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This paper introduces a generalized spatial regionalization problem, namely, PRUC ( P -Regions with User-defined Constraint) that partitions spatial areas into homogeneous regions. PRUC accounts for user-defined constraints imposed over aggregate region properties. We show that PRUC is an NP-Hard problem. To solve PRUC, we introduce GSLO (Global Search with Local Optimization), a parallel stochastic regionalization algorithm. GSLO is composed of two phases: (1) Global Search that initially partitions areas into regions that satisfy a user-defined constraint, and (2) Local Optimization that further improves the quality of the partitioning with respect to intra-region similarity. We conduct an extensive experimental study using real datasets to evaluate the performance of GSLO. Experimental results show that GSLO is up to 100× faster than the state-of-the-art algorithms. GSLO provides partitioning that is up to 6× better with respect to intra-region similarity. Furthermore, GSLO is able to handle 4× larger datasets than the state-of-the-art algorithms.