Trace alignment is the problem of finding the best possible execution sequence of a business process (BP) model that reproduces an (observed) execution trace of the same BP by pinpointing where it deviates. One limiting assumption that governs the state-of-the-art alignment algorithms relies in a static cost function assigning fixed costs to all the possible types of deviations related to a BP activity, thus neglecting the specific context in which the deviation takes place and flattening the analysis of its potential impact. In this paper, we relax this assumption by providing a technique based on theoretic manipulations of deterministic finite state automata (DFAs) to build optimal alignments driven by dedicated cost models that assign context-dependent variable costs to the deviations. We show how the algorithm can be implemented relying on automated planning in Artificial Intelligence (AI), which is proven to be an effective tool to address the alignment task in the case of BP models and event logs of remarkable size. Finally, we report on the results of experiments conducted in a real-life case study on incident management and on larger synthetic ones performed through three well-known planning systems to showcase the performance, scalability and versatility of our technique.