What you suggest with regards to the 20 previous IP is called seed caching, and yes, that is what many, probably most P2P network do. While it works most of the time on large networks, but it is obviously not the solution, because it cannot be guaranteed that any of the previously active 20,50, 100 nodes is still listening in a later time. Also, such caching and scanning does not solve the fundamental problem of knowing the seed IPs at the very first connection, prior when you populated the cache the first time. The question is, how we solve this problem without having a hard coded list of IPs that usually P2P software ship in the source code.
Other techniques and several research papers suggest that scanning of a wide range of IP by guessing what could be a connected node is an option as well. In theory it certainly works, if you scan the whole internet then soon or later you will find a connected node and in theory it does solves the problem of centralized bootstrapping, but all these papers also agree that such scanning could be terribly inefficient.
What I mentioned, mDNS and UDP multicasting work fine on local networks, and we are experimenting with IPv6 anycast on global network to solve this problem.
