The alignment of observed and modeled behavior is an essential element for organizations, since it opens the door for conformance checking and enhancement of processes. The state-of-the-art technique for computing alignments has exponential time and space complexity, hindering its applicability for medium and large instances. In this article, a novel approach is presented to tackle the challenge of computing an alignment for large-problem instances that correspond to well-formed process models. Given an observed trace, first it uses a novel replay technique to find an initial candidate trace in the model. Then a local search framework is applied to try to improve the alignment until no further improvement is possible. The implementation of ...