While the Global Navigation Satellite System (GNSS) has established as the predominant source for delivering highprecision and high-integrity services in numerous aeronautical applications, its susceptibility to interference due to the low signal strength has necessitated the development of Alternative Positioning, Navigation, and Timing (A-PNT). Multiple Distance Measuring Equipment (Multi-DME) navigation emerges as a promising candidate for A-PNT. Station selection should be considered for multi-DME based A-PNT, due to the limited channel recourses, and the constrained processing capability of the on-board devices. It is also beneficial to limit DME interference to GNSS L5/E5a. However, signal sources decreasing may degrade the navigation performance. Station selection is to make a tradeoff between the number of selected stations, interference on GNSS signals and performance of navigation. We propose a performance-based method to address this problem. The proposed performance-based method for multi-DME is based on the Gradient Boosting Machine (GBM) algorithm. The comparison with the widely used quasi-smallest PDOP method shows that the proposed method can achieve the RNP 1 requirement with fewer DME stations and less GNSS L5/E5a signal degradation.