Factors within a large-scale software system that simultaneously interact and strongly impact the system's response under a configuration are often difficult to identify. Although screening such a system for the existence of such interactions is important, determining their location is more useful for system engineers. Combinatorial interaction testing (CIT) concerns creation of test suites that nonadaptively either detect or locate the desired interactions, each of at most a specified size or show that no such set exists. Under the assumption that there are at most a given number of such interactions causing such a response, locating arrays (LAs) guarantee unique location for every such set of interactions and an algorithm to deal with outliers and nondeterministic behavior from real systems, we additionally require the LAs to have a "separation" between these collections. State-of-the-art approaches generate LAs that can locate at most one interaction of size at most three, due to the massive number of interaction combinations for larger parameters if no constraints are given. This paper presents LocAG, a two-stage algorithm that generates (unconstrained) LAs using a simple, but powerful partitioning strategy of these combinations. In particular, we are able to generate LAs with more factors, with any desired separation, and greater interaction size than existing approaches.