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Sequential Approximate Optimization (SAO) has been widely used in engineering optimization design problems to improve efficiency. The infilling strategy is one of the critical techniques of the SAO, which is of paramount importance to the surrogate model accuracy and optimization efficiency. In this paper, an adaptive parallel infill strategy for surrogate-based single-objective optimization is proposed within a multi-objective optimization framework to balance exploration and exploitation during the optimization process. Within this method, an inaccurate Pareto Front is adopted to assist the infilling of the sampling points. The proposed SAO method with its adaptive parallel sampling strategy is tested on several numerical test cases and an engineering test case with the optimization results compared to state-of-the-art optimization algorithms. The results show that the proposed SAO with the adaptive parallel sampling strategy possesses excellent performance and better stability. [ABSTRACT FROM AUTHOR]