  We introduce multi-goal multi agent path finding (MAPF$^{MG}$) which
generalizes the standard discrete multi-agent path finding (MAPF) problem.
While the task in MAPF is to navigate agents in an undirected graph from their
starting vertices to one individual goal vertex per agent, MAPF$^{MG}$ assigns
each agent multiple goal vertices and the task is to visit each of them at
least once. Solving MAPF$^{MG}$ not only requires finding collision free paths
for individual agents but also determining the order of visiting agent's goal
vertices so that common objectives like the sum-of-costs are optimized. We
suggest two novel algorithms using different paradigms to address MAPF$^{MG}$:
a heuristic search-based search algorithm called Hamiltonian-CBS (HCBS) and a
compilation-based algorithm built using the SMT paradigm, called
SMT-Hamiltonian-CBS (SMT-HCBS). Experimental comparison suggests limitations of
compilation-based approach.
