Locating arrays are designs used in combinatorial testing with the property that every set of d t-way interactions appears in a unique set of tests. Using a locating array to conduct fault testing ensures that faulty interactions can be located when there are d or fewer faults. Locating arrays are fairly new and few techniques have been explored for their construction. Most of the available work is limited to finding only one fault. Known general methods require a covering array of strength t+d and produce many more tests than are needed. We present Partitioned Search with Column Resampling (PSCR), a randomized computational search algorithmic framework to verify if an array is (d, t)-locating by partitioning the search space to decrease the number of comparisons. If a candidate array is not locating, random resampling is performed until a locating array is constructed or an iteration limit is reached. Results are compared against known locating array constructions from covering arrays of higher strength and against published results of mixed level locating arrays for parameters of real-world systems. The use of PSCR to build larger locating arrays from a variety of ingredient arrays is explored.