Acquisition functions for surrogate-assisted many-objective optimization require a delicate balance between convergence and diversity. However, the conflicting nature between many objectives may lead to an imbalance between exploration and exploitation, resulting in a low efficiency in search for a set of optimal solutions that can well balance convergence and diversity. To meet this challenge, we propose an adaptive model management strategy assisted by two sets of reference vectors, one set of adaptive reference vectors accounting for convergence while the other set of fixed reference vectors for diversity. Specifically, we first propose a new acquisition function that calculates an amplified upper confidence bound (AUCB). Two optimization processes are performed in parallel to optimize the acquisition function, each based on one of the two sets of reference vectors. Then, we select one promising candidate solution according to diversity or convergence from the nondominated solutions obtained by the two optimization processes. The experimental results on four suites of test functions as well as six real-world application problems demonstrate the competitive performance of the proposed reference vector-assisted adaptive model management strategy, in comparison with seven state-of-the-art surrogate-assisted evolutionary algorithms (SAEAs).