In the search for new structural alloys for high-temperature applications, refractory high-entropy alloys (RHEAs) have attracted significant attention due to their superior mechanical properties compared to nickel-based superalloys at high temperatures. The absence of principal elements in RHEA requires new physical and thermodynamic models apart from the knowledge accumulated in traditional structural alloy systems. In this study, we propose a feature selection strategy for a phase prediction model (BCC and non-BCC phases) for the RHEA dataset constructed through a literature survey. In addition to the collected composition, heat treatment conditions and phases, weight average physical properties and CALPHAD properties are complemented to build material descriptors. Datasets are overly high-dimensional compared to data points. To reduce the dimensionality of the phase prediction machine learning models, we compare two strategies of feature extraction methods: feature selection using genetic algorithm (GA) and Sure-Independence Screening and Sparsifying Operation (SISSO). Then feature impact on the models are analyzed in SHapley Additive exPlanations (SHAP). The phase prediction model based on the combination of descriptors selected from the GA showed good performance (F1-score> 0.9). From the model, several compositions forming BCC phase were inverse designed and experimentally verified.