Nowadays, business processes are increasingly supported by IT systems that produce massive amounts of event data during the execution of a process. This event data can be used to analyze the process using process mining techniques to discover the real process, measure conformance to a given process model, or to enhance existing models with performance information. While it is essential to map the produced events to activities of a given process model for conformance analysis and process model annotation, it is also an important step for the straightforward interpretation of process discovery results. In order to accomplish this mapping with minimal manual effort, we developed a semi-automatic approach that maps events to activities by transforming the mapping problem into the optimization of a constraint satisfaction problem. The approach uses log-replay techniques and has been evaluated using a real process collection from the financial services and telecommunication domains. The evaluation results demonstrate the robustness of the approach towards non-conformant execution and that the technique is able to efficiently reduce the number of possible mappings.