Process mining enables the analysis of complex systems using event data recorded during the execution of processes. Specifically, models of these processes can be discovered from event logs, i.e., sequences of events. However, the recorded events are often too fine-granular and result in unstructured models that are not meaningful for analysis. Log abstraction therefore aims to group together events to obtain a higher-level representation of the event sequences. While such a transformation shall be driven by the analysis goal, existing techniques force users to define how the abstraction is done, rather than what the result shall be. In this paper, we propose GECCO, an approach for log abstraction that enables users to impose requirements on the resulting log in terms of constraints. GECCO then groups events so that the constraints are satisfied and the distance to the original log is minimized. Since exhaustive log abstraction suffers from an exponential runtime complexity, GECCO also offers a heuristic approach guided by behavioral dependencies found in the log. We show that the abstraction quality of GECCO is superior to baseline solutions and demonstrate the relevance of considering constraints during log abstraction in real-life settings.