Software quality estimation is a challenging and time-consuming activity, and models are crucial to face the complexity of such activity on modern software applications. In this context, software refactoring is a crucial activity within development life-cycles where requirements and functionalities rapidly evolve. One main challenge is that the improvement of distinctive quality attributes may require contrasting refactoring actions on software, as for trade-off between performance and reliability (or other non-functional attributes). In such cases, multi-objective optimization can provide the designer with a wider view on these trade-offs and, consequently, can lead to identify suitable refactoring actions that take into account independent or even competing objectives. In this paper, we present an approach that exploits NSGA-II as the genetic algorithm to search optimal Pareto frontiers for software refactoring while considering many objectives. We consider performance and reliability variations of a model alternative with respect to an initial model, the amount of performance antipatterns detected on the model alternative, and the architectural distance, which quantifies the effort to obtain a model alternative from the initial one. We applied our approach on two case studies: a Train Ticket Booking Service, and CoCoME. We observed that our approach is able to improve performance (by up to 42\%) while preserving or even improving the reliability (by up to 32\%) of generated model alternatives. We also observed that there exists an order of preference of refactoring actions among model alternatives. We can state that performance antipatterns confirmed their ability to improve performance of a subject model in the context of many-objective optimization. In addition, the metric that we adopted for the architectural distance seems to be suitable for estimating the refactoring effort.