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Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for solving complex and computationally expensive optimization problems. However, most of the existing algorithms converge slowly in the later stage. This article proposes a novel two-stage data-driven evolutionary optimization (TS-DDEO) that meets the requirements of early exploration and later exploitation. In the first stage, a surrogate-assisted hierarchical particle swarm optimization method is used to find a promising area from the entire search space. In the second stage, we propose a best-data-driven optimization (BDDO) method with a strong exploitation ability to accelerate the optimization process. BDDO has a real-time update mechanism for the surrogate model and population and uses a predefined number of ranking-top solutions to update population and surrogates. BDDO combines three surrogate-assisted evolutionary sampling strategies: 1) surrogate-assisted differential evolution sampling; 2) surrogate-assisted local search; and 3) a surrogate-assisted full-crossover (FC) strategy which is proposed to integrate existing best genotypes in the population. Experiments and analysis have validated the effectiveness of the two-stage framework, the BDDO method, and the FC strategy. Moreover, the proposed algorithm is compared with five state-of-the-art SAEAs on high-dimensional benchmark functions. The result shows that TS-DDEO performs better both in effectiveness and robustness.