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Multi-Agent Path Finding (MAPF) aims to find a set of conflict-free paths for multiple agents on a given graph from parking locations to specified goal locations while optimizing related costs. Currently, existing MAPF studies often consider the simplified problem setup where each agent does not return to its parking location after completing its task on the underlying graph with uniform edge costs. Nevertheless, within some real-word scenarios such as the Unmanned Aircraft System (UAS), agents are situated in the underlying graph with non-uniform edge costs. These agents are required to travel from their respective parking locations to complete tasks, and then return without conflicts. Therefore, this paper explores a new version of MAPF, formally called Multi-Agent Path Finding with Heterogeneous edges and Roundtrips (MAPF-HR). In this version, all agents are engaged in completing tasks by navigating their respective conflict-free paths with roundtrips on the graph with heterogeneous edges. This paper investigates a novel algorithm for this problem, called Improved Conflict-Based Search (CBS) with Helpful Bypass (ICBS-HB), which improves the CBS framework by utilizing the scheme of bypassing conflicts during path finding execution. With extensive experiments on MAPF benchmark maps, it shows that ICBS-HB outperforms the state-of-the-art algorithms for dealing with MAPF-HR. [ABSTRACT FROM AUTHOR]