network, or Tier-1 ISPs. Similar to how packets still reach their destination on your home network connection, not all participants need to have a full routing table. The core Tier-1 routes can be online all the time —while nodes at the edges, such as average users, would be connected intermittently. Node discovery can occur along the edges by pre-selecting and offering partial routes to well-known nodes."
I am looking for a document explaining step by step the current routing process used in current Lightning Network to know the steps for finding the best optimized path when user A wants to send an off-chain payment to user B.
P.S. I know that it is possible to use any other routing algorithm as a plug-in; however, I would like to know the current routing protocol used in the current Lightning Network in details (step by step). I also appreciate it if you could propose a document explaining the current routing algorithm in Lightning Network. Thank you