  Multi-agent path finding (MAPF) attracts considerable attention in artificial
intelligence community as well as in robotics, and other fields such as
warehouse logistics. The task in the standard MAPF is to find paths through
which agents can navigate from their starting positions to specified individual
goal positions. The combination of two additional requirements makes the
problem computationally challenging: (i) agents must not collide with each
other and (ii) the paths must be optimal with respect to some objective. Two
major approaches to optimal MAPF solving include (1) dedicated search-based
methods, which solve MAPF directly, and (2) compilation-based methods that
reduce a MAPF instance to an instance in a different well established
formalism, for which an efficient solver exists. The compilation-based MAPF
solving can benefit from advancements accumulated during the development of the
target solver often decades long. We summarize and compare contemporary
compilation-based solvers for MAPF using formalisms like ASP, MIP, and SAT. We
show the lessons learned from past developments and current trends in the topic
and discuss its wider impact.
