Model transformations are an important cornerstone of model-driven engineering, a discipline which facilitates the abstraction of relevant information of a system as models. The success of the final system mainly depends on the optimization of these models through model transformations. Currently, the application of transformations is realized either by following the apply-as-long-as-possible strategy or by the provision of explicit rule orchestrations. This implies two main limitations. First, the optimization objectives are implicitly hidden in the transformation rules and their orchestration. Second, manually finding the best orchestration for a particular scenario is a major challenge due to the high number of possible combinations. To overcome these limitations, we present a novel framework that builds on the non-intrusive integration of optimization and model transformation technologies. In particular, we formulate the transformation orchestration task as an optimization problem, which allows for the efficient exploration of the transformation space and explication of the transformation objectives. Our generic framework provides several search algorithms and guides the user in providing a proper search configuration. We present different instantiations of our framework to demonstrate its feasibility, applicability, and benefits using several case studies. Copyright (C) 2016 John Wiley & Sons, Ltd.