Most state-of-the-art satisfiability (SAT) solvers are capable of solving large application instances with efficient branching heuristics. The VSIDS heuristic is widely used because of its robustness. This paper focuses on the inherent ties in VSIDS and proposes a new branching heuristic called TBVSIDS, which attempts to break the ties with the consideration of the interplay between the branching heuristic and learned clauses. However, a branching heuristic cannot cover all problems, and its performance improves when combined with an appropriate configuration. Therefore, we also propose a hybrid model of branching heuristics based on random forest. The efficiencies of TBVSIDS and hybrid branching heuristics are evaluated on benchmarks in SAT Competitions. By constructing a model that reduces the overfitting problem, we hope to realize a hybrid branching heuristic that is widely applicable to other solvers.